Repository: kakao/recoteam Branch: master Commit: 65fc78e25cd1 Files: 119 Total size: 5.0 MB Directory structure: gitextract_mz78veiu/ ├── README.md ├── docs/ │ └── arena/ │ ├── brunch.html │ ├── common.css │ ├── index.html │ ├── melon-en.html │ └── melon.html ├── onboarding/ │ └── README.md ├── paper_review/ │ ├── README.md │ ├── recsys/ │ │ └── recsys2021/ │ │ ├── "Serving Each User"- Supporting Different Eating Goals Through a Multi-List Recommender Interface.md │ │ ├── Accordion- a Trainable Simulator for Long-Term Interactive Systems.md │ │ ├── Burst-induced Multi-Armed Bandit for Learning Recommendation.md │ │ ├── Cold Start Similar Artists Ranking with Gravity-Inspired Graph Autoencoders.md │ │ ├── Debiased Explainable Pairwise Ranking from Implicit Feedback.md │ │ ├── Evaluating Off-Policy Evaluation- Sensitivity and Robustness.md │ │ ├── Follow the guides- disentangling human and algorithmic curation in online music consumption.md │ │ ├── I want to break free! Recommending friends from outside the echo chamber.md │ │ ├── Local Factor Models for Large-Scale Inductive Recommendation.md │ │ ├── Matrix Factorization for Collaborative Filtering Is Just Solving an Adjoint Latent Dirichlet Allocation Model After All.md │ │ ├── Mitigating Confounding Bias in Recommendation via Information Bottleneck.md │ │ ├── Negative Interactions for Improved Collaborative Filtering- Don’t go Deeper, go Higher.md │ │ ├── Next-item Recommendations in Short Sessions.md │ │ ├── ProtoCF- Prototypical Collaborative Filtering for Few-shot Item Recommendation.md │ │ ├── RecSys2021.md │ │ ├── Reverse Maximum Inner Product Search- How to efficiently find users who would like to buy my item?.md │ │ ├── Semi-Supervised Visual Representation Learning for Fashion Compatibility.md │ │ ├── Shared Neural Item Representation for Completely Cold Start Problem.md │ │ ├── Sparse Feature Factorization for Recommender Systems with Knowledge Graphs.md │ │ ├── The role of preference consistency, defaults and musical expertise in users’ exploration behavior in a genre exploration recommender.md │ │ ├── Together is Better- Hybrid Recommendations Combining Graph Embeddings and Contextualized Word Representations.md │ │ ├── Top-K Contextual Bandits with Equity of Exposure.md │ │ ├── Toward Unified Metrics for Accuracy and Diversity for Recommender Systems.md │ │ ├── Towards Source-Aligned Variational Models for Cross-Domain Recommendation.md │ │ ├── Transformers4Rec- Bridging the Gap between NLP and Sequential & Session-Based Recommendation.md │ │ └── Values of Exploration in Recommender Systems.md │ └── topics/ │ ├── Algorithmic Advances.md │ ├── Applications-Driven Advances.md │ ├── Bandits and Reinforcement Learning.md │ ├── Echo Chambers and Filter Bubbles.md │ ├── Interactive Recommendation.md │ ├── Language and Knowledge.md │ ├── Metrics and Evaluation.md │ ├── Practical Issues.md │ ├── Privacy, Fairness, Bias.md │ ├── Real-World Concerns.md │ ├── Scalable Performance.md │ ├── Theory and Practice.md │ └── Users in Focus.md ├── presentations/ │ └── README.md ├── programming_assignments/ │ ├── beale_ciphers/ │ │ ├── README.md │ │ ├── interview.md │ │ ├── solution/ │ │ │ ├── solve.cpp │ │ │ ├── solve.java │ │ │ └── solve.py │ │ └── testcase/ │ │ ├── README.md │ │ ├── large/ │ │ │ ├── test1.in │ │ │ ├── test1.out │ │ │ ├── test3.in │ │ │ ├── test3.out │ │ │ ├── test5.in │ │ │ ├── test5.out │ │ │ ├── test7.in │ │ │ ├── test7.out │ │ │ ├── test9.in │ │ │ └── test9.out │ │ └── small/ │ │ ├── sample.in │ │ ├── sample.out │ │ ├── test0.in │ │ ├── test0.out │ │ ├── test10.in │ │ ├── test10.out │ │ ├── test11.in │ │ ├── test11.out │ │ ├── test12.in │ │ ├── test12.out │ │ ├── test13.in │ │ ├── test13.out │ │ ├── test14.in │ │ ├── test14.out │ │ ├── test2.in │ │ ├── test2.out │ │ ├── test4.in │ │ ├── test4.out │ │ ├── test6.in │ │ ├── test6.out │ │ ├── test8.in │ │ └── test8.out │ ├── jukebox/ │ │ ├── .gitignore │ │ ├── README.md │ │ ├── listen_count.txt │ │ └── solution/ │ │ ├── 1. 데이터 전처리.ipynb │ │ ├── 2-1. Shallow AutoEncoder.ipynb │ │ ├── 2-2. EASE^R.ipynb │ │ ├── 3. (optional) Implicit을 이용한 Jukebox 풀이.ipynb │ │ ├── README.md │ │ └── code_using_ease/ │ │ ├── evaluate.py │ │ ├── evaluation/ │ │ │ ├── Evaluate.py │ │ │ ├── user_id.txt │ │ │ └── validation_data.txt │ │ ├── recommend_with_ease.py │ │ └── recommend_with_sgd.py │ └── mini_reco/ │ ├── README.md │ ├── evaluation.py │ ├── interview.md │ ├── solution/ │ │ └── solution.py │ └── testcase/ │ ├── input/ │ │ ├── input000.txt │ │ ├── input001.txt │ │ ├── input002.txt │ │ ├── input003.txt │ │ ├── input004.txt │ │ ├── input005.txt │ │ └── input006.txt │ └── output/ │ ├── output000.txt │ ├── output001.txt │ ├── output002.txt │ ├── output003.txt │ ├── output004.txt │ ├── output005.txt │ └── output006.txt └── publications/ └── sigir2023-update-period/ └── README.md ================================================ FILE CONTENTS ================================================ ================================================ FILE: README.md ================================================ # 카카오 추천팀 ## 소개 카카오 추천팀은 카카오의 다양한 서비스에 추천 기술을 제공하고 있습니다. 추천팀에서는 아래와 같은 업무를 하고 있습니다. - 추천 기술 고도화 (방향: 사용자의 장기적인 서비스 만족도 증가) - 추천/ML SaaS 플랫폼 개발 (방향: 높은 품질의 추천 기술을 쉽게 가져다 사용할 수 있는 플랫폼) - 대규모 추천 서비스를 지탱할 수 있는 안정적이고 효율적인 플랫폼 구축 저희에게 궁금한 점이나 하고 싶은 이야기가 있다면 [Discussions](https://github.com/kakao/recoteam/discussions)를 이용해주세요. ## 영입 지원 링크 (현재는 진행 중인 영입 공고가 없습니다.) ## 영입 기출 문제 추천팀 영입 과정에서 실제로 사용했던 기출 문제입니다. - [Mini Reco](programming_assignments/mini_reco) - [Jukebox](programming_assignments/jukebox) - [Beale Ciphers](programming_assignments/beale_ciphers) ## 오픈소스 추천팀에서 공개한 오픈소스 소프트웨어입니다. - [TOROS Buffalo](https://github.com/kakao/buffalo) - A fast and scalable production-ready open source project for recommender systems - [TOROS N2](https://github.com/kakao/n2) - lightweight approximate Nearest Neighbor library which runs fast even with large datasets - [python-ssdb](https://github.com/kakao/python-ssdb) - Python client for [SSDB](https://github.com/ideawu/ssdb) ## 지식 저장소 (논문 리뷰) 추천 관련 학회의 논문들을 읽고 정리한 것을 공개/공유하는 저장소입니다. - [카카오 추천팀 지식 저장소](paper_review/README.md) ## 발행 문서, 발표 영상 자료 모음 공개적으로 발행한 문서나, 발표 영상을 아래에 모아놓았습니다. ### 테크 블로그 / AI 리포트 #### 추천팀 소개 - `2022-06-17` [‘AI 추천 기술’을 선도하는 카카오 추천팀을 소개합니다.](https://tech.kakao.com/2022/06/16/data-recommendation-system/) - `2021-11-02` [charlie의 추천팀 인턴 생활기](https://tech.kakao.com/2021/11/02/charlie-internship/) - `2021-03-11` [카카오 AI 추천을 소개합니다.](https://tech.kakao.com/2021/03/11/kakao-ai/) - `2020-06-23` [데이터를 기반으로 새로운 경험을 선사하는 추천팀 이야기](https://tech.kakao.com/2020/06/23/recruit-algorithm-ml/) #### 추천 시스템 - `2023-03-02` [파이썬과 러스트](https://tech.kakao.com/2023/03/02/python-and-rust/) - `2022-12-12` [추천팀의 DDD 도입기](https://tech.kakao.com/2022/12/12/ddd-of-recommender-team/) - `2021-12-27` [카카오 AI추천 : 카카오의 콘텐츠 기반 필터링 (Content-based Filtering in Kakao)](https://tech.kakao.com/2021/12/27/content-based-filtering-in-kakao/) - `2021-10-18` [카카오 AI추천 : 협업 필터링 모델 선택 시의 기준에 대하여](https://tech.kakao.com/2021/10/18/collaborative-filtering/) - `2021-06-25` [카카오 AI추천 : 토픽 모델링과 MAB를 이용한 카카오 개인화 추천](https://tech.kakao.com/2021/06/25/kakao-ai-recommendation-01/) - `2021-05-20` [카카오 AI추천 : 카카오페이지와 멜론으로 살펴보는 카카오 연관 추천](https://tech.kakao.com/2021/05/20/kakao-ai-recommendation/) - `2018-01-31` [카카오내비 예측의 정확성 그리고 AI](https://brunch.co.kr/@kakao-it/193) - `2017-10-31` [카카오I 추천 엔진의 진화](https://brunch.co.kr/@kakao-it/136) - `2017-06-23` [내 손안의 AI 비서, 추천 알고리듬 - 카카오의 AI 추천 플랫폼, ‘토로스(TOROS)’](https://brunch.co.kr/@kakao-it/72) ### 논문 - [How Important is Periodic Model Update in Recommender Systems?](https://doi.org/10.1145/3539618.3591934) (SIGIR '23) - [Predicting Query-Item Relationship using Adversarial Training and Robust Modeling Techniques](https://amazonkddcup.github.io/papers/0620.pdf) (KDD Cup '22) - [Simple and Efficient Recommendation Strategy for Warm/Cold Sessions for RecSys Challenge 2022](https://dl.acm.org/doi/10.1145/3556702.3556851) (Recsys'22 Challenge) - [An Efficient Combinatorial Optimization Model Using Learning-to-Rank Distillation](https://www.aaai.org/AAAI22Papers/AAAI-4140.WooH.pdf) (AAAI '22) - [A Global DAG Task Scheduler Using Deep Reinforcement Learning and Graph Convolution Network](https://ieeexplore.ieee.org/abstract/document/9626004) (IEEE Access) - [Melon Playlist Dataset: a public dataset for audio-based playlist generation and music tagging](https://arxiv.org/abs/2102.00201) (ICASSP '21) - [How Low Can You Go? Reducing Frequency and Time Resolution in Current CNN Architectures for Music Auto-tagging](https://arxiv.org/abs/1911.04824) (EUSIPCO '20) - [FlexGraph: Flexible partitioning and storage for scalable graph mining](https://journals.plos.org/plosone/article/metrics?id=10.1371/journal.pone.0227032) (PLoS ONE) - [Artist and style exposure bias in collaborative filtering based music recommendations](https://arxiv.org/abs/1911.04827) (ISMIR '19 Workshop) - [Enhancing VAEs for Collaborative Filtering: Flexible Priors & Gating Mechanisms](https://arxiv.org/abs/1911.00936) (RecSys '19) - [Sequential and Diverse Recommendation with Long Tail](https://www.ijcai.org/proceedings/2019/380) (IJCAI '19) - [Automatic playlist continuation using a hybrid recommender system combining features from text and audio](https://arxiv.org/abs/1901.00450) (RecSys '18 Challenge) - [A study on intelligent personalized push notification with user history](https://ieeexplore.ieee.org/document/8258081) (BigData '17) ### if(kakao) #### if(kakao)25 > - `2025-09-23` [커뮤니티로 진화한 오픈채팅, AI로 슬기롭게 연결하다 (추천시스템 파트)](https://if.kakao.com/2025/session?sessionId=11) #### if(kakao)dev2022 > - `2022-12-08` [실험을 잘한다는 것은 무엇일까?](https://if.kakao.com/2022/session/4) - `2022-12-08` [Sequential Recommendation System 카카오 서비스 적용기](https://if.kakao.com/2022/session/8) - `2022-12-08` [Explainable Recommender System in 카카오웹툰](https://if.kakao.com/2022/session/9) #### if(kakao)2021 > - `2021-11-17` [ML로 기프트권 받을 유저 정하기](https://if.kakao.com/2021/session/26) - `2021-11-17` [BERT보다 10배 빠른 BERT 모델 구축](https://if.kakao.com/2021/session/27) - `2021-11-17` [TensorFlow Serving보다 10배 빠르게 서빙하기](https://if.kakao.com/2021/session/28) - `2021-11-17` [추천 시스템 airflow 2.0 도입기](https://if.kakao.com/2021/session/29) #### if(kakao)2020 > - `2020-11-18` [개인화 콘텐츠 푸시 고도화 후기](https://if.kakao.com/2020/session/93) - `2020-11-18` [추천 시스템, 써보지 않겠는가? 맥락과 취향 사이 줄타기](https://if.kakao.com/2020/session/125) #### if(kakao)dev2019 > - `2019-08-30` [둥꿍둥꿍 느낌 아는 음악 바텐더](https://if.kakao.com/2019/program?sessionId=1bfc0d56-3946-4e40-9ab1-523f16d8594a) - [발표 자료](https://mk.kakaocdn.net/dn/if-kakao/conf2019/%EB%B0%9C%ED%91%9C%EC%9E%90%EB%A3%8C_2019/T08-S01.pdf) / [발표 영상](https://mk-v1.kakaocdn.net/dn/if-kakao/conf2019/conf_video_2019/2_103_01_m1.mp4) - `2019-08-30` [Buffalo: Open Source Project for Recommender System](https://if.kakao.com/2019/program?sessionId=c59d4061-6914-4a65-8fb5-f0a0c6c65b93) - [발표 자료](https://mk.kakaocdn.net/dn/if-kakao/conf2019/%EB%B0%9C%ED%91%9C%EC%9E%90%EB%A3%8C_2019/T08-S02-Buffalo.pdf) / [발표 영상](https://mk-v1.kakaocdn.net/dn/if-kakao/conf2019/conf_video_2019/2_103_02_m1.mp4) - `2019-08-30` [상품 카탈로그 자동 생성 ML 모델 소개](https://if.kakao.com/2019/program?sessionId=dce0dd84-d054-4b80-8013-b3d58f61bbe8) - [발표 자료](https://mk.kakaocdn.net/dn/if-kakao/conf2019/%EB%B0%9C%ED%91%9C%EC%9E%90%EB%A3%8C_2019/T08-S04.pdf) / [발표 영상](https://mk-v1.kakaocdn.net/dn/if-kakao/conf2019/conf_video_2019/2_103_04_m1.mp4) #### if(kakao)dev2018 > - `2018-09-04` [눈으로 듣는 음악 추천 시스템](https://if.kakao.com/2018/program?sessionId=959a3047-0a08-4a42-99ce-35a9210ab49a) - [발표 자료](https://mk.kakaocdn.net/dn/if-kakao/conf2018/%E1%84%82%E1%85%AE%E1%86%AB%E1%84%8B%E1%85%B3%E1%84%85%E1%85%A9%20%E1%84%83%E1%85%B3%E1%86%AE%E1%84%82%E1%85%B3%E1%86%AB%20%E1%84%8B%E1%85%B3%E1%86%B7%E1%84%8B%E1%85%A1%E1%86%A8%20%E1%84%8E%E1%85%AE%E1%84%8E%E1%85%A5%E1%86%AB%20%E1%84%89%E1%85%B5%E1%84%89%E1%85%B3%E1%84%90%E1%85%A6%E1%86%B7.pdf) / [발표 영상](http://tv.kakao.com/v/391418802) - `2018-10-01` [눈으로 듣는 음악 추천 시스템](https://brunch.co.kr/@kakao-it/282) - `2018-09-04` [TOROS N2 - lightweight approximate Nearest Neighbor library](https://if.kakao.com/2018/program?sessionId=ad6ea793-70e6-495c-b154-c765e6339793) - [발표 자료](https://mk.kakaocdn.net/dn/if-kakao/conf2018/TOROS%20N2%20-%20lightweight%20approximate%20Nearest%20Neighbor%20library.pdf) / [발표 영상](http://tv.kakao.com/v/391419278) - `2018-11-21` [TOROS N2](https://brunch.co.kr/@kakao-it/300) ### 카카오 아레나 > [카카오 아레나 서비스 종료 및 데이터셋 다운로드 안내](https://github.com/kakao/recoteam/discussions/9) - `2018-12-31` [문제 해결을 위한 머신러닝 오픈 플랫폼, 카카오 아레나](https://brunch.co.kr/@kakao-it/321) #### 3회 대회 (Melon Playlist Continuation) - `2022-05-27` [카카오 AI추천 : 카카오 음악 추천을 경험해보고 싶다면? Melon Playlist Dataset (feats. Kakao Arena)](https://tech.kakao.com/2022/05/27/melon-playlist-dataset/) - `2020-04-28` [멜론 플레이리스트 데이터 탐색 - _카카오 아레나 3회 대회 (Part.2)_](https://brunch.co.kr/@kakao-it/343) - `2020-04-22` [멜론에서 음악 추천을 어떻게 할까? - _카카오 아레나 3회 대회 (Part.1)_](https://brunch.co.kr/@kakao-it/342) #### 2회 대회 (브런치 사용자를 위한 글 추천 대회) - `2019-07-04` [브런치 추천의 힘에 대한 6가지 기술(記述) - _카카오 아레나 2회 대회 (Part. 2)_](https://brunch.co.kr/@kakao-it/333) - `2019-06-24` [브런치 데이터의 탐색과 시각화 - _카카오 아레나 2회 대회 (Part.1)_](https://brunch.co.kr/@kakao-it/332) ### 외부 발표 - `2022-12-22` [Machine Learning Engineer 여행 가이드](/presentations/ksc2022/KSC2022_ML_Engineer_%EC%97%AC%ED%96%89%EA%B0%80%EC%9D%B4%EB%93%9C_%EC%B9%B4%EC%B9%B4%EC%98%A4_%EC%B6%94%EC%B2%9C%ED%8C%80_%EA%B9%80%EC%84%B1%EC%A7%84.pdf) @ KSC 2022 - `2021-12-15` [우리 생활 속 추천 시스템, 어떻게 발전해왔고 어떻게 발전해나가고 있는가?](https://www.youtube.com/watch?v=jJfXHo7nNe8) @ 데이터 그랜드 컨퍼런스 2021 - `2021-05-21` [추천 기술이 마주하고 있는 현실적인 문제들](https://www.youtube.com/watch?v=UUY8YEesIVY) - [발표 자료](/presentations/ai_frontier2021/AIFrontier2021_Recommender_system_in_real_world_nick.pdf) @ AI Frontiers Summit 2021 - `2020-11-25` [유저가 좋은 작품(웹툰)를 만났을 때 (유저의 탐색, 발견 그리고 만족도에 대하여 탐색적 분석하기)](https://deview.kr/2020/sessions/332) @ DEVIEW 2020 - `2019-08-18` [추천시스템, 이제는 돈이 되어야 한다.](https://archive.pycon.kr/2019/program/talk-detail/?id=136) @ PyCon Korea 2019 - `2018-08-19` [추천 시스템을 위한 어플리케이션 서버 개발 후기](https://archive.pycon.kr/2018/program/33) @ PyCon Korea 2018 - `2016-08-13` [TOROS: Python Framework for Recommender](https://archive.pycon.kr/2016apac/program/50) @ PyCon Korea 2016 ================================================ FILE: docs/arena/brunch.html ================================================ kakao dataset

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브런치 데이터셋 다운로드 및 이용에 따른 주의사항



본 데이터셋 다운로드 및 이용을 위해서는 반드시 아래 주의사항을 확인하여야 합니다.

  • 카카오는 데이터셋에 대한 소유자로 정당한 권리를 가지고 있습니다. 본 데이터셋은 비영리 연구 목적으로 공증된 관행에 합치되는 방법으로만 이용할 수 있습니다. 연구, 논문에 데이터를 이용/인용할 경우 ' Kakao (https://www.kakaocorp.com) ’와 같이 반드시 출처를 포함하여 표기하여야 하며 제공되는 데이터셋의 무단전재 및 재배포를 금지합니다.
  • 카카오는 데이터셋을 다른 목적으로 사용함에 따른 정확성, 적합성, 유효성을 보증하지 않습니다. 데이터셋 사용에 따른 책임은 전적으로 이용자에게 있으며, 카카오는 그 사용에 따른 책임으로 면책됩니다. 본 데이터셋 다운로드 및 이용에 따른 주의사항을 위반하거나 데이터셋의 다운로드 및 이용 과정에서 카카오에게 손해가 발생할 경우, 카카오에게 해당 손해를 배상할 책임이 있습니다.
  • 본 주의사항을 읽고 이에 동의를 한 경우에만 데이터셋 다운로드 및 이용이 가능합니다.


데이터셋 설명

이 데이터셋이 제공하는 정보는 2018년 10월 1일부터 2019년 3월 14일까지 브런치 서비스에서 수집된 정보의 일부분입니다.

  • read 디렉토리: 본 글 정보
    • read.tar은 2018년 10월 1일부터 2019년 3월 1일까지 일부 브런치 독자들이 본 글의 정보가 총 3,625개의 파일로 구성되어 있습니다.
    • 파일의 이름은 시작일_종료일 형태입니다. 예를 들어 2018110708_2018110709 파일은 2018년 11월 7일 오전 8시부터 2018년 11월 7일 오전 9시 전까지 본 글입니다.
    • 파일은 여러 줄로 이뤄져 있으며 하나의 줄은 브런치의 독자가 파일의 시간 동안 본 글을 시간 순으로 기록한 것입니다. 한 줄의 정보는 공백으로 구분되어 있으며 첫번 째가 독자의 암호화된 식별자이고 그 뒤로는 해당 독자가 본 글의 정보입니다.
    • 예를 들어 read/2019022823_2019030100 파일에 기록된 아래 정보는 #8a706ac921a11004bab941d22323efab 라는 독자가 2019년 2월 28일 23시에서 2019년 3월 1일 0시 사이에 @bakchacruz_34 @wo-motivator_133 @wo-motivator_133 를 순서대로 보았다는 뜻입니다. @wo-motivator_133 글이 두 번 나타난 것은 이 글을 보기 위해 두 번 방문했다는 뜻입니다.
      • #8a706ac921a11004bab941d22323efab @bakchacruz_34 @wo-motivator_133 @wo-motivator_133
    • 글을 보았다는 의미는 특정 글에 모바일, PC, 앱을 통해 접근했다는 뜻입니다. 머문 시간에 대한 정보가 제공되지 않기 때문에 실제로 글을 읽지 않고 이탈하는 등의 가능성도 있습니다.
  • metadata.json: 글의 메타데이터
    • 643,104 줄로 구성된 글의 메타데이터입니다.
    • 이 메타데이터에는 2018년 10월 1일부터 2019년 3월 14일까지 독자들이 본 글에 대한 정보입니다.
    • 작가가 비공개로 전환하였거나 삭제 등의 이유로 학습 데이터로 제공된 2018년 10월 1일부터 2019년 3월 1일 전까지의 본 글 정보에는 이 메타데이터에 없는 글이 있을 수 있습니다.
      • 개발 데이터와 평가 데이터에 포함된 글의 메타데이터도 포함되어 있습니다. 즉, 평가 대상자들이 2019년 3월 1일부터 2019년 3월 14일 사이에 본 모든 글에 대한 정보가 포함되어 있습니다.
    • 필드 설명
      • magazine_id: 이 글의 브런치 매거진 아이디 (없을 시는 0)
      • reg_ts: 이 글이 등록된 시간(유닉스 시간, 밀리초)
      • user_id: 작가 아이디
      • article_id: 글 번호
      • id: 글 식별자
      • title: 제목
      • sub_title: 부제목
      • display_url: 웹 주소
      • keyword_list: 작가가 부여한 글의 태그 정보
    • 메타데이터의 모든 정보는 작가의 비공개 여부 전환, 글 삭제, 수정 등으로 유효하지 않거나 변동될 수 있습니다.
  • contents 디렉토리: 글 본문 정보
    • 저작권을 보호하고자 본문에서 형태소 분석을 통해 추출된 정보를 암호화하여 제공합니다. 총 7개의 파일로 나뉘어있습니다.
    • 형태소 분석기는 카카오에서 공개한 khaiii 의 기본 옵션을 사용했습니다. 형태소 분석 결과의 어휘 정보는 임의의 숫자로 1:1 변환되었습니다. 동일 어휘의 경우, 품사와 관계없이 같은 숫자로 변환됩니다.
    • 형태소 분석에 대한 설명과 품사의 의미에 대해서는 별도 제공하지 않습니다.
    • 형태소 추출 전에 텍스트를 제외한 HTML과 같은 내용과 관계없는 정보는 제거 했으나 일부 정보가 남았을 수 있습니다.
    • 필드 설명
      • id: 글 식별자
      • morphs: 형태소 분석 결과
        • 리스트의 리스트로 구성되며, 리스트의 첫 번째 요소는 첫 어절의 분석 결과입니다.
        • 어휘와 품사는 / 구분자로 구분됩니다.
        • 예를 들어 "안녕하세요 브런치입니다"라는 문장은 khaiii 형태소분석기에서 "안녕/NNG + 하/XSA + 시/EP + 어요/EF", "브런치/NNP + 이/VCP + ㅂ니다/EC" 라고 분석되는데, 이 결과는 morphs에서 다음처럼 나타날 수 있습니다. [["8/NNG", "13/XSA", "81/EP", "888/EF"], ["0/NNP", "12913/VCP", "29/EC"]]
        • 여러 줄에 걸친 결과는 개행 구분 없이 리스트에 연속적으로 등장합니다. 예를 들어 "안녕하세요 브런치입니다\n안녕하세요"의 결과는 다음과 같습니다. [["8/NNG", "13/XSA", "81/EP", "888/EF"], ["0/NNP", "12913/VCP", "29/EC"], ["8/NNG", "13/XSA", "81/EP", "888/EF"]]
      • chars: 형태소 분석 결과
        • 형태소 분석 결과에서 어휘 부분을 문자 단위로 암호화환 결과입니다.
        • 한 어휘의 문자는 + 구분자로 결합합니다. 예를 들어 위 예의 "브런치입니다"는 chars 필드에서 다음처럼 나타날 수 있습니다. "0+1+2/NNP", "4/VCP", "9+29+33/EC"
    • metadata.json과 마찬가지로 개발 데이터와 평가 데이터의 글 본문도 포함되어 있습니다.
    • contents 정보는 본문이 없는 글의 경우 제공되지 않을 수 있습니다.
  • users.json: 사용자 정보
    • 가입한 사용자(작가 혹은 독자)의 정보입니다.
    • 필드 설명
      • keyword_list: 최근 며칠간 작가 글로 유입되었던 검색 키워드
      • following_list: 구독 중인 작가 리스트
      • id: 사용자 식별자
    • 총 310,758명의 정보가 있습니다. 탈퇴 등의 이유로 사용자 정보가 없을 수 있습니다.
  • magazine.json: 매거진 정보
    • 총 27,967개의 브런치 매거진 정보입니다.
    • 필드 설명
      • id: 매거진 식별자
      • magazine_tag_list: 작가가 부여한 매거진의 태그 정보
  • predict 디렉토리: 예측할 사용자 정보
    • dev.users: 개발 데이터입니다. 대회 기간에 예측한 성능을 평가하기 위해 제공한 사용자 3,000명 리스트입니다.
    • test.users: 평가 데이터입니다. 대회 종료 후 최종 순위를 결정하기 위해 제공한 사용자 5,000명의 리스트입니다.
    • 일부 사용자는 2018년 10월 1일부터 2019년 3월 1일까지 본 글이 없을 수도 있습니다.
  • 식별자에 대해서
    • 사용자 식별자와 콘텐츠 식별자는 식별자 값에 '_' 존재 여부로 나뉩니다.
================================================ FILE: docs/arena/common.css ================================================ @charset "utf-8"; /* 웹폰트 */ @import url('https://fonts.googleapis.com/css?family=Noto+Sans+KR:400,500&subset=korean'); @font-face { font-family: 'Noto Sans'; src:url(../font/NotoSansCJKkr-Regular.eot?#iefix) format('embedded-opentype'); font-weight: normal; font-style: normal; } @font-face { font-family: 'Noto Sans'; src:url(../font/NotoSansCJKkr-Medium.eot?#iefix) format('embedded-opentype'); font-weight: 500; font-style: normal; } @font-face { font-family: 'Noto Sans'; src:url(../font/NotoSansCJKkr-Bold.eot?#iefix) format('embedded-opentype'); font-weight: bold; font-style: normal; } /* reset */ body,div,dl,dt,dd,ul,ol,li,h1,h2,h3,h4,h5,h6,pre,code,form,fieldset,legend,textarea,p,blockquote,th,td,input,select,button{margin:0;padding:0} fieldset,img{border:0 none} dl,ul,ol,menu,li{list-style:none} blockquote, q{quotes:none} blockquote:before, blockquote:after,q:before, q:after{content:'';content:none} input,select,textarea,button{vertical-align:middle;font-size:100%} button{border:0 none;background-color:transparent;cursor:pointer} table{border-collapse:collapse;border-spacing:0} body{-webkit-text-size-adjust:none} input:checked[type='checkbox']{background-color:#666; -webkit-appearance:checkbox} input[type='text'],input[type='password'],input[type='submit'],input[type='search'],input[type='tel'],input[type='email'],html input[type='button'],input[type='reset']{-webkit-appearance:none;border-radius:0} input[type='search']::-webkit-search-cancel-button{-webkit-appearance:none} body{background:#fff} body,th,td,input,select,textarea,button{font-size:13px;line-height:1.5;font-family: 'Noto Sans CJK Kr', 'Noto Sans KR', 'Noto Sans', sans-serif;color:#222} a{color:#222;text-decoration:none} a:active, a:hover{text-decoration:none} address,caption,cite,code,dfn,em,var{font-style:normal;font-weight:normal} /* global */ #kakaoIndex{overflow:hidden;position:absolute;left:-9999px;width:0;height:1px;margin:0;padding:0} .ir_pm{display:block;overflow:hidden;font-size:1px;line-height:0;color:transparent} .ir_wa{display:block;overflow:hidden;position:relative;z-index:-1;width:100%;height:100%} .ir_caption{overflow:hidden;width:1px;font-size:1px;line-height:0;text-indent:-9999px} .screen_out{overflow:hidden;position:absolute;width:0;height:0;line-height:0;text-indent:-9999px} .show{display:block} .hide{display:none} .comm_layer{display:none;flex-direction:column;overflow:auto;position:fixed;top:0%;left:0%;z-index:1000;width:100%;height:100%;background:rgba(0,0,0,0.4);} .comm_layer .inner_layer{position:absolute;top:50%;left:50%;background-color:var(--color-white);border:1px solid #cecece;text-align:center;transform:translate(-50%,-50%);} .info_layer .inner_layer{top:139px;transform:translate(-50%, 0);width:498px;height:396px;box-sizing:border-box;} .info_layer .layer_head{display:flex;justify-content:center;align-items:center;height:80px;background-color:#fee500;} .info_layer .layer_head .tit_info{display: inline-block;font-size:21px;line-height:31px;letter-spacing:-1.05px;color:#1E1E1E;} .info_layer .layer_head .tit_info .logo_kakaoarena{display:inline-block;width:129px;} .info_layer .layer_body{padding:40px 60px 35px;background-color:#fff;} .info_layer .layer_body .txt_info{font-size:15px;line-height: 22px;color:#000000;} .info_layer .layer_body .txt_info .tit_item{display:block;margin-bottom:22px;font-size:16px;font-weight:bold;line-height:22px;} .info_layer .layer_body .link_detail{display:block;margin:30px auto 0;width:175px;height:50px;background-color:#fee500;font-size:15px;font-weight:500;line-height:50px;text-align:center;color:#1E1E1E;} .info_layer .layer_foot{display:flex;justify-content:space-between;} .info_layer .layer_foot .btn_alert{flex:1;width:50%;height:50px;background-color:#f5f5f5;border-top:1px solid #cecece;font-size:14px;font-weight:500;line-height:50px;text-align:center;color:#1E1E1E;} .info_layer .layer_foot .btn_alert ~ .btn_alert {border-left:1px solid #cecece;} .comm_layer.show{display:flex;} .notice_type{padding: 11px 0 80px;} .notice_type .doc-header .inner-header{max-width:1058px;margin:0 auto;} .notice_type .logo_kakaoarena{display:inline-block;width:148px;vertical-align:middle;} .notice_type .inner_main{max-width:1058px;margin:69px auto 0;} .notice_type .tit_notice{font-size:56px;font-weight:bold;line-height:83px;letter-spacing:-2.33px;color:#1E1E1E;} .notice_type .txt_notice{margin:28px 0 60px;font-size:18px;font-weight:500;line-height:32px;letter-spacing:-1px;color:#000000;} .notice_type .tbl_notice{margin-bottom:33px;border-top:1px solid #979797;border-bottom:1px solid #979797;} .notice_type .tbl_notice th,td{padding:0 42px 0;background-color:#fafafa;border-bottom:1px solid #dadbdc;font-size:14px;font-weight:normal;line-height:70px;color:#000000;text-align:left;vertical-align: middle;} .notice_type .tbl_notice .tit_item{font-size:15px;font-weight:500;} .notice_type .list_notice{margin-left:14px;} .notice_type .list_notice > li{position:relative;padding-left:10px;font-size:13px;line-height:25px;letter-spacing:-0.41px;color:#3C3C3C;} .notice_type .list_notice > li:before{content:'';position:absolute;top:50%;left:0;width:3px;height:3px;transform: translateY(-50%);background-color:#3C3C3C;border-radius: 100%;} .notice_type .link_notice{display:block;width:391px;height:70px;margin:60px auto 0;background-color: #FEE500;line-height:70px;font-size:18px;font-weight:500;color:#1E1E1E;text-align: center;} .tbl_comm{width:100%;border:0;border-spacing:0;table-layout:fixed;border-collapse:collapse;} ================================================ FILE: docs/arena/index.html ================================================ kakao arena

kakao arena

카카오 아레나가 종료되었습니다.

그동안 카카오 아레나 서비스를 이용해 주셔서 진심으로 감사드립니다. 아쉽게도 카카오 아레나 서비스가 2023년 7월 3일 종료되었음을 알려드립니다.
작성하신 게시글과 제출하신 자료에 대해 백업을 원하신다면 고객센터로 요청 바랍니다.
데이터 백업 기간이 종료되면 게시글과 자료는 모두 안전하게 파기될 예정입니다.

백업 기간, 백업 대상, 백업 방법으로 구성된 백업 정보
백업 기간 2023년 7월 3일(월) ~ 2023년 10월 4일(수)
백업 대상 본인이 작성한 글(글에 첨부된 이미지/파일), 대회 제출 소스 코드와 결과 파일
백업 방법 고객센터로 신청 시 이메일로 전달 (고객센터 로그인 필요)
유의사항
  • 백업 기간 이후에는 백업 신청 및 백업이 불가능합니다. 꼭 기간 내에 백업 신청을 완료해 주세요.
  • 고객센터 백업 신청은 로그인 후 신청이 가능합니다.
백업 신청 고객센터 바로가기
================================================ FILE: docs/arena/melon-en.html ================================================ kakao dataset

Melon Dataset

Melon Dataset Download Consent Form

Precautions Regarding the Download and Use of the Melon Dataset



Before proceeding with the download and utilization of this dataset, it is crucial to review and comply with the following precautions carefully

  • Kakao Entertainment is the lawful owner of the dataset and possesses all the necessary rights. The dataset is intended solely for non-profit research purposes and should be utilized in accordance with established industry practices. When utilizing or referencing the data for research or scholarly papers, it is mandatory to include the appropriate attribution as follows: "Kakao Entertainment, melon (www.melon.com)." Unauthorized reproduction or redistribution of the dataset is strictly prohibited.
  • Please be aware that Kakao Entertainment does not guarantee the accuracy, suitability, or validity of the dataset for purposes other than those specified. The user assumes full responsibility for the usage of the dataset, and Kakao Entertainment shall not be held accountable for any consequences or liabilities arising from its use. In case of any violation of the precautions regarding the download and use of this dataset, or if any damages occur to Kakao Entertainment during the process, the user shall be held responsible for compensating Kakao Entertainment for such damages.
  • By confirming your understanding and agreement to the above precautions, you may proceed with downloading and utilizing the dataset.


Dataset Description

Melon Playlist Dataset

This dataset contains 148,826 playlists composed of 649,091 unique songs and mel-spectrogram data for each song. The included playlists are the listed item in the Melon DJ Playlist service provided by Melon. In addition, Melon DJ Playlist consists of playlists both made by experts contracting with us in advance for quality assurance and filtered by the company’s quality standard among those submitted by Melon users who want to put on the Melon DJ Playlist. Each playlist contains songs and multiple sets of tags (included in the 30,652 unique tags) assigned by the playlist creator, along with its title.

Playlist Included

For setting contest questions, we will provide the entire playlist data separately as train.json composed of 115,071 playlists, val.json composed of 23,015 playlists, and test.json composed of 10,740 playlists. Unlike train.json, test.json and train.json have some of the songs and tags in their playlists masked for the submission of answers.

Field Description
  • id: Playlist ID
  • plylst_title: Playlist title
  • tags: tag list
  • songs: song list
  • like_cnt: like count
  • updt_date: update date
Mel-Spectrogram Included

Mel-spectrogram data are saved as a ‘{songID}.npy’ file name with the file extension npy. A number from 0 to 707988 is assigned as song ID, and each file is allocated to and stored in the {floor(ID / 1000)}/ directory. For example, the song with ID 415263 is saved as 415/415263.npy. The 2.1b.dev677 version of Essentia library was used to extract each mel-spectrogram. mel-spectrogram was calculated in the use of segments of a song’s 20~50 second-interval to reduce the 16Khz sample size rate, 512 frame size, 256 hop size, Hann window function, and data size and employed 48 mel-bands resolution so that Melon Playlist Dataset can contain about 240GB data.

Meta-Data Included

Melon Playlist Dataset provides song_meta.json, the song metadata saved in a separate json file format, and genre_gn_all.json, the mapping table for genre included in the song metadata. song_meta.json has metadata for a total of 707,989 songs, including all songs in train.json, val.json, and test.json. The field description included is as follows.

Field Description
  • _id: song ID
  • album_id: album ID
  • artist_id_basket: artist ID list
  • artist_name_basket: artist list
  • song_name: song title
  • song_gn_gnr_basket: song genre list
  • song_gn_dtl_gnr_basket: song detailed genre list
  • issue_date: issue date
* All information in the metadata may be invalid or subject to change due to the copyright holder’s privacy conversion, song deletion, metadata modification, and the like.

genre_gn_all.json contains a total of 254 genre codes, including genre information for 30 major category genre codes (included in song_gn_gnr_basket) and 224 detailed category genre codes (included in song_gn_gnr_basket).

================================================ FILE: docs/arena/melon.html ================================================ kakao dataset

멜론 데이터셋

멜론 데이터셋 다운로드 동의서

멜론 데이터셋 다운로드 및 이용에 따른 주의사항



본 데이터셋 다운로드 및 이용을 위해서는 반드시 아래 주의사항을 확인하여야 합니다.

  • 카카오 엔터테인먼트는 데이터셋에 대한 소유자로 정당한 권리를 가지고 있습니다. 본 데이터셋은 비영리 연구 목적으로 공증된 관행에 합치되는 방법으로만 이용할 수 있습니다. 연구, 논문에 데이터를 이용/인용할 경우 'Kakao Entertainment, melon (www.melon.com) ’와 같이 반드시 출처를 포함하여 표기하여야 하며 제공되는 데이터셋의 무단전재 및 재배포를 금지합니다.
  • 카카오 엔터테인먼트는 데이터셋을 다른 목적으로 사용함에 따른 정확성, 적합성, 유효성을 보증하지 않습니다. 데이터셋 사용에 따른 책임은 전적으로 이용자에게 있으며, 카카오 엔터테인먼트는 그 사용에 따른 책임으로 면책됩니다. 본 데이터셋 다운로드 및 이용에 따른 주의사항을 위반하거나 데이터셋의 다운로드 및 이용 과정에서 카카오 엔터테인먼트에게 손해가 발생할 경우, 카카오 엔터테인먼트에게 해당 손해를 배상할 책임이 있습니다.
  • 본 주의사항을 읽고 이에 동의를 한 경우에만 데이터셋 다운로드 및 이용이 가능합니다.


데이터셋 설명

이 데이터셋에는 649,091개의 고유 곡으로 구성된 148,826개의 플레이리스트와 각 곡에 대한 멜 스펙트로그램 데이터가 포함되어 있습니다. 포함된 플레이리스트는 멜론에서 제공하는 멜론 DJ 플레이리스트 서비스에 등재된 항목입니다. 또한, 멜론 DJ 플레이리스트는 당사와 사전 계약을 맺은 전문가가 품질 보증을 위해 만든 플레이리스트와 멜론 이용자가 멜론 DJ 플레이리스트에 올리고 싶은 플레이리스트 중 당사의 품질 기준에 의해 필터링된 플레이리스트로 구성됩니다. 각 재생목록에는 제목과 함께 재생목록 제작자가 지정한 노래와 여러 개의 태그(30,652개의 고유 태그에 포함)가 포함되어 있습니다.

  • song_meta.json: 곡 메타데이터
    • 총 707,989개의 곡에 대한 메타데이터가 수록되어 있습니다.
    • 개발 데이터와 평가 데이터에 수록된 모든 곡에 대한 메타데이터가 포함되어 있습니다.
    • 필드 설명
      • _id: 곡 ID
      • album_id: 앨범 ID
      • artist_id_basket: 아티스트 ID 리스트
      • artist_name_basket: 아티스트 리스트
      • song_name: 곡 제목
      • song_gn_gnr_basket: 곡 장르 리스트
      • song_gn_dtl_gnr_basket: 곡 세부 장르 리스트
      • issue_date: 발매일
    • 메타데이터의 모든 정보는 저작권자의 비공개 여부 전환, 곡 삭제, 메타데이터 수정 등으로 유효하지 않거나 변동될 수 있습니다.
  • genre_gn_all.json:
    • 곡 메타데이터에 수록된 장르에 대한 정보입니다. 위 song_meta.json 에서 song_gn_gnr_basket 과 song_gn_dtl_gnr_basket 에 들어가는 정보들에 대한 메타데이터입니다.
  • train.json:
    • 모델 학습용 파일로, 115,071개 플레이리스트의 원본 데이터가 수록되어 있습니다.
    • 필드 설명
      • id: 플레이리스트 ID
      • plylst_title: 플레이리스트 제목
      • tags: 태그 리스트
      • songs: 곡 리스트
      • like_cnt: 좋아요 개수
      • updt_date: 수정 날짜
  • val.json:
    • 공개 리더보드용 문제 파일로, 23,015개 플레이리스트에 대한 문제가 수록되어 있습니다. 모든 데이터가 수록되어있는 train 파일과는 다르게, 곡과 태그의 일부가 수록되어 있습니다.
    • 필드 설명
      • id: 플레이리스트 ID
      • plylst_title: 플레이리스트 제목
      • tags: 태그 리스트
      • songs: 곡 리스트
      • like_cnt: 좋아요 개수
      • updt_date: 수정 날짜
  • test.json:
    • 파이널 리더보드용 문제 파일로, 10,740개 플레이리스트에 대한 문제가 수록되어 있습니다. 모든 데이터가 수록되어있는 train 파일과는 다르게, 곡과 태그의 일부가 수록되어 있습니다.
    • 필드 설명
      • id: 플레이리스트 ID
      • plylst_title: 플레이리스트 제목
      • tags: 태그 리스트
      • songs: 곡 리스트
      • like_cnt: 좋아요 개수
      • updt_date: 수정 날짜
  • arena_mel_{0~39}.tar
    • 곡에 대한 mel-spectrogram 데이터를 담고있는 파일입니다. 위에 있는 파일들에서 등장하는 각 곡 ID마다 npy 파일 1개가 배정되어있습니다. numpy로 다음과 같이 로드할 수 있습니다. 
      import numpy as np

mel = np.load("0.npy")
    • 곡 ID는 0~707988 까지 배정되어 있으며, 곡ID.npy 의 파일 이름을 가지고 있습니다. 파일의 갯수가 많기 때문에, 각 npy 파일은 각각 {floor(ID / 1000)}/ 폴더 아래에 들어가있습니다. 예를 들어 곡 ID가 415263인 파일의 경우 415/415263.npy 로, 곡 ID가 53712인 경우 53/53712.npy 에 존재합니다.
================================================ FILE: onboarding/README.md ================================================ # 추천팀 온보딩 카카오 추천팀에 입사하기 전에 미리 보시면 좋을 내용들을 정리해놓은 문서입니다. ## 추천 기술 관련 자료 해당 내용에 링크된 자료는 방대하므로(특히 수학/ML 기초) 필요한 부분들 위주로 보시기 바랍니다. ### 수학/ML 기초 추천 시스템은 머신러닝의 응용 분야로서 머신러닝에 대한 기초지식을 탄탄히 다지는 것은 큰 도움이 됩니다. 기본적인 Linear Algebra, Statistical Inference, Convex Optimization에 대해 익숙하지 않다면 이에 대한 학습이 필요할 수 있습니다. 대표적인 ML 교재 최소 1개 이상을 정독해본 경험을 가지는 것을 추천해 드립니다. - [Introduction to Statistical Learning (ISLR)](https://www.statlearning.com/) - [Elements of Statistical Learning (ESL)](https://hastie.su.domains/Papers/ESLII.pdf) - [Machine Learning: A Probabilistic Perspective (Murphey 책)](https://probml.github.io/pml-book/) - [Pattern Recognition an Machine Learning (Bishop 책)](https://www.microsoft.com/en-us/research/uploads/prod/2006/01/Bishop-Pattern-Recognition-and-Machine-Learning-2006.pdf) - ... etc. 딥러닝 교재, 최신 추천시스템은 뉴럴넷을 활용하는 경우도 많고 자연어, 이미지 등의 데이터를 활용하는 경우도 있습니다. - [Deep Learning Book](https://www.deeplearningbook.org/) - ... etc. ### 추천 알고리즘 대표적인 올드 스쿨 알고리즘입니다. 해당 알고리즘들은 논문이 발표된지 오래되었지만, 아직도 대중적으로 많이 활용되고 있습니다. - iALS ([Collaborative Filtering for Implicit Feedback Datasets](http://yifanhu.net/PUB/cf.pdf)) - BPR ([BPR: Bayesian Personalized Ranking from Implicit Feedback](https://arxiv.org/pdf/1205.2618.pdf)) - LinUCB ([A Contextual-Bandit Approach to Personalized News Article Recommendation](https://arxiv.org/pdf/1003.0146.pdf)) 그 외, 벤치마크로 자주 등장하는 전통 알고리즘은 다음과 같습니다. - WARP ([Improving Pairwise Learning for Item Recommendation from Implicit Feedback](http://webia.lip6.fr/~gallinar/gallinari/uploads/Teaching/WSDM2014-rendle.pdf)) - SLIM ([SLIM: Sparse Linear Methods for Top-N Recommender Systems](https://ieeexplore.ieee.org/abstract/document/6137254)) 카카오 테크 블로그에 카카오 추천시스템에 대하여 주제별로 설명한 글들입니다. - [테크 블로그: 추천 시스템](/README.md/#%EC%B6%94%EC%B2%9C-%EC%8B%9C%EC%8A%A4%ED%85%9C) 추천 관련 최신 논문들을 서칭해보고 abstract와 related works를 읽어보면 최신 연구 방향과 그 기반이 되는 주요 논문들을 알 수 있습니다 - 추천 관련 대표 학회들: RecSys, WWW, SIGIR, KDD, WSDM, CIKM, AAAI, IJCAI, ICML, NeurIPS, ... etc. (좋은 논문인지와 별개로) 대표적으로 유명한 추천 알고리즘 논문들은 아래와 같습니다. - [BERT4Rec: Sequential Recommendation with Bidirectional Encoder Representations from Transformer, CIKM'19](https://arxiv.org/abs/1904.06690) - [Variational Autoencoders for Collaborative Filtering, WWW'18](https://dl.acm.org/doi/10.1145/3178876.3186150) - [Neural Collaborative Filtering, WWW'17](https://dl.acm.org/doi/10.1145/3038912.3052569) - [Recommending What Video to Watch Next: A Multitask Ranking System, RecSys'19](https://daiwk.github.io/assets/youtube-multitask.pdf) - [Collaborative Metric Learning, WWW'17](https://vision.cornell.edu/se3/wp-content/uploads/2017/03/WWW-fp0554-hsiehA.pdf) - [Convolutional Matrix Factorization for Document Context-Aware Recommendation, RecSys'16](http://uclab.khu.ac.kr/resources/publication/C_351.pdf) - ... etc. ### 그 외 #### 강화학습 실시간 추천시스템은 사용자와 상호작용하며 사용자들의 취향을 파악하고 추천해주는 시스템으로서 강화학습 framework이 잘 어울린다는 평가가 많습니다, 특히 Multi-Armed Bandit, Contextual-Bandit 등은 팀 내에서도 매우 많이 사용되고 있습니다 - [강화학습 대표 교재 (Reinforcement Learning: An Introduction)](http://incompleteideas.net/book/the-book.html) - [David Silver 강의](https://www.davidsilver.uk/teaching/) ## 머신러닝플랫폼 관련 자료 아래의 키워드는 모두 머신러닝플랫폼에서 중요한 것들이지만 업무에 필수는 아닙니다. 학습 비용이 만만치 않기 때문에 천천히 기반 다지는 것을 추천합니다. ### 방법론, 가이드 - [Domain Driven Design (DDD)](https://martinfowler.com/bliki/DomainDrivenDesign.html) - [Microservices (MSA)](https://learn.microsoft.com/en-us/azure/architecture/guide/architecture-styles/microservices) - [Event Driven Architecture (EDA)](https://learn.microsoft.com/en-us/azure/architecture/guide/architecture-styles/event-driven) - [Cloud Native](https://learn.microsoft.com/en-us/dotnet/architecture/cloud-native/definition) - [CI/CD](https://en.wikipedia.org/wiki/CI/CD) - [Test Driven Development (TDD)](https://martinfowler.com/bliki/TestDrivenDevelopment.html) ### 개발 자원 머신러닝플랫폼은 대부분 파이썬 3.10을 사용하고 있습니다. 아래는 개발할 때 많이 사용하는 라이브러리를 간추렸습니다. - [poetry](https://python-poetry.org/) - [pydantic](https://pydantic-docs.helpmanual.io/) - [pytest](https://pytest.org) - [mypy](https://mypy.readthedocs.io/) ## 팀 개발환경 및 플랫폼 ### 기본 개발환경 팀의 메인 개발언어는 Python, C++입니다. 코드 Editor로는 주로 Vim을 사용하고 있으나, 제약은 없으며 VSCode, PyCharm등 개발자 본인에게 가장 편한 editor를 사용할 수 있습니다. (단, 서버 내에서 작업하는 경우도 많기에, Vim에 대한 기본적인 사용법을 익혀두시면 유용합니다.) - [Vim](https://www.vim.org/) - [Vim adventures](https://vim-adventures.com/): Vim을 간단한 게임형태로 배워볼 수 있는 페이지입니다. 코드의 버전관리는 Git / GitHub를 사용하고 있습니다. - [git](https://git-scm.com/) - [Git/GitHub 안내서](https://subicura.com/git/guide/) 팀 내 대부분의 서비스는 docker 및 kubernetes를 기반으로 동작합니다. - [docker](https://www.docker.com/) - [초보를 위한 도커 안내서](https://subicura.com/2017/01/19/docker-guide-for-beginners-1.html) - [kubernetes](https://kubernetes.io/) - [쿠버네티스 안내서](https://subicura.com/k8s/guide/#%E1%84%80%E1%85%A1%E1%84%8B%E1%85%B5%E1%84%83%E1%85%B3) ### 플랫폼 #### Kafka 추천 시스템에서는 각 유저가 어떤 아이템을 소비했는지, 또 소비한 아이템에 대해 어떠한 반응을 보였는지에 대한 정보가 중요하게 사용됩니다. 이러한 정보는 서비스단에서 실시간으로 수집되어 [Kafka](https://kafka.apache.org/)를 통해 추천팀에서 받아볼 수 있는 형태로 전달되고 있습니다. 따라서 Kafka의 기본구조 및 동작 방식에 대해 미리 알아두시면 팀에서 실제 업무를 하실 때 많은 도움이 됩니다. - [Youtube강의-아파치 카프카](https://www.youtube.com/playlist?list=PL3Re5Ri5rZmkY46j6WcJXQYRlDRZSUQ1j) #### MongoDB [MongoDB](https://www.mongodb.com/)는 팀에서 가장 많이 사용하는 key-value storage 중 하나이며, 주 사용처는 다음과 같습니다. - 개별 유저에 대한 추천 결과 저장(캐시 용도) - Feature storage - 유저들의 아이템 소비 로그, 피드백 로그 저장 MongoDB 참고 자료 (팀 내에서 직접 관리를 하는 것은 아니기에 깊이 보실 필요는 없습니다. 아래에서는 3, 4, 5를 위주로 보셔도 괜찮습니다.) - [1편: 소개, 설치 및 데이터 모델링](https://velopert.com/436) - [2편: Database/Collection/Document 생성, 제거](https://velopert.com/457) - [3편: Document Query(조회) - find() 메소드](https://velopert.com/479) - [4편: find() 메소드 활용 - sort(), limit(), skip()](https://velopert.com/516) - [5편: Document 수정 - update() 메소드](https://velopert.com/545) - [pymongo docs](https://pymongo.readthedocs.io/en/stable/) - pymongo는 MongoDB의 python client로써, 팀에서 MongoDB를 다룰 때 주로 사용하고 있습니다. #### Hadoop [Hadoop](https://hadoop.apache.org/)을 구성하는 여러 가지 요소가 있지만, 팀에서는 주로 HDFS, Hive(Presto, Spark)를 많이 사용합니다. Hadoop의 개별 요소를 세세히 설명하기엔 양이 너무 방대하기에, 간단한 개념 위주로 링크를 정리했습니다. - HDFS: 유저 x 아이템 interaction 데이터 저장, 학습된 추천 모델 저장 등 - [hdfs 기본개념](https://kadensungbincho.tistory.com/30) - [hdfs 명령어 모음](https://blog.voidmainvoid.net/175) - Hive(Presto, Spark): 데이터 분석, 전처리 등에 사용 - [Hive, Presto, Spark 기본 설명](https://seoyoungh.github.io/data-science/distribute-system-1/) ================================================ FILE: paper_review/README.md ================================================


📝 카카오 추천팀 지식 저장소

카카오 추천팀에서 추천 관련 학회의 논문들을 읽고 정리하는 저장소입니다. 정리는 크게 4가지 방식으로 구성되어 있습니다. - Summary : 3줄 내외로 논문 내용을 요약합니다. - Approach : 논문에서 쓰인 접근법들을 정리합니다. - Results : 실험 결과에 대한 내용을 정리합니다. - Conclusion : 논문에 대한 본인의 생각을 정리합니다. 발표 자료를 학회별, 주제별로 정리한 링크는 다음과 같습니다. ### Conferences - [RecSys2021](recsys/recsys2021/RecSys2021.md) ### Topics - [Algorithmic Advances](topics/Algorithmic%20Advances.md) - [Applications-Driven Advances](topics/Applications-Driven%20Advances.md) - [Bandits and Reinforcement Learning](topics/Bandits%20and%20Reinforcement%20Learning.md) - [Echo Chambers and Filter Bubbles](topics/Echo%20Chambers%20and%20Filter%20Bubbles.md) - [Interactive Recommendation](topics/Interactive%20Recommendation.md) - [Language and Knowledge](topics/Language%20and%20Knowledge.md) - [Metrics and Evaluation](topics/Metrics%20and%20Evaluation.md) - [Practical Issues](topics/Practical%20Issues.md) - [Privacy, Fairness, Bias](topics/Privacy,%20Fairness,%20Bias.md) - [Real-World Concerns](topics/Real-World%20Concerns.md) - [Scalable Performance](topics/Scalable%20Performance.md) - [Theory and Practice](topics/Theory%20and%20Practice.md) - [Users in Focus](topics/Users%20in%20Focus.md) ================================================ FILE: paper_review/recsys/recsys2021/"Serving Each User"- Supporting Different Eating Goals Through a Multi-List Recommender Interface.md ================================================ # "Serving Each User"- Supporting Different Eating Goals Through a Multi-List Recommender Interface - Paper : - Authors : Alain Starke, Edis Asotic, Christoph Trattner - Reviewer : bell.park, marv.20 - Topics - [#Users_in_Focus](../../topics/Users%20in%20Focus.md) - #Diversity - [#RecSys2021](RecSys2021.md) ## Summary - 음식 추천 시스템에서, 유저의 다양한 목적을 만족시키기 위해 어떻게 노출시키면 좋을지(인터페이스)에 대해서 연구한 논문입니다. - 추천 결과를 single-list와 multi-list 각각의 방법으로 노출했을 때 어떠한 차이가 있는지 유저 스터디로 비교 분석하였습니다. - 리스트 간의 순서를 정하는 모델이나 로직이 없다는 것은 아쉽지만, 현실적인 접근이라고 생각됩니다. ## Approach - 기본적으로 현재 보고있는 레시피와 유사한 레시피를 추천하는 연관 추천 환경입니다. - 저자들이 직접 레시피 데이터를 긁어와서 5가지 추천 리스트를 구성하였습니다. - Similar recipies - 레시피 이름 TF-IDF indexing후 top-5 similarity - Fewer Calories - top-40 similarity 후 칼로리 작은 순서대로 top-5 - Fewer Carbohydrates - top-40 similarity 후 탄수화물 작은 순서대로 top-5 - Less Fat - top-40 similarity 후 지방 작은 순서대로 top-5 - More Fiber - top-40 similarity 후 섬유질 큰 순서대로 top-5 - 366명의 실험 참가자를 모집해서 실험을 진행하였습니다. - 실험 참가자 마다 5번의 실험을 진행 - 참가자가 레시피를 검색해서 들어가면 아래 2가지 중 하나의 화면이 노출 - 미리 준비된 5개의 리스트 중 하나를 골라 노출 - 5개의 리스트를 전부 노출 - 설명은 붙이는 경우도 있고 안붙이는 경우(Similar recipies)도 있음 - 참가자는 레시피를 하나 고르고 레시피와 추천에 대해 만족도를 리포트 ## Results - 참가자의 피드백을 Structural Equation Modeling (SEM) 기법으로 분석하였습니다. - 주목할 만한 결론은 다음과 같습니다. - Multi-list로 노출하면 설명 여부와 상관 없이 참가자들이 더 다양하게 추천된다고 느낍니다. (higher **perceived** diversity) - 실제로 다양하게 노출하는 것과는 다르고, 참가자들이 그렇게 느꼈다는 부분이 중요하다고 합니다. - 참가자들이 다양하게 추천된다고 느끼면, 아래 두 가지 현상이 나타납니다. - 하나의 아이템을 고르는데는 어려움을 느낍니다. (higher level of diversity, higher level of choice difficulty) - 추천의 만족도가 증가합니다. (perceived diversity was also positively related to choice satisfaction) - 참가자들이 추천이 나온 이유를 이해하면, 추천이 더 다양하다고 느낍니다. - Single-list 노출 시에는 추천에 대한 설명을 붙여주었을 때 참가자 만족도가 올라가지만, Multi-list 노출 시에는 설명이 있을 때 만족도가 소폭 하락하였습니다. ================================================ FILE: paper_review/recsys/recsys2021/Accordion- a Trainable Simulator for Long-Term Interactive Systems.md ================================================ # Accordion- a Trainable Simulator for Long-Term Interactive Systems - Paper : - Authors : James McInerney, Ehtsham Elahi, Justin Basilico, Yves Raimond, Tony Jebara - Reviewer : hee.yoon - Topics - [#Metrics_and_Evaluation](../../topics/Metrics%20and%20Evaluation.md) - [#RecSys2021](RecSys2021.md) ## Summary - 유저와 인터렉션이 있는 시스템 기반의 트레인 가능한 시뮬레이터를 개발하였습니다. - 구성은 다음과 같습니다. - 유저가 visit 할지 여부를 결정하는 visit model - 유저에게 해당 시점에 어떤 아이템이 추천될지 결정하는 recommedation imitator - 유저가 추천된 아이템을 클릭할지 결정하는 user selection model - 컨트리뷰션 - 이 중에서 visit model 를 inhomogeneous Poisson process 로 구현한 부분이 중요한 컨트리뷰션이라고 볼 수 있습니다. - (비교 시뮬레이터가 Norm IPS인데) 왜 Norm IPS 에 비해, sim2real gap 을 더 줄일 수 있는가? - 추천 퀄리티에 따라 impression수 자체가 차이가 날 수 있는 부분을 시뮬레이션에 녹여 모델링함 - code: ## Approach - Simulator Data Generation Algorithm: - 구조도 - Visit Model - Global Intensity + State-based intensity + Recent Activity intensity using Hawkes - user_state, time 이 주어졌을 때 유저의 intensity를 리턴 - Recommender Imitator (= Impression Model?) - user_state 가 주어졌을 때, item 을 리턴 - 컨트롤 폴리시 목적으로는 imitator 를 학습하여 사용할 수도 있고, - 타겟 폴리시 목적으로는 실험하고자 하는 모델로 대체하여 사용할 수 있는 것으로 추정. (Non negative Matrix Factorization 으로 Hyperparameter Fitting 시뮬레이션 Section 4.2 참고) - User Selection Model - user_state, item 이 주어졌을때 reward 를 리턴 ### Visit Model - - - Inhomogeneous Poisson Process: - Hawkes Intensity: - 과거 추천 아이템에 유저가 긍정적으로 반응했을 경우 더 커짐 - ### Marking Distribution = Recommendation Imitator (Impression Model) * User Selection Model - Both the impression model and user selection model use as - input: a bag of words representation of previous user interactions with items - and map these though a dense network - output: to a multinomial distribution over items. ## Results AB 테스트 결과를 얼마나 재현 가능한가? 를 평가하였습니다. ================================================ FILE: paper_review/recsys/recsys2021/Burst-induced Multi-Armed Bandit for Learning Recommendation.md ================================================ # Burst-induced Multi-Armed Bandit for Learning Recommendation - Paper : - Authors : Rodrigo Alves, Antoine Ledent, Marius Kloft - Reviewer : charlie.cs - Topics - [#Algorithmic_Advances](../../topics/Algorithmic%20Advances.md) - [#Bandits_and_Reinforcement_Learning](../../topics/Bandits%20and%20Reinforcement%20Learning.md) - [#RecSys2021](RecSys2021.md) ## Summary - non-stationary & context-free MAB 상황에서 Cold-start recommendation (CSR) 을 위한 방법인 BMAB (Burst-induced MAB)을 제시하였습니다. - 기존 non-stationary MAB(EXP3, Discounted-UCB etc.)의 방식과 비교되는 특징은 다음과 같습니다. 1. context-free: feature vector가 필요하지 않습니다. 2. reward 분포의 변화를 확인하는 대신, 시스템의 temporal dynamics를 활용합니다. ## Approach ### Intuition - 추천 환경에는 크게 두가지 상태가 있다고 가정: loyal (stable) state 그리고 curious (unstable) state - 전체 time horizon은 일정 구간으로 나뉘어져서, 두 state 중 하나가 발생한다고 가정함 - loyal state는 구간에 상관없이, curious state는 구간마다 stationary payoff distribution를 가진다고 주장 - state 마다 MAB 모델을 세우고, 특정 state 상황에 해당하는 모델을 이용하여 추천을 진행 ### Burst-induced MAB (BMAB) - Algorithm 1. 두 state (loyal, curious)마다 각각 K개의 beta parameter를 두고, orcale이 timestamp마다 어떤 state인지 알려줌 2. state를 확인하면, 해당 state의 beta parameter를 통해 일반적인 Thompson Sampling 추천을 진행 3. 만약 curious (s = 1) 에서 loyal (s = 0) 상태로 넘어가는 경우, curious state에 해당하는 beta parameter를 decay ### State Detector - 매 timestamp 마다 어떤 state인지 파악하는 orcale을 구성하기 위해서는 homoheneous Poisson process에 대한 intensity (`lambda_L`)가 알려져 있다는 가정이 요구됨 - intensity (function)는 쉽게 말하면 특정 구간에서 발생한 이벤트의 rate - 이 가정의 존재 이유는 문제 초기 정의 시, time series 가 두가지 stochastic point process의 mixture에 의해 생성된다는 가정이 있었기 때문 - loyal: a homogeneous Possion process (HPP) with intensity `lambda_L` - curious: a piece-wise homogeneous Poisson process (PW-HPP) with intensity `lambda_C(t)` - 해당 intensity를 몰라도 쉽게 유추할 수 있다고 주장 - 예시 (HPP with `lambda_L=3`, PW-HPP with `lambda_C in (0.15, 15)`) ![image-20211123140547188](https://tva1.sinaimg.cn/large/008i3skNgy1gwp03l9ztij32wq0rawlv.jpg) - Algorithm - state를 추정할 timestep 구간을 사이즈가 `Delta` 인 window로 나누고, 해당 구간이 intensity 가 `lambda_L` 인 Possion process에서 생성되었는지 검증 - 즉, window 내 분포는 shape가 `Delta-1` 이고 scale이 `lambda_L` 인 Gamma distribution을 따르는지 확인 - 해당 분포를 따른다면 loyal (`0`) 그렇지 않다면 curious (`1`) image-20211115224032770 - `q` 는 Gamma 분포의 quantile function - quantile function의 shape값이 `lambda-1` 인 이유는 `t_{i-\Delta+1}` 부터 event counting이 진행되기 때문 - hypothesis testing의 목적은 burst period를 확인하기 위한 목적 (calm period는 loyal 에게 dominated) - 만약 `delta=0.95`라면 test는 다음과 같이 해석될 수 있음 : scale이 `lambda_L`인 event가 `Delta-1`번 발생할때까지 걸리는 time interval 분포 중, interval `Delta_i`가 분포의 quntaile 5% 내에 존재하는가? - 쉽게 말하면, 기존에 이벤트가 `N` 번 발생하는데 `X` 만큼 걸렸는데, `Y`는 그보다 더 짧은가? - 해당 intensity를 몰라도 쉽게 유추할 수 있다고 주장 - solve with EM - Burstiness scale: A parsimonious model for characterizing random series of events. In Proceedings of the 22nd ACM SIGKDD ## Results - 합성 데이터, 실제 데이터 모두를 사용해서 제안한 방법을 평가하였습니다. - 제안한 방법들: BMAB-O (oracle), BMAB-R (detector) - 실제 데이터의 경우, 전체 timeseries에서 일정 구간은 `lambda_L` 을 추정하는 구간으로 사용하고 나머지는 평가에 사용하였습니다. - metric: average of the observed reward (`R(T)/N`), and its standard deviation - the user liked (Behance, MovieLens), searched (Google trends) or clicked on (Outbrain) - baseline은 크게 세가지로 나뉩니다. - stationary: TS - non-stationary: EXP3 - piece-wise stationary: EXP3DD, DUCB, MUCB, WMD image-20211115222133822 - `K` : the number of arms, `N`: the number of events, `T`: the observed time - 제안한 BMAB-R이 모든 dataset에서 reward가 우세하였습니다. - MovieLens의 경우 제안한 방법이 TS과 거의 차이가 없었는데 이는 가장 인기있는 다섯개의 아이템이 stationary 하기 때문이라고 주장하였습니다. ================================================ FILE: paper_review/recsys/recsys2021/Cold Start Similar Artists Ranking with Gravity-Inspired Graph Autoencoders.md ================================================ # Cold Start Similar Artists Ranking with Gravity-Inspired Graph Autoencoders - Paper : - Authors : Guillaume Salha-Galvan, Romain Hennequin, Benjamin Chapus, Viet-Anh Tran, Michalis Vazirgiannis - Reviewer : tony.yoo - Topics - [#Real-World_Concerns](../../topics/Real-World%20Concerns.md) - #Cold_Start - #Graph - [#RecSys2021](RecSys2021.md) ## Summary - Directed graph로 정의된 item network에 대해 link prediction task을 수행한 논문입니다. - Directed 기반의 similarity를 구하기 위해 gravity 기반의 매커니즘을 도입하여 단 방향 선호도를 예측 가능하게 만들었습니다. - Cold item (노드 피쳐는 있으나 adjacent 정보가 isolated 된 상황)에 대해 masking과 VAE기반의 구조로 접근하여 성능 향상을 내었습니다. ## Approach ### Gravity-Inspired similiarity ![gravity-inspired-vae-overview](https://user-images.githubusercontent.com/38134957/165449090-f409022d-2da1-440d-87ab-b89a821e17ee.png) $$ \begin{aligned} \hat{A}_{ij} &= \sigma \left( \log \frac{Gm_j}{\Vert z_i - z_j \Vert_2^2} \right)\\ &= \sigma \left( \underbrace{\log Gm_j}_{\text{denoted}~\tilde{m}_j} - \log\Vert z_i - z_j \Vert_2^2 \right) \end{aligned} $$ 즉, VAE기반의 GNN를 태워 얻은 $\tilde{Z} = [Z; \tilde{M}], Z\in \mathbb{R}^{n \times d}, \tilde{M}\in \mathbb{R}^{n }$ 로 similiarity score $\hat{A}_{ij}$를 예측합니다. ### Loss - VAE 기반의 encoding 모델로 GNN을 사용하였습니다. $$ q(\tilde{Z} \vert A, X) = \Pi_{i=1}^n q(\tilde{z}_i\vert A, X) $$ $$ q(\tilde{z}_i \vert A, X) = \mathcal{N}\left( \tilde{z}_i \vert \mu_i, \text{diag}(\sigma_{i}^2)\right) $$ $$ \begin{cases} \mu = GNN_{\mu}(A, X) \\ \sigma = GNN_{\sigma}(A, X) \end{cases} $$ - $P(A)$ 를 최대화하려면 다음의 ELBO를 최대화 하면 됩니다. (jensen's inequality로 증명 가능). $$ \mathcal{L} = \underbrace{E_{q(Z |A,X)} \left[ \log p(A|Z) \right]}_{\text{Reconstruction Loss}} − \underbrace{D_{KL}(q(Z|A,X) \Vert p(Z))}_{\text{Regularization Loss}}, $$ - Reconstruction Loss - $q$ 에 대한 평균을 구하기 어렵기 때문에 $A$ 가 bernoulli distribution을 따른다는 가정 하에 몬테카를로 근사를 이용해서 cross entropy 를 계산합니다. $$ \mathcal{L}_{Reconstruction} = BCE(A, \hat{A}) $$ - Regularization Loss - 둘 사이의 KL divergence를 구해야하는데 $p(z)$ 를 normal distribution이라 가정하면 다음과 같이 계산됩니다. $$ \mathcal{L}_{Regularization} = \frac{1}{2} \sum_d\sum_i^k exp(\sigma_{ii, b}^2) + \mu_{i, b} - \sigma_{ii, b} - 1 $$ ### Cold Start Similiar Items Ranking warm item 수를 $n$, cold item 의 갯수를 $m$ 이라 하면, adjacent matrix $A \in \mathbb{R}^{(n + m) \times (n +m)}$ 에서 cold item의 row는 zero vector로 masking 됩니다. $A$ 를 GNN 기반의 VAE 모델을 통해 다음과 같이 예측할 수 있습니다. 여기서 $\lambda$ 는 influence 와 proxmity사이의 trade off를 튜닝하는 데 사용되며 이는 popularity bias를 control하는 걸 의미합니다. 이렇게 예측된 similairity로 부터 top $k$ 개를 추천하게 됩니다. $$ \hat{A}_{ij} = \sigma \left( \underbrace{\tilde{m}_j}_{\text{influence of j}} -\lambda \underbrace{\log \Vert z_i - z_j\Vert_2^2}_{\text{proximity of i and j}} \right) $$ ### Other Methods - [VGAE](https://arxiv.org/abs/1611.07308): - Undirected graph 에 대해 $\hat{A} = \sigma \left(z_i^{T}z_j\right)$ 를 통해 예측합니다. 다만, 이렇게 계산하면 symmetric 하다는 단점이 존재합니다. - Sour-Targ GVAE: - Directed graph 에 대해 $\hat{A} = \sigma\left( z_i^{(s)T}z_j^{(t)}\right)$, $z^{(s)} = z[:d/2]$, $z^{(t)}=z[d/2:]$. 단, $d$는 짝수이고, 이렇게 계산하면 non-symmetric이 됩니다. ## Results ### Dataset - [Deezer](https://www.deezer.com/soon) 의 24,270 수의 artist 들로 구성 된 directed graph입니다. - Node feature는 56 dimension을 가지며 다음 component들로 구성되어 있습니다. - Genre vector (32-dim) - Country vector (20-dim) - Mood vector (4-dim) - Train, valid, test 는 8:1:1 로 split. Valid와 test의 경우엔 cold 노드들로 구성되어 있기 때문에 neigbor edge는 masking 되어있습니다. ### Metric - Recall, MAP, NDCG를 사용하였습니다. ### Performance ![exp](https://user-images.githubusercontent.com/38134957/165449118-bc1e4374-4dfa-4f80-a779-c4a7175abe7f.png) - Gravity 매커니즘이 큰 폭으로 outperform하였습니다. - Source.-Targ. 버전이 최근 연구에 대해 약간 우위를 보입니다. Non-symmetric 성질을 띈다는 점에 주목할 수 있습니다. Symmetric인 GAE, GVAE는 더 낮은 걸 보았을때 Non-symmetric 방법이 우수함을 의미합니다. - Source.-Targ. 에서 VAE 가 AE보다 좋은 결과를 보였지만, Gravity 버전에서는 반대의 결과를 보였습니다. 상황에 따라 VAE vs AE의 성능이 달라지게 됩니다. #### Mass parameter - 정성적 분석: 왼쪽은 artist별 mass의 크기와 링크 사이를 visualization 한 결과입니다. 빨간색 노드들이 레게 아티스트들 이고, mass가 큰 것 중에 하나를 예로 들은게 레게의 유명한 아티스트 Bob Marley입니다. - 정량적 분석: 오른쪽은 mass (아티스트들) 사이의 여러 measure (popularity, in-degree, page rank) 로 상관관계 분석을 해보았습니다. 결과를 보았을 때, mass가 높다고 measure 값들이 꼭 높은 것은 아니지만 어느정도 상관관계가 있다는것을 보여주었습니다.
#### Impact of attributes - Node feature를 많이 쓸수록 성능이 향상되었습니다. #### Popularity-diversity trade off - $\lambda$ 를 높힐 수록 popular한 item의 rank 빈도가 많아지고, 줄이면 distance에 의한 계산만 하기 때문에 줄어들게 됩니다. ## Conclusion - 그래프 방법론을 이용하여 similar item 추천을 non-symetric한 상황에서 다루어 성능을 향상시킨 논문입니다. - Cold-start 상황에서 masking, VAE 방법론등의 이점을 적용하였습니다. ### Critical view of points - Cold 아이템의 경우 adjacent 정보를 masking (0으로 패딩)하면 모두 동일한 피쳐로 간주되게 됩니다. - Cold start 상황에 대해서만 평가를 진행해보았을 때의 우위 비교가 없어 아쉬웠습니다. - 실험에 사용된 benchmark 모델들은 비교적 최근 논문이 적어서(STAR-GCN, DEAL 빼곤 옛날 논문이라) 아쉬웠습니다. | Model 이름 | 학회 년도 | 인용수 | | ------------------------------------------------------------ | ---------- | ------ | | [DropoutNet](https://www.cs.toronto.edu/~mvolkovs/nips2017_deepcf.pdf) | NIPS 2017 | 104 | | [Graph VAE](https://arxiv.org/abs/1609.02907) | ICLR 2017 | 1,267 | | [STAR-GCN](https://arxiv.org/abs/1905.13129) | IJCAI 2019 | 72 | | [DEAL](https://arxiv.org/abs/2007.08053) | IJCAI 2020 | 11 | ================================================ FILE: paper_review/recsys/recsys2021/Debiased Explainable Pairwise Ranking from Implicit Feedback.md ================================================ # Debiased Explainable Pairwise Ranking from Implicit Feedback - Paper : - Authors : Khalil Damak, Sami Khenissi, Olfa Nasraoui - Reviewer : hee.yoon - Topics - [#Privacy_Fairness_Bias](../../topics/Privacy,%20Fairness,%20Bias.md) - #Matrix_Factorization - #Explainable_Recommendation - [#RecSys2021](RecSys2021.md) ## Summary - 기존 Bayesian Personalized Ranking(BPR) 대비하여 explainability를 늘리고 exposure bias를 잡은 논문입니다. - 기존 BPR 모델은 설명 불가능한 블랙박스 모델이었습니다. -> a novel explainable loss function and a corresponding Matrix Factorization-based model called Explainable Bayesian Personalized Ranking (EBPR) that generates recommendations along with item-based explanations. - 기존 BPR 모델은 Missing Not At Random (MNAR) 데이터 특성 때문에 exposure bias에 취약했었습니다. -> an unbiased estimator for the ideal EBPR loss. ## Approach ### BPR - objective function: ### Explainable BPR - objective function: - E_ui+ (1 - E_ui-) 부분은 (u, i+, i-) 인스턴스의 컨트리뷰션의 비중을 정하는 역할을 합니다. Positive 아이템의 설명력이 높을수록, negative 아이템의 설명력이 낮을수록 학습 기여도가 높습니다. 결과적으로 생성된 추천결과의 상위 아이템들은 더 높은 설명력을 가질 것이라고 기대할 수 있습니다. - For instance, in the extreme case where either the positive item is not explainable at all or the negative item is completely explainable, the update equation is zeroed out. Hence, no contribution will come from the corresponding instance to the learning. This is reasonable and desirable since the aforementioned case depicts a non explainable preference, where either the positive item is not explainable or the negative item is explainable. Either case undermines the explainability of the preference. (설명가능하지 않은 아이템을 소비한 것은 학습에 포함이 안됩니다. 아래 E_ui 정의를 참고하면, 유저가 소비한 아이템의 이웃 아이템을 유저가 소비한 이력이 없으면 학습에 포함이 안됩니다.) - explainability matrix: - E_ui = items the user interacted from the neighboring items / len(neighboring items) - 이웃한 아이템 중에서 해당 유저와의 인터랙션이 발생한 아이템의 비중입니다. - similarity의 계산: 별도의 데이터가 아닌, rating 메트릭스 기반으로 cosine similarity를 계산합니다. - for a specific item, the more neighboring items a given user has interacted with, the higher the explainability of that item will be to this user. - 학습 시작 전, 미리 계산하는 방식입니다. - - - neighborhood size - - 추천 결과 서빙시 explainability 기반으로 해석된 결과를 제공 가능합니다. (참조 논문에서 언급한 방식) - 참조 논문(Using Explainability for Constrained Matrix Factorization): - item 기반 explainability 사용시: - - user 기반 explainability 사용시: - ### Unbiased Explainable BPR (UEBPR) - objective function: - - 가정 - - Y_u,i: user 가 item 과 인터렉션을 했는지 여부 (예: 클릭 여부) = 노출이 되고, 관련성도 있다 - O_u,i: user 에게 item 이 노출됐는지 여부 - - R_u,i: user 에게 item 이 관련성이 있는지 여부 - - #### Unbiased BPR Loss (UBPR) - objective function: #### Ideal Explainable BPR - objective function: #### Partially Unbiased Explainable BPR (pUEBPR) - objective function: ## Results ================================================ FILE: paper_review/recsys/recsys2021/Evaluating Off-Policy Evaluation- Sensitivity and Robustness.md ================================================ # Evaluating Off-Policy Evaluation- Sensitivity and Robustness - Paper : - Authors : Yuta Saito, Takuma Udagawa, Haruka Kiyohara, Kazuki Mogi, Yusuke Narita, Kei Tateno - Reviewer : iggy.ll - Topics - [#Metrics_and_Evaluation](../../topics/Metrics%20and%20Evaluation.md) - [#RecSys2021](RecSys2021.md) ## Summary - 이 논문의 목표는 online에 올려보지 않고 모델을 평가하는 것입니다. ![image](https://user-images.githubusercontent.com/38134957/165455983-1bb220ad-6dfd-4a13-8289-acb2cd085277.png) - 모델: 유저가 페이지에 접속했을 때, 유저의 정보, 시간 정보 등을 활용해 A안/B안/C안 중 어떤게 나을 지 확률적으로 결정합니다. e.g., [0.4, 0.3, 0,3] ![image](https://user-images.githubusercontent.com/38134957/165455992-47c46f81-78d5-4adb-adde-5324939f8ed3.png) - context x: 유저가 접속한 시간, 유저 정보 등. - action: 보여준 페이지 레이아웃 - reward:유저가 클릭했거나 안 했거나, 우리가 보여준 레이아웃에 따른 유저의 행동 결과(숫자) 여기서 문제는 $p(r_i...)$를 알 수가 없다는 점과, 모델이 아이템을 선택해서 보여주어야 그에 대한 결과를 만들 수 있다는 점이 있습니다. ## Approach Off Policy Evaluation은 두 가지 분류로 나눌 수 있습니다. 1. Direct Method (DM): mean reward 자체를 estimate하는 방법 2. Inverse Propensity Weight (IPW), SNIPW: logging policy, or base policy의 log를 요구하는 방법 그리고 저 두 가지 방법을 함께 사용하는 방법들도 있습니다.: DR, SNDR, Switch-DR, DRos DM은 모델을 하나 더 만들어야 하기 때문에, 이 모델에 관한 하이퍼패러미터를 또 신경써주어야 합니다. ![image](https://user-images.githubusercontent.com/38134957/165455998-662b684f-72fb-4243-b7ad-dfa4b279b2b6.png) ## Conclusion - mean reward를 estimate하기 어렵기 때문에 계열의 방법은 사용하지 않는게 좋을 것 같습니다. - SNIPW가 일반적으로 가장 괜찮았습니다. (적절히 Calibration해줄 수 있다면 IPW를 써도 괜찮을 것 같습니다.) - 적절히 Calibration해줄 수 있다면 logging policy를 estimate한 값으로 (logging policy를 따라하도록 다른 모델을 학습해서) 사용해도 나쁘지 않아 보입니다. - 이건 조금 이상한게, logging policy를 이미 갖고 있으면 이를 사용하지 왜 다른 estimator를 더 만들어야 하는지는 잘 모르겠습니다. ![image](https://user-images.githubusercontent.com/38134957/165456009-7fd20f91-122e-43fd-b3a3-105809c1cfa4.png) ================================================ FILE: paper_review/recsys/recsys2021/Follow the guides- disentangling human and algorithmic curation in online music consumption.md ================================================ # Follow the guides- disentangling human and algorithmic curation in online music consumption - Paper : - Authors : Quentin Villermet, Jérémie Poiroux, Manuel Moussallam, Thomas Louail, Camille Roth - Reviewer : jinny.kk - Topics - [#Applications-Driven_Advances](../../topics/Applications-Driven%20Advances.md) - #Music_Recommendation - [#RecSys2021](RecSys2021.md) ## Summary - Contribution 1. algorithmic guidance에 대한 유저의 태도에 따라 유저군을 선분류하고 각 유저군별로 나눠서 콘텐츠 소비 방식을 분석하였습니다. - “추천”이라는 개입이 유저의 소비 컨텐츠 다양성에 어떤 영향을 끼치는가는 논란이 많은 뜨거운 감자였다. 기존 연구들의 대부분은 유저들을 뭉뚱그려서 혹은 binary category (성별, 나이)로 나누어서 결과를 분석했는데 이 논문의 저자들은 유저가 플랫폼을 사용하는 타입별로 그 영향이 다르게 나타나므로 유저들의 그룹을 access mode에 따라 구분해서 영향을 분석하였습니다. 2. platform recommendation을 algorithmic 과 editorial로 나눠서 살펴보았습니다. 3. platform recommendation과 offline radio recommendation 간의 관계를 살펴보았습니다. - Key Observations - 음악 플랫폼에서 유저들이 음악을 주로 소비하는 경로 access mode (organic, algorithmic, editorial)에 따라 네 가지 유저그룹으로 (a, e, o, o+) 나누고, 유저들이 소비하는 음악의 다양성 (두 가지 디멘션: dispersion & artist popularity)을 유저 그룹별로 복합적으로 분석한 논문입니다. (그래서 정리하면서 좀 헷갈림...) - 소비의 diversity를 두 가지 디멘션에서 보았는데, 유저가 총 소비한 곡들 중 unique 곡들의 비중 측면 (dispersion)과 유저가 소비하는 음악의 아티스트의 인기도 측면 (popularity)입니다. - dispersion 측면에선 - very organic users 보다 어떤 형태로든지 추천을 사용하는 유저들의 dispersion 값이 높았고, - 각각의 유저 클래스에서 각자의 main access mode를 통한 소비의 dispersion이 낮았습니다 (=그쪽에서 exploitation이 일어나는 것을 관찰하였습니다.) - (오프라인 vs 플랫폼) 라디오 프로그램들의 플레이리스트 dispersion < 온라인 플랫폼 내 대부분 유저들의 소비 dispersion - artist popularity 측면에선 - algorithmic user들은 인기 있는 곡을 under-consume했고 editorial user들은 인기 있는 곡을 over consume하는 모습을 보였으며, - 모든 유저 클래스에 대해서 공통적으로 대체로 algorithmic access mode를 통해서는 덜 인기있는 곡들이, editorial access mode를 통해서는 인기 있는 곡들이 소비되는 경향이 보였습니다. - (오프라인 vs 플랫폼) 라디오 플레이리스트나 온라인 플랫폼 유저들이나 곡들의 평균 popularity는 비슷비슷했습니다. - 그리고 dispersion과 artist popularity간에 mild correlation도 관찰되었습니다. ## Results ### Dataset - Deezer (프랑스 음악 스트리밍 플랫폼) 2019년 1년동안 8639명의 구독자들의 play history (총 51m 개) (어떤 유저가 어떤 가수의 어떤 노래를 몇 분간 들었는지) + 노래에 접근한 경로 (access mode) (직접 검색, 추천 등) - 동일 기간동안 프랑스의 라디오 방송국 39곳의 플레이리스트 히스토리를 사용하였습니다. ### User Practices #### Modes of access and user behavior classes - Three types of content access mode - organic (self-selected) - algorithmic (suggested by recommendation engine) - editorial (human curation) - 유저의 플레이 히스토리에서 각각의 access mode의 비율 (Pa (algorithmic), Pe (editorial), Po (organic))에 따라 유저 클래스를 4가지로 분류함. - `fig 1` 에 나타나듯 대부분의 유저가 organic mode 에 많이 의존하고 있긴 한데 - 그럼에도 불구하고 구분이 가능하긴 하고 k means를 통해 `user class`을 4가지로 나누었습니다. - a (989명), e (655명), o (1614명), o+ (5381명) - 각 유저 클래스별로 number of plays의 분포는 비슷했습니다 (= 모든 클래스에는 active한 유저 덜 active한 유저가 모두 있습니다. 평균 activity는 e 유저 클래스에서 다소 낮긴 했습니다) (`fig 1 - right`) #### Two dimensions of diversity - dispersion: (functional diversity - denoting the lack of redundancy in the listening history) - 정의 = S (number of unique songs) / P (number of plays) - `fig 2 - left` - 각 유저 클래스별로 linear model을 fit해서 경향성을 보았더니 모든 유저 클래스에서 activity (P) 와 dispersion은 inverse relationship을 보였습니다. - 하지만 동일 P에 대해선, o+ 인 유저들이 가장 낮은 dispersion을 보였습니다. 즉, algorithmic이든 editorial이든 어떤 형태로든 플랫폼의 추천 모드를 활용하는 유저군들에서 dispersion 값이 더 높게 나타났습니다. - o+ 유저들은 플랫폼을 “digital librarian”이 아니라 “digital library”로 사용하는 것이라고 표현하였습니다. - “even a moderate use of some form of recommendation is generally associated with a higher level of exploration.”라고 해석하였습니다. - `fig 3` - 각 유저 클래스에서 각 access mode 별로 dispersion 값들을 확인했는데 모든 유저 클래스에 대해 각 클래스가 중점적으로 사용하는 access mode에서의 dispersion 값이 낮았다. 예를 들어 algorithmic 유저 클래스에선 alogrithmic access mode에서 dispersion이 낮고 이랬다. - “Users tend to prioritize exploitation in their preferred mode of access, and favor exploration in the others, in terms of more dispersed plays.” - artist popularity (semantic diversity - denoting the tilt toward songs by more popular artists.) - 정의 = 그 아티스트의 곡들의 재생 횟수를 바탕으로 아티스트들을 4개의 인기도 구간으로 나눔 (각 인기도 구간의 재생 횟수 합이 비슷하게 되도록) - 인기도 구간: (높은 인기도) v1 - v2 - v3 - v4 (낮은 인기도) - `Table 2` - 곡들은 아티스트의 인기도에 상관없이 대부분 organic access mode를 통해 소비되는 비중이 가장 높았다. - algorithmic access mode는 중간 인기도의 곡들을 주로 소비하는 통로가 됨을 알 수 있고, editorial access mode는 높은 인기도의 곡들의 비중이 많음. organic은 제일 인기 있거나 제일 인기 낮은 곡들의 비중이 많음. - `fig 4 -left` - artist popularity와 dispersion이 서로 연관이 되어 있다. 인기도 낮은 아티스트 곡 소비하는 (x축 우측) 유저들의 dispersion 값이 더 높더라 (y축). #### User types and access mode biases - user type, access mode, diversity가 어떻게 상호 작용을 하는지 “disentangle”한 그래프가 `fig 5.` 그래프의 y축이 완전히 이해 가는 것은 아님. - 각 유저 타입별로 소비하는 곡들의 인기도 경향성이 어떻게 되는지를 보여준 건데, access mode에 따라 세분화한 게 밑에 있는 그림. - `fig 5 - top` : algorithmic users under-consume popular artists, editorial users over-consume popular artists, organic users favor less popular artists in monotonous manner, and very organic users 는 인기도 양 극단에서의 소비가 “약간 더” 많다. (그림에서 잘 보이지 않기는 하는 듯..) - `fig 5 - bottom` : 유저 타입 구분 없이 모두 전반적으로, algorithmic access로 덜 유명한 아티스트 곡 소비가 되고 editorial access는 인기 있는 아티스트 곡 소비로 치우치고 organic은 그 사이 어디쯤을 보여주는 것으로 해석함. ### The diversity of human-assisted guidance - 바로 위에서 관찰한 것 중에서, algorithm으로는 덜 유명한 곡 소비를, editor들은 유명한 곡 소비를 이끌어내는 경향성이 보인다는 점이 있는데, 이를 좀더 확인하기 위해 전통적인 오프라인의 editorial 추천이라고 볼 수 있는 라디오 프로그램 플레이리스트를 분석했다. - `fig 6 - left` - 대부분의 user type이 라디오 프로그램들보다 높은 dispersion을 보여줬다. 즉 라디오 프로그램은 보다 제한적인 카탈로그에서의 exploitation으로 기울어져 있다는 이야기. - 그리고 색깔 그라데이션 보면 알 수 있듯, dispersion과 popularity의 mild correlation도 볼 수 있다. - `fig 6 - right`: 대부분의 user type이 중간 부근에 있다. 즉 해석하면 “while online music listening practices seem to foster functional diversity (dispersion), in terms of semantic diversity (popularity) they seem, on average, to be neither significantly above nor significantly below the mass of the radios we focus on.” ### Concluding Remarks - future work로 언급하는 것들 - “the chronology of access modes to a song probably carries valuable information.” (특정 곡이 어떤 access mode를 통해 최초 발견되었는가.) - “user trajectories and transitions between classes” ## Conclusion - 우리의 경우도 비즈니스 로직이 항상 끼어 들어가서 human curation에 의한 것과 알고리즘에 의한 것이 복합적으로 섞여 있는 경우가 많은 것 같아서 공감이 되었다. 몇 가지 디테일들은 잘 이해 못 한 것도 있는데, 나름 흥미로운 논문이었다. - (diversity를 functional diversity (number of unique songs played / total number of plays) 와 semantic diversity (popularity) 로 나누고, semantic diversity를 보기 위해 왜 embedding space를 사용한 diversity가 아니라 인기도를 보았는지를 기술했는데, 그 이유가 잘 이해가 안 갔다.) - primary access mode 별로 유저들을 분류하고, 각 access mode 별로 소비하는 음악의 다양성이 어떻게 달라지는지 분석하고, 알고리즘이든 사람이든 큐레이션을 이용하는 유저집단이 좀더 다양한 소비를 한다는 분석 내용이 인상적이었다. - 기존의 filter bubble 효과를 주장한 논문들과는 달리 이 논문에선 오히려 추천 알고리즘을 이용하는 유저군에서 다양성 수치가 높게 나왔다는 점이 의외였고 추천 알고리즘에 의해 filter bubble에 갇힌다가 myth일 수도 있겠다는 생각이 들었다. 문제는 이 논문이 사용한 데이터셋인 Deezer 음악 플랫폼이 사용하는 추천 알고리즘이 무엇인지에 대한 설명이 없다는 점이다. 추천 알고리즘과 filter bubble에 대해 상반된 결론을 내리는 논문들을 다 모아놓고 리뷰해보면 어떨지. ================================================ FILE: paper_review/recsys/recsys2021/I want to break free! Recommending friends from outside the echo chamber.md ================================================ # I want to break free! Recommending friends from outside the echo chamber - Paper : - Authors : Antonela Tommasel, Juan Manuel Rodriguez, Daniela Godoy - Reviewer : iggy.ll - Topics - [#Echo_Chambers_and_Filter_Bubbles](../../topics/Echo%20Chambers%20and%20Filter%20Bubbles.md) - [#RecSys2021](RecSys2021.md) ## Summary - 논문에서 제안하는 GNN 모델에서는 사실 별로 특별히 느끼는 점이 없었습니다. - Echo chamber로 인해 나타날 것이라 생각이 드는 현상이나 가설을 실험으로 잘 재현한다음 풀어내는데, 이게 정말 잘 된 것 같아서 공유합니다. ## Approach ### 친구 추천 유저 집합 U, 아이템 집합 I가 존재한다고 가정하자. 기존의 추천이 다루는 것은 다음과 같습니다. 1. p(r_{ui}\vert u \in U, i \in I) (연관추천) 2. \text{sim}(i \in I, j \in I) (아이템추천) 친구 추천은 p(r_{uv}|u \in U, v \in U)을 푸는 것이 목표입니다. 기존의 데이터는 주로 - 유저-아이템 인터랙션 (u, i, c) where u \in U and i \in I, and c is context w.r.t. user-item relationship. 이런 형태의 데이터가 주어지는데, 친구 추천에서는 다음과 같은 데이터가 새롭게 주어집니다. - 유저-유저 인터랙션 (u, v, c) where u, v \in U, and c is context user-user relationship 그리고 기존의 (u, i, c)가 존재하지 않을 수도 있고, 추천 팀이 담당하는 서비스 중에서는 `mm에서의 친구 추천`이 친구 추천을 요구하는 영역 중 하나입니다. `친구 추천`을 다루는 추천 영역이 지금은 많지 않지만, 지금까지는 이런 문제에 그리 큰 관심이 없었던가, 기존 연관 추천/아이템 추천 문제로 캐스팅해서 풀고 있었던 것 같습니다. 친구 추천이 가진 특성을 활용해서, 연관/아이템 추천을 방법보다 더 좋은 성과를 낼 수 있다면 팀 내에서, 그리고 회사 내의 서비스에 적용할 만한 요소는 많을 것 같습니다. ### (가정) Relevancy보다 Diversity가 더 중요하다. 논문 내에서 암묵적으로 가정하고 있는 것들을 정리해보면 이렇습니다. 친구 관계 그래프에서는 일반적으로 유저들은 작은 그룹(클러스터)로 묶일 수 있고, 유저-유저 인터랙션은 대부분 이 클러스터 안에서 이뤄지고, 또한 한 클러스터 내의 유저들의 아이템 소비 패턴도 유사합니다. 이를 고려하지 않는 추천 시스템이 일반적으로 이 커뮤니티 내부에서만 추천을 만드는 경향이 있습니다. 이를테면, MF 모델을 사용한다면 (클러스터가 완벽히 분리된다고 가정한다면) 큰 interaction matrix M은 사실 다음과 같이 분해될 수 있습니다. $$ M \simeq \begin{bmatrix}M_1 & 0 & 0 \\0 & M_2& 0 \\ 0 & 0 & M_3 \end{bmatrix} $$ 이러한 matrix에 대해 MF 모델은 사실 많은 MF 모델 여러 개를 만드는 것과 유사한 효과를 만듭니다. 또한, 클러스터 밖의 추천/유사도 비교를 힘들게 만듭니다. 따라서, 모델은 클러스터 내부의 유저와 그 유저들이 소비하는 아이템 이외의 추천을 생성하지 않으며, 이 효과는 추천 시스템이 deploy될 수록 고착화된다고 볼 수 있고, 이는 서비스/지표에 해롭습니다. 따라서 Diversity나 Novelty를 고려한 평가가 이뤄져야 한다는 것이 이 논문의 주장인 것 같습니다. 이 가정이 설득력이 있다는 생각은 들긴 하는데, 논문에서 자세한 근거를 제시하지는 않았습니다. ================================================ FILE: paper_review/recsys/recsys2021/Local Factor Models for Large-Scale Inductive Recommendation.md ================================================ # Local Factor Models for Large-Scale Inductive Recommendation - Paper : - Authors : Longqi Yang, Tobias Schnabel, Paul N. Bennett, Susan Dumais - Reviewer : bell.park - Topics - [#Scalable_Performance](../../topics/Scalable%20Performance.md) - #Local_Model - [#RecSys2021](RecSys2021.md) ## Summary - User-Item co-clustering을 사용해서 Local Model의 개수를 늘릴 수 있도록 추천 모델을 디자인한 논문입니다. - User 기준 inductive 상황에서도 모델이 추천 결과를 계산할 수 있도록, item에 대해서만 embedding 을 학습하였습니다. - 추천 성능도 기존 local model, global model 모두에 대해서 개선이 되었습니다. - 그런데, 이걸 local model이라고 부를 수 있는 구조인지 의문이 들었습니다. ## Approach ### 문제 인식 - Local Model은 user subgroup에 대해서만 추천을 하는 모델을 여러개 만들어, subgroup 마다 다른 모델로 추천을 하는 방식입니다. - User subgroup마다 소비 취향이 다를 것이다라는 가정이 있고, 여러 선행 연구에서 괜찮은 접근임이 이미 검증되었습니다. - User subgroup마다 모델을 만들어야 해서, 모델이 무겁다면 subgroup 개수에 제한이 생깁니다. - 선행 연구에서는 대부분 40-50개 수준이고 100개 정도 쓰는 모델(rGLSVD)은 파라미터가 10억개나 됩니다. - Subgroup을 나누는 단계와 Subgroup의 추천을 계산하는 단계가 나뉘어 있고 이로 인해 inductive 상황에서 추천이 어렵습니다. - Subgroup을 나누는 것도 학습이 필요한데, 선행 연구 대부분이 이걸 inductive 상황에서 못하는 모델입니다. (factorization) ### 제안 모델 - 이 논문에서는 User representation을 소비한 item의 embedding으로 표현하였습니다. (Fig1에서 (b)) - item embedding을 N-head self-attention을 돌려서 N 차원 벡터로 표현하였습니다. - Differentiable Latent Co-Clustering에 User representation, Item representation을 넣어서 학습하였습니다. (Fig1에서 (c)) - 이름이 거창하긴 하지만 실제로는 ReLU activation 이후, Min-Sum pooling이 전부입니다. - ReLU 가 negative score를 제거, 클러스터 멤버십 기능을 하게 됩니다. - 학습은 선행 연구(VAE-CF) 따라서 Softmax loss로 학습하였습니다. - 클러스터 개수는 512개에서 2048개까지 늘려보았다고 합니다. ![image](https://user-images.githubusercontent.com/38134957/165453119-86f76cbe-a56d-4fb5-b5eb-548e35e49394.png) ## Results ![image](https://user-images.githubusercontent.com/38134957/165453125-67be3ed8-fe00-46dd-a645-b3ec4c7b52b2.png) - 기존 모델들 대비 성능이 소폭 좋긴한데, 큰 차이는 아닙니다. ![image](https://user-images.githubusercontent.com/38134957/165453135-058c39a8-67d8-4174-b41e-21aae392bc14.png) - 같은 성능을 더 적은 파라미터로 만들었다는데에 의의가 있습니다. ![image](https://user-images.githubusercontent.com/38134957/165453142-8e4006b4-1db4-4b96-b07d-5927f9ac7e62.png) - 클러스터 개수를 늘리면 당연하게도 성능이 추천 증가하게 됩니다. ================================================ FILE: paper_review/recsys/recsys2021/Matrix Factorization for Collaborative Filtering Is Just Solving an Adjoint Latent Dirichlet Allocation Model After All.md ================================================ # Matrix Factorization for Collaborative Filtering Is Just Solving an Adjoint Latent Dirichlet Allocation Model After All - Paper : - Authors : Florian Wilhelm - Reviewer : tony.yoo - Topics - [#Theory_and_Practice](../../topics/Theory%20and%20Practice.md) - #Matrix_Factorization - [#RecSys2021](RecSys2021.md) ## Summary - Matrix Factorization 문제를 Latent Dirichlet Allocation 으로 접근하여 interpretability를 향상시켰습니다. - 추천시트템에 맞게 Bias term을 추가(기존 단점 개선)한 LDA4Rec 을 제안하여 Classic LDA 대비 성능 향상이 있었습니다. - LDA4Rec의 rating 예측으로 MF, NMF(Non-negative MF), SNMF(Semi-NMP)의 personalized ranking 처럼 사용 할 수 있다는 걸 증명하였습니다. (증명 관점에서는 다루지 않겠습니다.) ## Approach ### Matrix Factorization User, item 에 대한 latent vector 에 item에 대한 bias 가 있는 MF를 벤치마킹하였습니다. $$ \hat{x} = < \mathbf{x}_u , \mathbf{h}_i > + b_i $$ ### LDA Approach 아래의 [Probabilistic Graph Model, PGM](https://en.wikipedia.org/wiki/Graphical_model) 을 보면, 관측되는 $i_{us}$ 를 이용하여 다른 변수들을 [EM algorithm](https://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm) 을 통해 unsupervised 방법으로 학습해나가게 됩니다. (기존 모델은 [smoothed LDA](https://www.jmlr.org/papers/volume3/blei03a/blei03a.pdf)) | 기존 | 변형 | | ------------------------------------------------------------ | ------------------------------------------------------------ | | image-20220111110340092 | LDA4Rec | Notation: $\boldsymbol{\varphi}_k \in \mathbb{R}^{\vert \mathcal{I} \vert}$, $\boldsymbol{\theta}_u \in \mathbb{R}^{\mathcal{\vert K \vert}}$ (보충: $\mathbf{c} \in \mathbb{R}^{\vert \mathcal{I} \vert}$) $$ \begin{align} \delta_i &\sim LogNormal(\mu_\delta, \sigma_\delta) \\ z_{us} &\sim Categorical(\boldsymbol{\theta}_u) \\ i_{us} &\sim p(i_{us} \vert \boldsymbol{\varphi}_{z_{us}}, \delta_i, \lambda_i) \\ p(i_{us} &\vert \boldsymbol{\varphi}_{z_{us}}, \delta_i, \lambda_i) := Categorical(\Vert \mathbf{c} \Vert_1^{-1}\mathbf{c}) \\ \mathbf{c} &= \boldsymbol{\varphi}_{z_{us}} + \lambda_u \cdot \boldsymbol{\delta} \end{align} $$ ## Results ### Datasets - Split: train(90%), valid(5%), test(5%) - The explicit feedback of these datasets was treated as implicit. | Movielens-1M, MoiveLens-100K | Goodbooks | | - | - | | 1 million movie ratings across 6,040 users and 3,706 movies
100 thousand interactions across 610 users and 9,724 movies | 6 million interactions across 53,425 users and 10,001 books | **Note**: LDA4Rec의 evaluation 과정에서 rating 예측을 item 하나씩 해야하기 때문에 유저당 10000개씩만 샘플링 하여 측정하였습니다. > The bottleneck of LDA4Rec is the prediction of the personalized rankings for which we need a high number of samples per user to compute a stable ranking. Thus for each user 10,000 items were sampled. ### Performance - MoiveLens-100K 에서 성능 향상이 있었습니다. ex1 아쉽게도 Goodbooks에서 LDA4Rec 비교가 빠져 있지만, MF가 SNMF 보다 성능 면에서는 우수했습니다. ex2 ## Conclusion - Traditional LDA 를 the popularity of items 과 conformity of user를 통합하여 성능 향상을 이끌어 내었습니다. - MF의 personalized ranking과 NMF, SNMF, LDA4Rec의 personalized ranking으로 transformable하다는 걸 증명하였습니다. - (MF대비) accuracy의 큰 손실 없이 interpretability를 높혔습니다. ### Question & View - Q. Item에 대한 user의 bias로 접근하였는데, 굳이 종속적인 방법으로 할 필요가 있을까? - Evalutaion 이 느리다는 단점 때문에 실용면에서 떨어집니다. - Q. Latent representation의 most_similar 값으로 추천을 하면 성능이 어떨까? - Accuracy 손실이 적다고 했는데, 데이터 셋 향샹을 보인건 겨우 movielen-100K 뿐입니다. - Q. MRR과 recall은 높지만, precision이 좀 떨어지는 걸로 봐서 implicit nDCG 측정이 있었다면 어땠을까? ================================================ FILE: paper_review/recsys/recsys2021/Mitigating Confounding Bias in Recommendation via Information Bottleneck.md ================================================ # Mitigating Confounding Bias in Recommendation via Information Bottleneck - Paper : - Authors : Dugang Liu, Pengxiang Cheng, Hong Zhu, Zhenhua Dong, Xiuqiang He, Weike Pan, Zhong Ming - Reviewer : charlie.cs - Topics - [#Privacy_Fairness_Bias](../../topics/Privacy,%20Fairness,%20Bias.md) - #Bias - [#RecSys2021](RecSys2021.md) ## Summary - 추천 시스템에서 수집한 feedback 데이터의 bias를 효율적으로 완화(alleviate)할 수 있는 debiased information bottleneck (DIB) objective function을 제시하였습니다. - 제시된 DIB objective function은 intractable 한데, 이를 information theory에 기반하여 tractable 한 solution으로 derive할 수 있었습니다. - 기존 추천 시스템에서 debiased를 위한 대부분의 방법들은 bias generation process를 고려하지 않았기 때문에 특정 bias 가 발생하는 현상에서만 적용할 수 있는 문제가 있었습니다. - Related works: (1) heuristic-based (2) inverse propensity score-based (3) unbiased data augmentation (4) some theoretical tools-based - 해당 논문에서는 confounding bias 라는 포괄적 형태의 bias를 정의하고, 이 bias를 완화하는 것에 초점을 두었습니다. ## Approach ### Confounding Bias ![image](https://s2.loli.net/2022/01/11/wOSW7EnrHGF3CuR.png) - 일반적인 추천 시스템의 feedback event 생성 process는 Figure 1.(a)와 같습니다. - variable (the feature vector) `x`는 다음과 같은 세개의 변수로 구성되어 있다고 가정 - Instrumental variables `I`, Confounder variables `C`, Adjustment variables `A` - 세 변수 중 `I`와 `C`는 treatment `T` 를 결정하고, 이는 outcome `y`에 간접적으로 영향을 미침 - `T`는 시스템이 추천할 아이템을 선택하거나 아이템들을 rank 하는 과정을 의미하고, `y`는 추천 결과 (e.g. click) - 이 부분에서 position bias, popularity bias와 같은 다양한 bias가 feedback에 영향을 줌 - `C` 와 `A`는 직접적으로 `y` 에 영향을 미침 - unbiased feedback이 생성됨 - 세 변수에 대한 구체적인 정의는 없지만, site된 논문(*Learning disentangled representations for counterfactual regression, ICLR 2020*)에서 예시를 통해 어느정도 이해할 수 있었음 - 어떤 환자에 대한 context `x`를 기반으로 치료 방법 `T`를 정하고, 치료에 따른 결과 `y`가 있다고 가정 - `I`는 환자의 재정 상태를 나타낼 수 있음: 부자면 높은 수준의 치료를 받거나 가난하면 저렴한 치료를 받아야 한다. 다만, 이것이 직접적으로 치료 결과에 영향을 미치진 않음 - `C` 는 환자의 나이를 나타낼 수 있음: 나이에 따라 어떤 치료를 받는지도 결정되고, 나이가 치료 결과에 직접적인 영향을 미침 - `A`는 환자의 유전적 정보를 나타낼 수 있음: 유전적 정보를 가지고 어떤 치료를 받을지는 일반적으로 고려하진 않지만, 이것이 치료 결과에 직접적인 영향을 미침 - Confounding bias는 특정 bias들의 collection을 나타내며, 추천 시스템에서 간접적인 영향으로 인해 발생하는 the confusion of the observed feedback을 의미하게 됩니다. - 쉽게 말하면 Figure 1.(a) 와 1.(b)의 차이가 confounding bias - Figure 1.(b)는 `x`를 고려하지 않은 추천이므로, uniform random 추천을 생각할 수 있습니다. ### The proposed method: DIB objective function ![image](https://s2.loli.net/2022/01/11/AMLDoOWieNzfFnp.png) - 이 논문에서는 위에서 언급한 confounding bias가 embedding representation에 반영된다고 가정하고, embedding vector에 포함된 biased component `r`과 unbiased component `z`를 각각 학습 후, 실제 추천을 진행할 때는 `z`로만 구성된 feature vector로 treatment `T`를 선택하는 방향을 제시하였습니다. - `r`과 `z`를 제대로 학습하기 위해서는 다음과 같은 조건들을 만족해야 합니다. 1. biased된 변수의 영향을 줄이기 위해서 `z` 가 `x`에 대해 overfit 되면 안됩니다. 2. `z`는 label `y`를 정확하게 예측할 수 있도록 학습합니다. (direct effect 최대화) 3. `r`과 `z` 는 가능한 독립이어야 합니다. (to get a better distinction) 4. `r` 도 (`z` 정도 까지는 아니지만) `y` 를 예측할 수 있도록 학습합니다. (indirect effect) - 위와 같은 네 가지 조건을 만족하기 위해 다음과 같은 DIB objective function을 최소화 하는 방향으로 학습합니다. ![image](https://s2.loli.net/2022/01/11/t4miVPOTF3BjWwc.png) - `I(z;x)` 는 `x`와 `z`의 mutual information을 나타냅니다. - 이 함수는 최적화 하기에는 intractable 하므로, information theory에 기반하여 다음과 같이 conditional entropy 형태로 표현할 수 있습니다. ![image](https://s2.loli.net/2022/01/11/3HfXnKrsVFodJlw.png) - (a)는 `y`와 `y_z`간 cross entropy, (b)는 `y` 와 `y_r` 간 cross entropy, (c)는 `y`와 `y_{z,r}` 간 cross entropy - 여기서 `y_z`는 unbiased component `z`를 사용해서 생성된 label 이고, `y_r` 과 `y_{z,r}` 도 비슷한 맥락으로 생성된 label - (d)는 embedding representation의 robustness를 추가하기 위한 regularization term - variational approximation을 활용하여 `z`는 Gaussian 분포를 따른다고 가정했습니다. ### Complement optimization process of DIB ![image](https://s2.loli.net/2022/01/11/TiRa7SY62OHDKdX.png) ## Results - 기존의 추천 모델 Matrix Factorization (MF)과 neural collaborative filtering (NCF)에 DIB를 적용하여 학습했을 때, 상대적으로 어느정도의 성능 향상이 있는지 실험하였습니다. - 측정 metrics: AUC, precision (P@K), recall (R@K), 그리고 nDCG(@50) - 두 개의 dataset을 사용: Yahoo! R3, Product - Yahoo! R3: 15,400 명 사용자의 1,000개 곡에 대한 ratings - Product: 300,000 명 사용자의 122개 광고에 대한 click records - test를 위해 unbiased 데이터를 확보해야 하는데, 이를 위해 일정 유저 군에게 랜덤 추천을 진행했다고 합니다. - Baselines - MF, NCF (classic reco models) / IPS, SNIPS (IPS-based) / AT, Rel, CVIB (theoretical tools-based) ### MF ![image](https://s2.loli.net/2022/01/11/CD2OhbjpTRe3ukA.png) - 제안한 DIB-MF가 가장 높은 성능을 보였습니다. - dataset 사이즈가 커질수록 상대적으로 높은 성능을 보였습니다. ### NCF ![image](https://s2.loli.net/2022/01/11/LGXFpr7stONHVjd.png) - metric@K 가 높을수록 좋은 성능을 보였습니다. ================================================ FILE: paper_review/recsys/recsys2021/Negative Interactions for Improved Collaborative Filtering- Don’t go Deeper, go Higher.md ================================================ # Negative Interactions for Improved Collaborative Filtering- Don’t go Deeper, go Higher - Paper : - Authors : Harald Steck, Dawen Liang - Reviewer : marv.20 - Topics - [#Theory_and_Practice](../../topics/Theory%20and%20Practice.md) - #Netflix - #High-Order_Interactions - [#RecSys2021](RecSys2021.md) ## Summary - Collaborative Filtering 모델에서 higher-order interaction을 어떻게 할 것인지에 대한 방법론을 새롭게 제안하고 있습니다. - Linear full-rank model을 통해 higher-order interaction을 넣을 수 있게 하였고, 그 결과 큰 데이터셋에서 딥러닝 기반 방법론들보다 좋은 성능을 보였습니다. ## Approach 이 논문이 다루는 모델은 SLIM -> EASE(Embarrassingly Shallow AutoEncoder) -> Pair(this paper) 순으로 발전시켰습니다. EASE와 이 논문에서 제안한 Pair만 보면 다음과 같습니다. ### EASE - - hidden layer가 없는 autoencoder 모델입니다. 파라미터는 item-item weight matrix $B$입니다. objective는 다음과 같습니다. 이 때 X는 interaction matrix, F는 Frobenius norm을 의미합니다. ![image](https://user-images.githubusercontent.com/38134957/165149044-ef3a3166-7cf8-4f72-a7e4-a0f62376bd15.png) - solution은 다음과 같습니다. ![image](https://user-images.githubusercontent.com/38134957/165149050-9ad54dd4-a2e0-4f84-a84a-274f0beae18b.png) ### Pair (this paper) - Relation의 용어에 대한 설명은 다음과 같습니다. - pairwise($B_{ij}$ ) : 유저가 item i를 소비하였을 때, item j 의 선호 예측값을 의미합니다. 따라서 유저가 i랑 k를 소비 한다면, item j에 대한 선호도 예측값은 가 됩니다. - triplet : $(i, k, j)$는 위 정보를 바로 반영합니다. 유저가 i, k를 소비하였을 때 item j에 대한 선호도 예측값을 의미합 니다. - EASE 구조에 higher-order matrix를 추가한 간단한 extension입니다. EASE에서 학습하는 파라미터 은 각각의 의 미가 item i와 item j의 pairwise한 관계를 캡쳐한다고 볼수 있습니다. 따라서 유저가 i와 k 2개의 아이템을 볼 경우 이를 모델은 $B_{ij} + B_{kj}$를 통해 점수를 내게 됩니다. 이를 직접적으로 넣기 위해서, triplet relation (i, k, j)와 같은 higher order interaction을 뽑아서 넣어주었습니다. 이 때 넣을 수 있는 relation이 매우 커지는 데, 이는 등장 횟수로 잘라주었습니다. ![image](https://user-images.githubusercontent.com/38134957/165149170-88ca1444-63ad-4974-a35d-f5c3be75f5d8.png) - EASE 구조를 이해한다면, 옆에다가 간단한 triplet relation matrix만 추가되었다고 보시면 됩니다. ![image](https://user-images.githubusercontent.com/38134957/165149222-fde9d3a5-dbbb-42d4-9ceb-88150dc537f9.png) ## Results - triplet ralation을 추가함에 따라, VAE관련 모델들과 유사하거나 특정 데이터셋에서는 더 좋은 성능을 보여주었습니다. ![image](https://user-images.githubusercontent.com/38134957/165149511-222df3aa-d06f-4180-a1eb-46d4e49be98f.png) - 이 그림은 higher order interaction이 score에 어떤 역할을 하는지를 보여주는 겁니다. pairwise relation은 positive value에 치중되어 있고, triplet relation은 negative value에 치중되어 영향을 줍니다. ![image](https://user-images.githubusercontent.com/38134957/165149528-e60a1189-495b-4b1f-8345-fae5128c2e7f.png) ## Conclusion - 아직까지도 단순한 user-item interaction feature를 가지고도 발전할 여지가 많습니다. 위 구조는, 기존 EASE에다가 정 말 단순하게 많이 등장하는 triplet을 넣어서 학습한 구조이기 때문에 확장이 매우 쉽습니다. 그럼에도 기존 다양한 딥러닝 기반 방식들보다 성능이 비슷하거나 더 좋다는 것은, 온라인 실험상에서의 이점까지 고려할 때 좋은 모델인 것 같습니다. 식 이 쉬운것도 좋은 것 같습니다. - 다만 이 high-order interaction을 단순히 등장 횟수로만 자르는 건 cf의 약점인 cold-start item들에 대해 더 취약해질 것 같습니다. ================================================ FILE: paper_review/recsys/recsys2021/Next-item Recommendations in Short Sessions.md ================================================ # Next-item Recommendations in Short Sessions - Paper : - Authors : Wenzhuo Song, Shoujin Wang, Yan Wang, Shengsheng Wang - Reviewer : marv.20 - Topics - [#Algorithmic_Advances](../../topics/Algorithmic%20Advances.md) - #Sequential_Recommendation - #Cold_Start - #Few-Shot_Learning - [#RecSys2021](RecSys2021.md) ## Summary - 짧은 길이의 세션에 대해, 유사한 유저들의 세션을 가져온 다음(global module), 유저의 현재 세션과 결합(local module)한 뒤 Few-Shot Learning을 통해 추천(prediction module)하는 모델을 제안하였습니다. - Delicious, Reddit 데이터셋에서 기존 single / multi session 기반 모델들보다 좋은 성능을 보여주었습니다. 세션길이가 짧을 때 더 우수한 상대 지표를 보여주었습니다. ## Approach ### 1. 문제 정의 - 실제 환경에서의 세션 기반 추천에서 대부분은 매우 짧은 세션입니다. 짧은 세션에서는 문맥에 대한 정보가 매우 제한적이고, 유사한 유저의 정보를 효율적으로 사용하지 못하며, 관련 있는 세션들을 어떻게 결합할 지에 대한 연구도 잘 이뤄지지 못했습니다. - 이 논문에서는 현재 세션과 유사한 세션을 찾고, 이를 현재 세션의 정보와 결합하여 추천을 내보내는 INSERT 모델을 제안하였습니다. ### 2. 모델 구조 ![image](https://user-images.githubusercontent.com/38134957/165445878-9401f397-dd0f-4e7d-9d21-b07ed0e9c092.png) - Global Module : 유사한 유저들의 세션 정보를 활용하는 모듈입니다. - Candidate Similar Session Sets : 같은 아이템을 얼마나 interact하는 지의 여부로 판단됩니다. - Session Encoder : weighted sum of item embedding입니다. - SSRN : candidate에서 item embedding 각각에 대해 RNN을 구한 다음 similarity의 max pool을 취하게 됩니다. ![image](https://user-images.githubusercontent.com/38134957/165445889-6967f8e4-0a42-4055-9526-898bfd4d42ad.png) - Local Module : item sequence -> GRU - Prediction Module : MLP + softmax ## Results ![image](https://user-images.githubusercontent.com/38134957/165445895-50c7edb3-0f98-4e93-ba34-5f070497c0e3.png) ![image](https://user-images.githubusercontent.com/38134957/165445903-1bc7da8b-2913-491e-8ea5-e7a9a7e6a79f.png) - Delicious, Reddit에서 짧은 세션들을 뽑아 평가하였습니다. - 논문에서 제안된 모델이 기존 session-based 모델들보다 짧은 세션에서 더 좋은 성능을 보였습니다. ## Conclusion - FSL이라고 하지만 FSL의 장점인 in-context learning이 잘 발휘되어 보이지는 않았습니다. - 세션 기반 추천에서 유사 유저의 세션을 넣는 방법은 참고할 만한 부분인 것 같습니다. ================================================ FILE: paper_review/recsys/recsys2021/ProtoCF- Prototypical Collaborative Filtering for Few-shot Item Recommendation.md ================================================ # ProtoCF- Prototypical Collaborative Filtering for Few-shot Item Recommendation - Paper : - Authors : Aravind Sankar, Junting Wang, Adit Krishnan, Hari Sundaram - Reviewer : matthew.g - Topics - [#Language_and_Knowledge](../../topics/Language%20and%20Knowledge.md) - #Few-Shot_Learning - [#RecSys2021](RecSys2021.md) ## Summary - Long-tail item (interaction 갯수가 작은 대다수의 아이템) 에 대해서 성능을 떨어지는 문제를 개선하고자 한 논문입니다. - Item side information 없이 neural base recommender의 capability 만을 이용한 것이 특징입니다. ### Contribution - Few-shot Item Recommendation - 피드백이 풍부한 head item으로 base recommender를 학습한 뒤, 이를 기반으로 fine-tuning하는 컨셉입니다. - Tail item의 단점인 head item과의 distribution mismatch 를 극복하고자 하였습니다. - 피드백이 풍부한 head item 데이터를 Meta Learning set up (support set & query set) 으로 변경하였습니다. - Data-rich head item에 대한 interaction으로부터 데이터를 sub-sampling하여 tail item의 피드백과 비슷한 distribution을 모사하였습니다. - Discriminative Prototype Learning - Tail item이 sparse interaction을 가진다는 단점을 보완하고자 하였습니다. - 특정 그룹을 대표하는 벡터들을 이용하여 Base Recommender를 teacher로 삼고 Knowledge Distilation을 진행하였습니다. - Architecture-agnostic Knowledge Transfer - Base recommender로 아무 NN 모델 (CF, GNN, AE 등)이나 사용 가능하다는 장점이 있습니다. ## Approach ![image](https://user-images.githubusercontent.com/38134957/165454645-80f8cb0a-7010-4714-8733-47dc73cbfd42.png) - ProtoCF Framework - head item으로 Neural Recommender를 pre-train합니다. - tail item을 head item의 특징을 이용하여 분류할 수 있도록 Meta Learning (1) / Knowledge Distillation (2) 을 적용합니다. - (1) 과 (2)를 gate algorithm으로 섞어서 각 아이템을 나타내는 $e_i$를 구합니다. ### Preliminaries - user/item encoder의 자세한 구조는 이해하지 않아도 됩니다. ![image](https://user-images.githubusercontent.com/38134957/165454668-11019734-63a6-4d4e-b314-d60b0658cf3c.png) - user/item latent feature 간의 dot product와 실제 feedback으로 손실함수를 생성합니다. ![image](https://user-images.githubusercontent.com/38134957/165454676-8092178e-f18b-4f9f-b6a4-8ab5e05f7b97.png) - 아이템 간의 proximity (유사도) 를 구해내서 이를 knowledge distillation 단에서 사용합니다. ![image](https://user-images.githubusercontent.com/38134957/165454684-224a27fe-12fc-43ce-828c-3dcb8e4d40c8.png) ### Pre-trained Neural Based Recommender - head item 만을 이용하여 user/item encoder를 생성합니다. - 다양한 종류의 모델을 아무거나 사용할 수 있습니다. (논문에서는 BPR, VAE, CDAE를 사용함.) - 대신, NN 모델이여야 합니다. - tail item에 대해서도 embedding을 뽑아낼 수 있도록, 또한 이후에 knowledge distillation을 이용하여 학습시킬 수 있도록 위함입니다. ### Few-Shot Item Recommendation meta learning 방식으로 데이터 셋을 쪼개서 학습을 진행하였습니다. #### Task Formulation - head item 데이터를 sub-sampling하여 tail item 과 비슷한 상황을 가진 데이터 형태로 모사하였습니다. - 전체 head item 중 개의 아이템만 샘플링하였습니다. - head item i에 대해서 support set, query set으로 나누어서 meta learning방식으로 학습을 진행하였습니다. ![image](https://user-images.githubusercontent.com/38134957/165454705-d58d10d4-b8ac-4e5c-a0ec-cc7582317c51.png) #### Item Prototype & Knowledge Distillation - item 에 대한 representation을 mean vector of the embedded support user set S_i 로 표현하였습니다. - 논문에서는 아이템을 소비한 유저들을 중심으로 한 clustering의 결과로 해석하였습니다. ![image](https://user-images.githubusercontent.com/38134957/165454713-2f76743c-804d-4c58-9380-0352e323c8f4.png) - 그러나 해당 prototype만으로는 문제가 있는데, - 데이터가 매우 sparse해서 tail item에 대해서는 해당 값이 매우 noisy할 수 있습니다. - tail item에 대해서는 데이터의 분별력이 떨어지므로, 아이템 별로 거의 비슷한 값이 나올 수 있습니다. - 추가적으로 분별 가능한 inductive bias 역할을 하는 새로운 term이 필요합니다! #### Group Embedding - tail item을 좀 더 분별력 있게 설명하려면 head item과의 item - item proximity를 이용할 수 있습니다. - 그러나 아이템의 갯수가 많아지게 되면 pairwise proximity 를 직접 저장하고 불러오는 데에 한계가 생깁니다. - 따라서, Group Embedding 을 이용하여 item - item proximity를 저차원으로 묘사합니다. ![image](https://user-images.githubusercontent.com/38134957/165454723-e40ea681-8fdc-407e-b172-a5b3ff19ecc0.png) - 직관적으로 생각해서 의 각 벡터가 아이템의 특정한 정보 (국가, 카테고리, 장소, 업종) 등을 표현한다고 생각하면 됩니다. (MMoE랑 비슷한 느낌으로 이해하면 좋을 듯.) - Group enhanced prototype $g_i$-> $z_i$와 $p_i$를 learnable parameter를 이용하여 attention을 처리하였습니다. ![image](https://user-images.githubusercontent.com/38134957/165454757-cc599602-a7f7-40a6-8c95-32db9d4ca7bb.png) #### Knowledge Distillation - Base Recommender를 통해 구한 item-item proximity에 대한 정보를 $Z_M$에 심습니다. - $R_B$을 기준으로 i와 가장 비슷한 아이템 n=10개의 아이템에 대해서 - base recommender / group-enhanced prototype 간의 Cross Entropy를 최소화하고자 하는 것입니다. ![image](https://user-images.githubusercontent.com/38134957/165454773-0b40f9f1-ee4c-474b-864f-ac2c9dbcf80c.png) ### Final Item Embedding - $R_B$, $Z_M$로 구한 item embedding의 gated result로 최종 item embedding $e_i$를 구할 수 있습니다. ![image](https://user-images.githubusercontent.com/38134957/165454780-0f1df03f-fdce-44ce-b91e-61bad1458cd2.png) ### Few-shot Recommender Training - query set Q를 이용하여 query set에 속한 user와의 relevance score를 생성합니다. (by cosine similiarity) - 이 때 pair 는 값이 애초에 1이므로 Negative Cross Entropy를 최소화하는 방향으로 학습 진행하면 됩니다. ![image](https://user-images.githubusercontent.com/38134957/165454796-cdcfc957-e5fc-4286-9cfe-f978a026a337.png) - 이 때 p_F를 구하는 방법으로 두 가지 방식이 있습니다. - Multimodial Log-Likelihood ( 에 속하는 모든 아이템에 대한 softmax) - Logistic Log-Likelihood ## Results ### Overall - Epinions, Yelp, Weeplaces, Gowalla에서 실험을 진행하였습니다. - NCF Autoencoder > latent-factor models - ProtoCF는 SOTA를 overall item에서 앞서는 것을 확인할 수 있었습니다. ![image](https://user-images.githubusercontent.com/38134957/165454805-57c15ef4-2d29-4b67-9a8d-85a16e47cd5c.png) ### Few-shot Recommendation Result - interaction 갯수가 적은 구간일수록 ProtoCF >> baseline 경향이 강해졌습니다. - 아래 지표는 item들을 popularity 순서대로 그룹화한 것인데, interaction 갯수가 낮은 구간에서 성능 차이가 더 발생하는 것을 확인할 수 있었습니다. ![image](https://user-images.githubusercontent.com/38134957/165454818-c911170a-7571-49f8-aa3a-c54b2b347f98.png) ### Ablation Study - few-shot performance (long tail items with less than 20 interactions) 만을 기재하였습니다. - 모든 부분이 critical 하게 성능에 영향을 준 것은 아니나 (모델 자체가 와 의 앙상블이므로) 각 모듈이 성능 향상에 영향을 끼쳤습니다. ![image](https://user-images.githubusercontent.com/38134957/165454837-af5810a4-a248-4298-b710-371b86431932.png) ### Parameter Sensitivity - $\lambda=0.01$ 에서 제일 성능이 좋고, 이후에는 커질수록 성능이 하락하였습니다. - $N$(task에서의 sample size)는 클수록 성능이 좋아지는 것을 확인할 수 있었습니다. ================================================ FILE: paper_review/recsys/recsys2021/RecSys2021.md ================================================ # RecSys2021 - ["Serving Each User"- Supporting Different Eating Goals Through a Multi-List Recommender Interface]("Serving%20Each%20User"-%20Supporting%20Different%20Eating%20Goals%20Through%20a%20Multi-List%20Recommender%20Interface.md) - [Accordion- a Trainable Simulator for Long-Term Interactive Systems](Accordion-%20a%20Trainable%20Simulator%20for%20Long-Term%20Interactive%20Systems.md) - [Burst-induced Multi-Armed Bandit for Learning Recommendation](Burst-induced%20Multi-Armed%20Bandit%20for%20Learning%20Recommendation.md) - [Cold Start Similar Artists Ranking with Gravity-Inspired Graph Autoencoders](Cold%20Start%20Similar%20Artists%20Ranking%20with%20Gravity-Inspired%20Graph%20Autoencoders.md) - [Debiased Explainable Pairwise Ranking from Implicit Feedback](Debiased%20Explainable%20Pairwise%20Ranking%20from%20Implicit%20Feedback.md) - [Evaluating Off-Policy Evaluation- Sensitivity and Robustness](Evaluating%20Off-Policy%20Evaluation-%20Sensitivity%20and%20Robustness.md) - [Follow the guides- disentangling human and algorithmic curation in online music consumption](Follow%20the%20guides-%20disentangling%20human%20and%20algorithmic%20curation%20in%20online%20music%20consumption.md) - [I want to break free! Recommending friends from outside the echo chamber](I%20want%20to%20break%20free!%20Recommending%20friends%20from%20outside%20the%20echo%20chamber.md) - [Local Factor Models for Large-Scale Inductive Recommendation](Local%20Factor%20Models%20for%20Large-Scale%20Inductive%20Recommendation.md) - [Matrix Factorization for Collaborative Filtering Is Just Solving an Adjoint Latent Dirichlet Allocation Model After All](Matrix%20Factorization%20for%20Collaborative%20Filtering%20Is%20Just%20Solving%20an%20Adjoint%20Latent%20Dirichlet%20Allocation%20Model%20After%20All.md) - [Mitigating Confounding Bias in Recommendation via Information Bottleneck](Mitigating%20Confounding%20Bias%20in%20Recommendation%20via%20Information%20Bottleneck.md) - [Negative Interactions for Improved Collaborative Filtering- Don’t go Deeper, go Higher](Negative%20Interactions%20for%20Improved%20Collaborative%20Filtering-%20Don’t%20go%20Deeper,%20go%20Higher.md) - [Next-item Recommendations in Short Sessions](Next-item%20Recommendations%20in%20Short%20Sessions.md) - [ProtoCF- Prototypical Collaborative Filtering for Few-shot Item Recommendation](ProtoCF-%20Prototypical%20Collaborative%20Filtering%20for%20Few-shot%20Item%20Recommendation.md) - [Reverse Maximum Inner Product Search- How to efficiently find users who would like to buy my item?](Reverse%20Maximum%20Inner%20Product%20Search-%20How%20to%20efficiently%20find%20users%20who%20would%20like%20to%20buy%20my%20item%3F.md) - [Semi-Supervised Visual Representation Learning for Fashion Compatibility](Semi-Supervised%20Visual%20Representation%20Learning%20for%20Fashion%20Compatibility.md) - [Shared Neural Item Representation for Completely Cold Start Problem](Shared%20Neural%20Item%20Representation%20for%20Completely%20Cold%20Start%20Problem.md) - [Sparse Feature Factorization for Recommender Systems with Knowledge Graphs](Sparse%20Feature%20Factorization%20for%20Recommender%20Systems%20with%20Knowledge%20Graphs.md) - [The role of preference consistency, defaults and musical expertise in users’ exploration behavior in a genre exploration recommender](The%20role%20of%20preference%20consistency%2C%20defaults%20and%20musical%20expertise%20in%20users’%20exploration%20behavior%20in%20a%20genre%20exploration%20recommender.md) - [Together is Better- Hybrid Recommendations Combining Graph Embeddings and Contextualized Word Representations](Together%20is%20Better-%20Hybrid%20Recommendations%20Combining%20Graph%20Embeddings%20and%20Contextualized%20Word%20Representations.md) - [Top-K Contextual Bandits with Equity of Exposure](Top-K%20Contextual%20Bandits%20with%20Equity%20of%20Exposure.md) - [Towards Source-Aligned Variational Models for Cross-Domain Recommendation](Towards%20Source-Aligned%20Variational%20Models%20for%20Cross-Domain%20Recommendation.md) - [Toward Unified Metrics for Accuracy and Diversity for Recommender Systems](Toward%20Unified%20Metrics%20for%20Accuracy%20and%20Diversity%20for%20Recommender%20Systems.md) - [Transformers4Rec- Bridging the Gap between NLP and Sequential & Session-Based Recommendation](Transformers4Rec-%20Bridging%20the%20Gap%20between%20NLP%20and%20Sequential%20&%20Session-Based%20Recommendation.md) - [Values of Exploration in Recommender Systems](Values%20of%20Exploration%20in%20Recommender%20Systems.md) ================================================ FILE: paper_review/recsys/recsys2021/Reverse Maximum Inner Product Search- How to efficiently find users who would like to buy my item?.md ================================================ # Reverse Maximum Inner Product Search- How to efficiently find users who would like to buy my item? - Paper : - Authors : Daichi Amagata, Takahiro Hara - Reviewer : iggy.ll - Topics - [#Scalable_Performance](../../topics/Scalable%20Performance.md) - #Inner_Product_Search - [#RecSys2021](RecSys2021.md) ## Summary ## Approach ### Notations - u_i in Q (User vectors) - p_j in P (Item vectors) - : dot product between a and b. ### Maximum Inner Product Search (MIPS) Given a user u_i \in Q, Find \text{Topk}(u_i) = \text{argtopk}_{p_j \in P} ### Reverse Inner Product Search (R-MIPS) Given an item q \in P, Find a set of users u_i such that q \in \text{TopK}(u_i) ### Main claim with simple preprocessing, those three questions can be answered in constant time: 1. Given query item q is included in \text{Topk}(u_i) of the user u_i 2. Given query item q is not included in \text{Topk}(u_i) of the user u_i 3. Given query item q is not included in \text{Topk}(u_i) of all users u_i of some (not any) set of users u_i, or block B. #### Constructing Block B 1. Perform Descending Sort Q, P according to their L2 norm. i.e., \|\|u_i\|\| \geq \|\|u_j\|\| if i < j. 2. appropriately partition user vectors Q. e.g., Q = [u_1, u_2, ...,u_6], then B_1 = [u_1,u_2, u_3], and B_2 = [u_4, u_5, u_6] 3. define L_i (it is easier to write in python here) `L_i = np.array(sorted(dot(u_i, P[:50, :]), ascending=False))` `L(B) = np.min([L_i for u_i in B], axis=0)` L_i is sorted values of dot products between user u_i and item vectors with top-k norms. Claim 1. Given u_i, q, if \leq L_i[k], then q \notin \text{TopK}(u_i) proof: L_i[k] is dot product between u_i and item p such that p is in top-K ranking in norm. Thus p cannot be higher than rank k and dot product with q is lower than dot product with p. Thus q cannot be in \text{TopK}(u_i) Claim 2. Given u_i, q, if \geq \|\|u_i\|\| \|\| p_k\|\|, then q \in \text{TopK}(u_i) proof: Let p to be a true top-k item. \|\|u_i\|\| \|\| p\|\| \geq \|\|u_i\|\| \|\| p_k\|\| \geq holds. Thus q must be in top-k ranking Claim 3. Given q, a block B and u_i is a first vector in B, \|\|u_i\|\| \|\|q\|\| \leq L(B)[k], then q \notin \text{TopK}(u_i) for all u_i \in B proof: \max_{u_i \in B} \leq \|\|u_i\|\| \|\|q\|\| \leq L(B)[k]. Then by Claim 1, it holds ### Procedure ```text given item query vector q ret = {} for B in Blocks: if we can skip block B using Claim 3: continue; for u in B: if we can skip u using Claim 1: continue if u, q satisfy Claim 2: ret.add(u) else: let TopK(u) using exhaustie search; if q in TopK(u) ret.add(u) return ret ``` Note: - We can parallelize easily along with Blocks. - Worst Case bound is equal to Exhaustive Search - No theoretical bound is given ## Conclusion - 생각해보면 쓰이는 수학/프로그래밍 테크 기술이 난이도가 고등학교때 기하와 벡터 배웠을 때 딱 그 정도만 쓰는 것 같은데 아이디어가 진짜 좋은 것 같습니다. - 개선 여지가 많은 것 같다. 특히, Block Construction 부분에서, 블록 내부의 벡터들의 순서나, 블록 사이의 관계 측면에서 뭔가 개선할 여지가 있을 것 같은데 하는 생각이 듭니다. 아이디어를 일부로 약간만 풀고 세부적인 테크닉들은 공개 안 한 것 같습니다. ================================================ FILE: paper_review/recsys/recsys2021/Semi-Supervised Visual Representation Learning for Fashion Compatibility.md ================================================ # Semi-Supervised Visual Representation Learning for Fashion Compatibility - Paper : - Authors : Ambareesh Revanur, Vijay Kuma, Deepthi Sharma - Reviewer : matthew.g - Topics - [#Real-World_Concerns](../../topics/Real-World%20Concerns.md) - #Semi-Supervised_Learning - [#RecSys2021](RecSys2021.md) ## Summary - Semi-Supervised Learning을 사용한 다른 모델들과 다르게, conditional mask를 통해서 color와 pattern 같은 attribute를 학습하는 것이 아니라 color, shape를 직접적으로 변경해주는 self-supervised learning의 방법론을 적용하였습니다. - pseudo-labeling를 이용하여 unlabeled-image를 이용하여 학습을 진행하였습니다. - Polyvore, Polyvore-D, newly created Fashion outfit dataset에 대해서, 적은 수의 labeled data를 사용하였고, text 등과 같은 metadata 를 전혀 사용하지 않았음에도 supervised method에 준하는 결과를 만들었습니다. ## Introduction ### Fashion Compatibility - 이 논문의 main task. 한글로 번역하면 **잘 어울리는 룩 만들기** 정도?로 볼 수 있을 것 같습니다. > compose matching clothing items that are appealing and complement well. ### Problem & Contribution - 기존에는 handcraft labeling 을 했었으나 그걸 매번 진행하기에는 번거롭고 cost가 많이 듭니다. - 이를 해결하고자 **semi-supervised learning** 기법을 적용하였습니다. - 적은 양의 labeled data, 많은 양의 unlabeled data를 이용하여 supervised training에 준하는 학습 효과를 냄과 동시에, supervised learning의 단점인 overfitting을 해소하고, 일반화 성능을 끌어올리고자 하였습니다. - 다양한 기법 및 방법론이 존재하는데, 더 자세한 내용은 이 [포스팅](https://sanghyu.tistory.com/177)이 도움이 되었으니 읽어보시면 좋을 것 같습니다. - 이 논문에서는 다양한 기법 중에 아래와 같은 기법들을 도입하였습니다. - Proxy-label 기법 (labeled data로 학습한 뒤, unlabeled data를 labeling하고 그걸로 재학습.) - consistency regularization 기법 (기존 데이터에 대해서 일부 perturbated 된 데이터에 대해서도 예측의 결과는 일관성이 있어야 한다.) ### Main Assumption - 기존 모델들처럼 각각의 attrbute를 implicit하게 배우는 것이 아니라 (MMoE와 같은 형태로 K개로 표현된 FFN의 모음으로 모델 구성.), explicit하게 attribute를 설정 (color, shape) 하고 해당 부분에 대한 특징을 표현하는 Representation을 찾고자 하였습니다. ## Approach - 원하는 것은 `visual representation for the task of fashion compatibility`를 학습하는 것입니다. - Metric Learning을 적용한 목적함수를 설계하여 compatible한 아이템끼리의 embedding은 가깝게 하고자 하였습니다. - 이를 위해 (Anchor, pseudo-positive, negative) triplet을 만들어 학습을 진행하였습니다. ### Loss $$ \mathcal{L} = \mathcal{L_l} + \lambda_{ss}\mathcal{L_{ss}} + \lambda_{pseudo}\mathcal{L_{pseudo}}\\ \mathcal{L_l} = \max{(0, d(\phi_A, \phi_P) - d(\phi_A, \phi_N) + m)}\\ \mathcal{L_ss} = \max{(0, d(\hat{\phi_{u}}, \hat{\phi_{[s]}}) - d(\hat{\phi_{u}}, \hat{\phi_{[a]}}) + m)}\\ \mathcal{L_{pseudo}} = \max{(0, d(\hat{\phi_{A}}, \hat{\phi_{P}}) - d(\hat{\phi_{u}}, \hat{\phi_{N}}) + m)} $$ - Loss on Labeled item 기존에 존재하는 labeled data (A, P, N) 에 대해서는 A와 P는 가깝게, A와 N은 멀어지도록 학습을 진행하였습니다. 추가로 margin loss도 두었습니다. ### Loss on Consistency Regularization - Self-supervised learning에서 일반적으로 사용되는 접근을 차용하였습니다. - Consistency Regularization의 가설 중 `perturbation`에 해당하는 전처리 방법을 self-supervised learning 관련 논문에서 영감을 받아 적용하였습니다. - `fashion compatibility를 위해서는 fashion item을 구분하는 중요한 attribute (color, shape)에 대한 구분 능력이 필요하다`는 전제를 이용하여, 한 아이템에 대해서 color와 shape를 바꾼 negative sample과의 discrepancy를 늘리는 방향으로 학습을 진행하였습니다. - 이러한 방법론들이 이미지를 돌리거나, color jittering을 하거나, 이미지에 대한 직소 퍼즐 형태의 퀴즈를 풀거나 하는 self-supervised learning에서의 pretext task와 비슷한 경향이 있어서 논문에서 그렇게 언급한 것으로 보입니다. ### Data Augmentation on Pseudo-Labeled Data - (A, P, N) 에 대해서 embedding space에서의 nearest element (A', P', N')를 on-the-fly로 계산하고 이에 대한 margin loss를 계산하였습니다. - 계산 상의 속도를 높이고자 mini-batch 내에서만 nearest element를 찾는 방법을 취하였습니다. ### Model Structure - siamese network와 비슷한 구조를 가지고 있습니다. - ImageNet pretrained CNN (ResNet18) -> fully-connected layer per category ($W_c$) - 학습 파라미터는 다음과 같습니다. - 256 batch size for labeled data, 1024 batch size for unlabeled data - margin $m$ 을 0.4 for margin loss - $\lambda_{ss}=0.1\quad\lambda_{pseudo}=1$ - adam optimizer, lr 5e-5, 10 epochs ## Results - Polyvore (패션 커머스 서비스, ssense에 최근 합병됨) dataset, Polyvore-disjoint (Polyvore 중에서 train/valid/test에 중복된 이미지가 없도록 처리한 것), Fashion outfits (e-commerce platform에서 데이터를 크롤링하고 **같은 세션에서 산 아이템의 경우 compatible하다고 가정**)를 이용하여 학습을 진행하였습니다. - 5%의 labeled data만을 이용하여 supervised learning에 준하는 학습 결과를 얻을 수 있었으며 100%를 적용하면 supervised model들을 상회하는 성능을 보여주었습니다. ================================================ FILE: paper_review/recsys/recsys2021/Shared Neural Item Representation for Completely Cold Start Problem.md ================================================ # Shared Neural Item Representation for Completely Cold Start Problem - Paper : - Authors : Ramin Raziperchikolaei, Guannan Liang, Young-joo Chung - Reviewer : matthew.g - Topics - [#Practical_Issues](../../topics/Practical%20Issues.md) - #Cold_Start - #Representation_Learning - [#RecSys2021](RecSys2021.md) ## Summary - Complete item cold start 환경에서의 새로운 hybrid 모델을 제안하였습니다. - User Interaction vector가 단순 user one-hot encoding vector보다 학습 과정에서 더 좋은 성능을 낸다는 것을 증명하였습니다. ## Approach ### User Interaction Vector - User Interaction Vector를 표현하는 방식에는 두 가지가 있습니다. 1. User ID 1. User ID에 상응하는 임베딩을 뽑아냄. 2. embedding matrix $E^u \in \mathbb{R}^{d^u}$ 에서 $z^u_j = I^u_jE^u \in \mathbb{R}^{d^u}$를 뽑아냄. 2. Interaction Vector 1. $z^u_i = g^u(R_{j,:}) = \sigma(...\sigma(R_j, W^u_1)W^u_2)... W^u_L)$ - 이 중에서 (어찌보면 당연히,, ) 2번이 더 나은 결과가 나옵니다. - 이를 증명하는 방법으로 아래와 같은 방법들을 사용하였습니다. - training loss / recall이 가장 빠르고 높은 지점에서 수렴된다. - prob density at initialization 이 가장 normal distribution에 가깝다. - prob density at convergence 이 가장 normal distribution에 가깝다. - 이러한 점을 해석해보면 아래와 같이 정리가 가능합니다. - **$W^u_1 \in \mathbb{R^{n \cross p}}$ 으로부터의 output은 user가 interact했던 아이템들의 임베딩의 합이다.** ### Sharing neural Item rep with the hidden item embeddings - Item representations from the item model을 user model에서의 hidden item embedding으로 사용하였습니다. $$ \sum_{j,k\in S^+\bigcup{S^-}}{||(\vb{z}^u_j)^T\vb{z}^i_k - \vb{R}_{ij}||^2} s.t. \\ \vb{z}^u_j = g^u(\vb{R}_{j,:}) = \sigma(...\sigma(\sigma(\vb{R}_{j,:}\vb{W}^u_1)\vb{W}^u_2)...\vb{W}^u_L)\\ \vb{W}^u_1 = g^i(\vb{X}), \quad \vb{z}^i_k = g^i(\vb{X}_k,:) $$ ### Faster training with a simpler formulation - 각 미니 배치마다 모든 아이템에 대한 $W^u_1$을 계산하는 것은 비효율적이라고 지적하였습니다. - 그래서 한 번 구해놓은 $W^u_1$을 이용해서 각 유저가 소비한 아이템 ($p \in N_j$) 에 대해서만 $g_i$ 값을 구하는 식으로 처리하였습니다. $$ \vb{y}_j = \vb{R}_{j,:}\vb{W}^u_1 = R_{j,:}g^i(\vb{X}) = \Sigma_{p\in N_j}g^i(\vb{X}_{p,:}) $$ ### Attention mechanism in learning uesr representations - 유저가 소비한 **모든 아이템이 같은 가중치를 가질 필요는 없다**고 주장하였습니다. - user의 representation을 구할 때에 k-th item rep와 비슷한 아이템일수록 높은 attention을 주는 구조로 각 아이템 vector에 weight를 부여하였습니다. $$ \sum_{j,k\in S^+\bigcup{S^-}}{||(\vb{z}^u_j)^T\vb{z}^i_k - \vb{R}_{ij}||^2} s.t. \\ \vb{z}^u_j = g^u(\sigma(\vb{y_j})), \quad \vb{y}_j = \Sigma_{p \in N_j}\alpha_{pk}g^i(\vb{X}_{p, :}), \quad \vb{z}^i_k = g^i(\vb{X}_k,:) $$ - 이 때 가중치 $\alpha_{pk}$를 주는 방식을 여러 가지로 두고 이에 대한 실험을 진행하였습니다. - dot product similarity - cosine similarity - general (with weight matrix) - 그리고 나서 attention과 같이 softmax 처리하여 $\alpha_{pk}$를 구하고 이를 weight으로 정하였습니다. ## Results ### Dataset - CiteULike: 사용자가 인용을 저장하고 학술 논문에 공유 할 수있는 웹 서비스입니다. - Ichiba 1M, Ichiba 20M: *Rakuten Ichiba* (일본 온라인 전자 상거래 플랫폼) interaction 데이터. ### Result #### Shared Item Representation - Sharing item rep이 더 적은 iteration에서 더 나은 recall을 보여주었습니다. - parameter 수가 많아지는 대규모 데이터셋에서 더 좋은 성능을 보여주었습니다. #### Attention Mechanism - Attention mechanism이 성능 향상에 도움이 되었다고 합니다. - Attention의 경우에도 attention 계산 시에 아래와 같은 두 종류로 모델을 나누었습니다. - item $i_k$ 그대로 사용하는 경우 (attention) - $i_k$는 제외하는 경우 (attention_rm_item) - attention의 경우가 training set recall이 더 높았습니다. - 그러나 general과 dot similarity의 경우 overfitting에 취약했던 반면, cosine similarity의 경우 Ichiba1M 데이터셋에 대해 overfitting은 적으면서도 (normalization의 효과로 보임), 가장 높은 recall을 기록하였습니다. #### Shared Item Representation & dataset size Sharing item rep의 경우, 데이터셋의 크기가 작을 수록 더 모델 성능에 도움을 주는 것으로 확인되었습니다. (데이터셋의 크기가 작을 수록 nonshared와 성능 차이가 더 크다.) #### Comparison with other models Cold-start 상황 해결을 다룬 다른 모델 (DropoutNet-WMF, ACCM, DeepMusic, CDL) 대비 CiteULike 데이터셋에서 높은 test recall을 기록하였습니다. ================================================ FILE: paper_review/recsys/recsys2021/Sparse Feature Factorization for Recommender Systems with Knowledge Graphs.md ================================================ # Sparse Feature Factorization for Recommender Systems with Knowledge Graphs - Paper : - Authors : Vito Walter Anelli, Tommaso Di Noia, Eugenio Di Sciascio, Antonio Ferrara, Alberto Carlo Maria Mancino - Reviewer : bell.park - Topics - [#Language_and_Knowledge](../../topics/Language%20and%20Knowledge.md) - #Knowledge_Graphs - [#RecSys2021](RecSys2021.md) ## Summary - 지식그래프(Knowledge Graph)와 엔트로피 기반 feature selection을 결합해서 만든 추천 모델을 제안한 논문입니다. - 아이템 수에 따라 모델 복잡도(embedding)가 선형적으로 증가하는 기존 모델과 다르게 아이템 수가 늘어나도 모델 복잡도가 크게 증가하지 않습니다. - nDCG는 나쁘지만(MP보다도 나쁜 케이스도 있음), diversity 측면에서 좋은 부분이 있습니다. - 그러나 실험 신뢰도가 낮은 편입니다. MP > MF 케이스도 있는데 저는 결과를 납득하기 어려웠습니다. ## Approach ### 문제 인식 - 최근에 DL 기반 추천 모델들이 많이 사용되지만, 이 모델들은 아이템 수가 늘어나면 embedding 개수를 늘려야해서 모델 복잡도가 계속해서 증가하는 단점이 있습니다. - Content-based와 접목시켜 만든 하이브리드 모델들도 아이템마다 feature를 concatenate하는 전략이 일반적이라 모델이 무거워지게 됩니다. ### 제안 모델 - 이 논문에서는 각 아이템의 특성을 지식 그래프에서 가져오고, 아이템의 추천 점수를 특성의 추천 점수 weighted sum으로 계산하였습니다. - 예를 들어, 아래 그래프에서 `Rijksmuseum`의 추천 점수는 ``, ``의 추천 점수의 weighted sum이 됩니다. - 각 특성 점수의 weight는 유저별로 다르게 적용이 되고, 정확하게는 user-feature 조합의 information gain으로 계산하였습니다. - information gain은 유저가 positive interaction한 아이템의 feature set을 대상으로 특정 feature를 넣었을 때와 제외했을 때의 entropy 차이를 의미합니다. - 예를 들어, 아래 그래프에서 모든 아이템은 다 `` 특성이 있어서 information gain이 0이 됩니다. - 대신 Pink가 고른 아이템 중 2개가 ``를 가지고 있어서 이 경우는 information gain이 0보다 크게 됩니다. - 각 특성의 점수는 MF 스타일의 간단한 방식으로 계산 (user embedding dot feature embedding + user bias)하였습니다. ![image](https://user-images.githubusercontent.com/38134957/165144120-18389566-f60f-45ac-b64f-d0d089fec67f.png) ## Results ![image](https://user-images.githubusercontent.com/38134957/165144152-0fbeb043-11b6-4265-a6ca-f733787071e7.png) ![image](https://user-images.githubusercontent.com/38134957/165144170-2732047d-f6f9-4689-8298-568659352c4c.png) ![image](https://user-images.githubusercontent.com/38134957/165144161-ab065bdc-3a27-4058-b2aa-cad0883d66c6.png) - Movielens-1M, Facebook Books, Yahoo! Movies에서 평가하였습니다. - 저자들은 괜찮은 수준이라고 얘기하긴 하지만, nDCG 차이가 많이 나는 편입니다. Facebook Books의 경우 다른 메서드도 성능이 안좋긴하지만 MP보다도 결과가 안좋았습니다. nDCG가 추천 퀄리티를 담보하진 않지만 차이가 너무나는데 contribution이라고 보기 어렵다고 생각됩니다. ================================================ FILE: paper_review/recsys/recsys2021/The role of preference consistency, defaults and musical expertise in users’ exploration behavior in a genre exploration recommender.md ================================================ # The role of preference consistency, defaults and musical expertise in users’ exploration behavior in a genre exploration recommender - Paper : - Authors : Yu Liang, Martijn C. Willemsen - Reviewer : jinny.kk - Topics - [#Interactive_Recommendation](../../topics/Interactive%20Recommendation.md) - #Music_Recommendation - [#RecSys2021](RecSys2021.md) ## Summary - 유저의 preference가 시간이 지남에 따라 어떻게 발전하는지는 많이 연구되지 않았다는 문제의식에서 출발하여 음악 도메인에서 유저들의 short-term, long-term preference간의 관계를 이해해보고자 한 논문입니다. ## Approach ### 접근 방법 - 음악 도메인에서 유저들의 short-term, long-term preference간의 관계를 이해해보자. - 정의: short-term은 session 내에서의 소비, long-term은 whole history에서의 소비를 뜻한다. - 그걸 이해하면 시간에 따라 유저의 취향이 어떻게 발전하는지 이해할 수 있을 것이고, 유저가 새로운 취향을 탐색할 때 어떻게 행동하는지 이해할 수 있을 것이고, 탐색 툴에서 우리가 유저를 어떻게 서포팅해주면 좋을지도 생각해볼 수 있을 것이기 때문이다. - 왜냐? - 유저의 취향이 시간이 지남에 따라 어떻게 발전하는지 취향의 stability가 있는지, 그들간의 관계는 under-explored되었다. - 이전 연구들이 보인 것들은, 단기 취향 ≠ 장기 취향인 것 같더라, 그리고 음악 도메인에선 유저의 음악적 전문성에 따라 청취 행태 (다양성, 추천 시스템 사용 방식)가 다르더라 정도였다. - 논문의 도메인: 음악 ### Research Questions - RQ 1: 시간에 따라 유저 취향이 어떻게 변화하는지 이해해보자. (users's preference consistency) - 스터디 디자인: data는 (다른 스터디에서 수집한) 스포티파이에서 319명의 유저들의 청취 기록을 사용했다. short (최근 4주), medium (최근 6달), long-term (모든 기록) preference는 track-level, artist-level, tag-level로 측정했다. - 유저의 음악적 전문성이 높을수록 (높은 MSAE 점수) 시간에 따른 더 일관된 (consistent) 취향을 가지더라. - short-term 과 medium-term 취향의 일관성이나, medium-term과 long-term 취향의 일관성 > short-term과 long-term 취향의 일관성. (어찌 보면 당연하긴 한 듯하지만..) - RQ 2: 유저는 새로운 취향을 어떤 방식으로 탐색할까? - (유저의 음악적 전문성에 따라 새로운 음악 장르를 탐색하는 방식이 달라질까?) - 스터디 디자인: 저자들이 수행한 이전 연구가 이미 있고, 거기에 새로운 분석을 추가한 느낌이다. 어쨌든, 유저들에게 장르 목록을 주고 탐색할 장르를 선택하게 했다. - 유저들은 현재 취향에 가까운 장르를 탐색하는 경향을 보였다. - 유저의 음악적 전문성이 낮을수록 (낮은 MSAE 점수) 취향이 less stable 하더라. 그래서 탐색할 때 (well-developed된) long-term 취향의 장르에 가까운 장르를 탐색하더라. - 유저의 음악적 전문성이 높을수록 (높은 MSAE 점수) 취향이 stable 하더라. 그래서 short, medium, long-term 취향의 것을 비슷비슷한 수준으로 탐색하더라. - RQ 3: 그렇다면 유저가 현재 취향보다 좀더 멀리 떨어진 취향을 탐색하도록 넛지할 수 있을까? - 스터디 디자인: 저자들이 고안한 interaction tool을 유저들이 사용하게 하였고, 2 X 3의 default conditions에서 between-subjects로 실험을 진행했다. 설정이 유저가 더 기존 취향으로부터 더 멀리 탐색하도록 넛지할 수 있는지 등을 분석하였다. - 2 X 3 default conditions - genre presentation order: 유저 취향에서 가까운 순 - 유저 취향에서 멀리 있는 순 - 장르 내 플레이 리스트의 personalization-level을 컨트롤하는 slider position: fully personalized - middle - fully representative - RQ 3-1: 시스템의 Default order of genre presentation에 따라 유저가 현재 취향에서 좀더 먼 취향을 탐색하도록 넛지할 수 있을까? - 넛지할 수 있더라. 하지만 음악적 전문성이 높을수록 이에 영향 받는 정도가 적더라. - RQ 3-2: 시스템의 slider position의 default 세팅에 따라 유저들이 선택하는 추천의 개인화 정도가 달라질까? - 유저의 slider interaction 횟수에 따라 유저별로 경향성이 다르게 나타났다. Fig 6 참고. - low interaction group: final slider position은 default slider position에 강하게 영향 받았다. - medium interaction group: default slider position의 반대 방향으로 slider를 이동시켰다. - high interaction group: default에 덜 영향을 받았고, mixed position으로 slider를 이동시켰다. - 대체로 유저들이 선택한 slider position으로 미루어 볼 때, 최적은 personalization과 representativeness 사이 어딘가에서 형성되더라. - RQ 3-3: 유저들이 기꺼이 탐색하고자 하는 거리가 유저의 음악적 전문성에 따라 달리 나타날까? - path model을 구축해서 (Fig 7) default setting이 유저의 (현재 취향으로부터의) 탐색 거리에 영향을 끼칠 수 있다고 분석했다. ## Conclusion - `Strong Points?` - 음악적 전문성에 따라 시간에 따른 유저 취향의 일관성 정도가 다르다는 걸 분석했다는 점이 흥미로웠다. - 유저들이 컨트롤할 수 있는 어떠한 디폴트 세팅이 주어졌을 때 어떤 방식으로 새로운 장르를 탐색하는지 분석한 점이 흥미로웠다. - `Weak Points?` - 논문에서는 "취향"을 CB적으로 정의하였고, CF적으로 정의한 것은 아니다. - 분석 논문인 것 같고, 그래서 이를 추천 시스템이 어떻게 반영해야 하는지의 방향성을 제시하지는 않는 것 같다. - 음악 도메인이라 유저의 전문성이 하나의 factor가 되었는데, 다른 도메인에선 다른 것이 factor가 될 수 있을 것 같다. ================================================ FILE: paper_review/recsys/recsys2021/Together is Better- Hybrid Recommendations Combining Graph Embeddings and Contextualized Word Representations.md ================================================ # Together is Better- Hybrid Recommendations Combining Graph Embeddings and Contextualized Word Representations - Paper : - Authors : Marco Polignano, Cataldo Musto, Marco de Gemmis, Pasquale Lops, Giovanni Semeraro - Reviewer : tony.yoo - Topics - [#Language_and_Knowledge](../../topics/Language%20and%20Knowledge.md) - #Graph - #Sequence_Modeling - [#RecSys2021](RecSys2021.md) ## Summary Main author: [Marco Polignano](https://scholar.google.it/citations?user=sjQSYGQAAAAJ&hl=it) - BERT 기반의 감정 분석 연구를 많이 하신것 같습니다. - 두 가지 다른 정보(interaction feedback, text information)로 부터 user, item 임베딩을 얻는 hybrid 방법 제시하였습니다. - 정보를 융합하는 방법은 두 가지 concatenation 방법을 제시하였습니다. - 기본 architecture: Two-tower 모델과 같습니다. 양쪽 방향이 같은 구조를 띄무로 한쪽 방향에 대해서만 표현하였습니다. | Entity-based | Feature-based | |--|--| | | | |각 entity의 intrinsic charateristic 을 배움 | heterogenous 한 두 entity 사이의 relationship을 배움 | 다음의 두가지 모듈로 구성되있고, Sota 모델로 바꾸는게 쉽게 가능합니다. - Collaborative Filtering 모듈: graph embedding 방법을 사용합니다. - Content-based 모듈: contextual word representation 방법을 사용합니다. ## Approach ### Graph Embedding 다음 두개의 모델 사용. (이 외에도 TransR, TransD, ... 많은 모델 존재. [survey paper](https://www.mdpi.com/2073-8994/13/3/485/htm) 참고.) - [TransE, NIPS'13](https://papers.nips.cc/paper/2013/hash/1cecc7a77928ca8133fa24680a88d2f9-Abstract.html) - [TransH, AAAI'14](https://ojs.aaai.org/index.php/AAAI/article/view/8870) 이 모델은 본래 Knowledge graph 에서 entity(head)-relation-entity(tail)의 triple 정보를 임베딩에 반영하고자 한 방법. 추천시스템에서 유저, 아이템을 entity, 평점을 relation으로 생각 가능. 다음과 같은 관계로 임베딩. | - | TransE | TransH | | -------------- | ------------------------------------------------------------ | ------------------------------------------------------------ | | Architecture | | | | Score function | $\Vert \textbf{h} + \textbf{d}_r - \textbf{t} \Vert _{2}^2$ | $\Vert \textbf{h}_{\bot} + \textbf{d}*r - \textbf{t}_{\bot} \Vert _{2}^2$ | > TransE 에서 "동일 entity가 여러 relation에서 구분이 안된다"는 단점을 TransH에서 hyperplane을 도입시킴으로써 해결. ### Contextual Word Reprentation Text 정보를 임베딩. 둘다 Transformer 기반의 모델. (자세한 설명 생략) - [BERT, NAACL'19](https://arxiv.org/abs/1810.04805) - [USE, ICLR'19](https://arxiv.org/abs/1804.07461) ## Results ### Dataset 비교적 적은 데이터셋. 참고할 점은 train, test 셋을 나눌때, positive 비율을 train과 동일하게 나눔. ### Protocol [TestRating](https://dl.acm.org/doi/10.1145/2043932.2043996) strategy 사용. 각 유저별로 테스트 셋에 있는 rating만 예측. ranking을 구할때는 예측한 평점들을 sorting하여 구함. > **비평:** 이 방법을 사용하면 topk 보다 test 아이템의 수가 적으면 무조껀 ranking안에 포함되고, 순서 맞추기 싸움이 됨. 기본적으로 ndcg가 높음. > > ### Performance | error-based | ranking-based | | ------------------------------------------------------------ | ------------------------------------------------------------ | | ![image](https://user-images.githubusercontent.com/38134957/165453712-4c0144d4-9802-4c9b-8ac9-4bc9578647c4.png) | ![image](https://user-images.githubusercontent.com/38134957/165453719-41a29bbd-3260-446f-8d0d-df40f7293eaf.png) | | ![image](https://user-images.githubusercontent.com/38134957/165453712-4c0144d4-9802-4c9b-8ac9-4bc9578647c4.png) | ![image](https://user-images.githubusercontent.com/38134957/165454052-433ede9d-1b49-4a8f-bc79-51a69dfe878a.png) | - TransE 와 TransH의 우위는 domain 에 따라 다르다. - 논문 제목에서 강조하듯 Together is better. Collaborative 방법과 content방법의 시너지 효과. - concatenate 방법은 Feature based 방법이 더 효과적. [Open benchmark - Movielens 1M](https://paperswithcode.com/sota/collaborative-filtering-on-movielens-1m?metric=nDCG%4010) 위의 오픈 벤치 마킹 정보에 의한 nDCG@10 Score와는 다른 test evaluation 프로토콜을 사용하였기 때문에 참고 부탁드립니다. ## Conclusion - user, item 임베딩을 얻는 두가지 hybrid 방법(entity, feature-based)을 제시하였습니다. - 모델 architecture가 simple하여 sota 모델을 쉽게 적용 가능할 수 있고 성능도 우수합니다. ### Weak points - CF 기반 모델에서 interaction 정보만 사용할 거면 굳이 graph model을 쓸 필요는 없을 것 같습니다. CF Sota를 넣어도 될 것 같습니다. > 저자는 이후에 knowledge graph정보를 추가로 넣어 볼 예정이라고하였는데 baseline으로 사용할 big picture?... > > attention 매커니즘도 적용해 볼 것이라고 했는데, 왜 안해봤을까.. 분명해봤는데 성능이 안좋은것이었을까?.. 하는 의문이 있었습니다. - Test protocol로 TestRating 기법을 사용했는데, 이 방법은 ranking 비교에는 좀 맞지 않은 설정입니다. 차라리 leave-one-out 을 사용하는게 좋을것 같습니다. ================================================ FILE: paper_review/recsys/recsys2021/Top-K Contextual Bandits with Equity of Exposure.md ================================================ # Top-K Contextual Bandits with Equity of Exposure - Paper : - Authors : Olivier Jeunen, Bart Goethals - Reviewer : charlie.cs - Topics - [#Algorithmic_Advances](../../topics/Algorithmic%20Advances.md) - [#Bandits_and_Reinforcement_Learning](../../topics/Bandits%20and%20Reinforcement%20Learning.md) - [#RecSys2021](RecSys2021.md) ## Summary - "equity of exposure" principle 이 어떻게 추천을 위한 top-K contextual bandit의 문제에 적용될 수 있는지 조사(investigate)한 논문입니다. - equity of exposure: 동일한 relevance를 가진 아이템들은 동일한 노출이 있을 것을 기대하게 됩니다.(_items of equal relevance should receive equal exposure in expectation_) - 기존 추천 시스템의 사용자 중심 utility(click or relevance)에 대한 최적화 방식은 시스템 내 다른 관계자(stakeholders)들에겐 악영향을 끼칠 수 있습니다. - 예시) 음악 스트리밍, 음식 배달, e-commerce, 그리고 viewtab - top-K contextual bandits 추천에서 relevance-fairness trade-off 문제를 다룰 수 있는 EARS (Exposure-Aware aRm Selection) 알고리즘을 제시하였습니다. - model-agnostic algorithm이라 기존 bandit system에 적용이 가능합니다. ## Approach ### Intuition - 사용자마다 추천 결과에 적용된 diversify의 반응이 다르며, 랜덤한 추천에 대해서 얼마나 열려(openness)있는지의 정도 또한 다양하다는 것을 관찰한 연구가 있습니다. - _Investigating Listeners’ Responses to Divergent Recommendations. R. Mehrotra, et al. RecSys' 20_ - 이를 통해 단순히 모든 사용자에게 relevance-fairness의 trade-off 정도를 동일하게 적용하기 보다는 특정 유저 군에 한하여 적용하면 좋을 수 있습니다. - 예시) good choice for _diverse_ and _average_ users, but worse for _focused_ users. - ![image](https://s2.loli.net/2021/12/14/SAWGsy6zX3rC5aP.png) - x-axis: top-12 items for a given user. - y-axis: the probability of relevance over these items for that user. ### Exposure-Aware aRm Selection (EARS) - 아이템이 클릭될 확률 `P(C)` 는 사용자가 이 아이템이 연관 있다고 고려할 확률 `P(R)`과 그 사용자에게 노출될 확률 `P(E)` 로 factorize될 수 있습니다. - - 그리고 fairness of exposure을 목적하는 알고리즘은 다음과 같은 두 조건부 확률 분포 간 statistical divergence, 즉 disparity를 최소화하는 것으로 볼 수 있습니다.: `D(P(A|R); P(A|C))` - 본 논문에서는 f-divergences로 Hellinger distance를 사용합니다. - EARS algorithm Figure - - Default bandit 알고리즘으로 logistic regression thompson sampling을 사용합니다. - _An Empirical Evaluation of Thompson Sampling. L. Li, et al. NIPS' 11_ - EARS의 목적은 최대 ε 만큼의 expected clicks을 잃으면서 disparity를 최소화하는 것입니다. - Algorithm 4.(3)의 greedy policy에서 얻을 수 있는 추천 결과에 diversifying(shuffling)을 적용했을 경우(4.(4)의 equity policy), 최대 (1 - ε) * 100 % 만큼의 expected clicks 을 보존하는 선까지 disparity를 최소화합니다. - In experiments, `ε={0.01, 0.025, 0.05, 0.1}` - shuffle 방식은 random shuffling - 위에서 설명한 ε 조건을 만족할 수 있을 때까지 K값을 감소시키면서 shuffle을 진행합니다. - Why? 상위 추천 결과에서 shuffle을 진행해야 expected clicks 손해가 적고, 그에 따른 disparity 감소가 크기 때문입니다. ## Results ([github](https://github.com/olivierjeunen/EARS-recsys-2021)) - Real-world data from the Deezer music streaming platform - Relevance information between 862 playlists (items) and 974,960 users. - Users are represented by a dense 97d feature vector. - 추천 결과 수: top- `K`=12 - 매 round 마다 사용자를 20,000명 복원 추출하여 추천 결과 제공하고, batch로 parameter를 업데이트합니다. - EARS algorithm에서 tolerance parameter ε 값을 조절해가며 실험하였습니다.: `{0.01, 0.025, 0.05, 0.1}` - baseline은 greedy approach - Carousel-기반의 추천 환경 (_Personalization in Music Streaming Apps with Contextual Bandits. W.Bendada. et al. Recsys' 20_) - - 사용자가 추천 결과를 보다가 중간에 포기할 확률 abandonment parameter `γ(=0.9)` 을 포함합니다. - EARS에서 사용할 Expected clicks 값 계산 - Greedy approach - - Shuffling approach - greedy 와 동일하지만, 추천 결과를 K개까지 shuffling 한 모든 조합에 대해서 expected clicks을 일일이 구해야하므로 `O(K!)` 만큼의 비용이 소모됩니다. - 논문에서는 이를 효율적으로 계산하기 위한 방법을 제시했고, `O(K*2^(K-1)*(K-1))`까지 복잡도를 줄였다고 합니다. ### 실험 결과 ![image](https://s2.loli.net/2021/12/14/X9FnyGpm5DLSN7T.png) - Figure 4(a): EARS’ Impact on Expected Reward - `ε=0.01`일 때 greedy 보다 성능이 좋았는데, 이에 대한 이유를 두 가지로 설명합니다. - (1) EARS의 rank 방식을 통해 positional bias를 완화하여 모델이 `P(R)` 대신 `P(C)`를 학습하게 됩니다. - (2) top-K list를 랜덤으로 섞으면서 매 라운드마다 배치로 학습할 데이터가 더욱 diverse 해집니다. - Figure 4(b): EARS’ Impact on Exposure Disparity - greedy 방식이 가장 큰 disparity를 보였고, ε이 증가할수록 조금씩 감소합니다. - Figure 4(c): EARS’ Relevance-Fairness Trade-Off - Rounds 20부터 수렴까지 4(a)와 4(b)의 measurement를 plot - expected clicks과 expected disparity의 linear한 관계를 확인할 수 있었습니다. - `ε=0.01`의 경우 greedy 방식에 비교했을 때, expected reward 증가와 disparity 감소를 보입니다. ## Conclusion - 컨텐츠의 노출에 따라 수익이 발생하는 환경이면 이와 관련된 이슈가 있을 것 같다는 생각이 들었습니다. - 제안된 EARS 알고리즘은 cost가 높고, 단순 랜덤 셔플 방식이라 실제로 적용하기는 좋아보이지 않았습니다. (K 또한 낮았음) - 다만, 사용자에 따라 다양화가 적용되는 정도가 달라져야 한다는 insight를 얻을 수 있어서 좋았습니다. ================================================ FILE: paper_review/recsys/recsys2021/Toward Unified Metrics for Accuracy and Diversity for Recommender Systems.md ================================================ # Toward Unified Metrics for Accuracy and Diversity for Recommender Systems - Paper : - Authors : Javier Parapar, Filip Radlinski - Reviewer : iggy.ll - Topics - [#Metrics_and_Evaluation](../../topics/Metrics%20and%20Evaluation.md) - #Diversity - [#RecSys2021](RecSys2021.md) ## Summary ## Approach ### 왜 다양성이 중요한가 추천 시스템을 평가하는 방법은 대부분 Information Retrieval (IR)에서 가져왔다고 생각합니다. NDCG를 비롯한 랭킹 메트릭도 마찬가지인데, 추천 시스템에서 고민하던 요소는 대부분 IR에서 비슷하게 고민했던 것들이지만, 디테일한 부분에서 다른 점이 많이 발생합니다. ### Diversity에 대한 대한 요구 추천 시스템뿐만 아니라, IR에서도 다양성은 중요한 metric 중 하나인데, 이는 주로 Ambiguity 때문입니다. 검색 엔진이 "재규어"라는 입력을 받을 경우 자동차 브랜드와, 고양잇과 동물에 대한 문서를 모두 찾아주어야 하고, 이러한 Ambiguity가 추천 시스템에서는 유저의 취향에 대응됩니다. 유저는 대체로 여러 취향을 가지고, 추천의 결과가 한 가지 종류의 아이템으로만 이루어져 있다면 추천이 불완전하다고 생각할 것입니다. 유저가 로맨스 영화와 호러 영화를 둘 다 좋아한다고 했을 때, 로맨스 영화만 추천하는 추천 모델은 불완전한 모델입니다. ### Novelty에 대한 요구 추천은 대부분 list 형태로 주어지며, 유저는 list를 좌에서 우로, 혹은 위에서 아래로 탐색하는 경우가 일반적입니다. $N$개의 추천 아이템이 주어진 경우, $k \leq N$인 $k$을 유저가 클릭한 경우, 유저가 $1, \dots, k-1$까지 보지 않았던 이유가 분명히 존재할 것이며, 이는 rank가 $k$ 미만인 아이템이 유저가 relevant하지 않았다고 판단했기 때문일 가능성이 높으며, $i_1, i_2, \dots, i_{k-1}$는 서로 닮아 있을 가능성이 높습니다. 이를 대비해서, $k$번째 아이템은 이전의 아이템과 충분히 다른 아이템인 게 더 좋을 수도 있습니다. 즉, Novelty는 추천 시스템이 실패했을 때를 대비한 보험이라 생각할 수 있습니다. OTT 영화 추천을 예시로 들면, 유저가 로맨스를 좋아할 것이라 판단한 후에 로맨스 영화 5개를 추천했을 때, 추천이 성공적이었다 해도 유저는 랭크 상위의 영화 1-2개 정도밖에 보지 않을 것인데, 추천에 임의로 다른 영화를 한 두개 섞는다고 하면, 이 판단이 틀렸다고 하더라도 한 번의 기회를 더 얻을 수 있을 것입니다. ### Diversity와 Novelty를 고려한 Metric $\alpha\beta$-nDCG #### Notation - $\alpha_\phi$: 토픽(취향이나 선호도, 이하 토픽이라 칭함) - 유저는 topic의 집합을 선호도로 갖고 있으며 $p(\alpha_\phi \vert u)$는 유저가 그 토픽을 선호할 확률을 나타낸다. - 아이템 또한, topic의 집합을 갖고 있으며, 이 논문에서는 아이템의 토픽은 알려져 있다고 가정한다. 특정 유저 $u$가 rank $S \in \{1, 2, \dots, n\}$에 있는 item $i$를 선호할 확률은 $$ p(R=1 \vert u, i) = 1 - \prod_{\phi} [1 - p(\alpha_\phi \vert u, i) p(\alpha_\phi \vert u, S)] $$ 로 정의된다. #### Diversity Consideration $p(\alpha_\phi \vert u, i)$ (Diversity Term)는 Diversity를 고려한 식이다. 기존 ndcg에서 item 단위의 hit을 고려하는 것과는 별개로, topic 단위의 hit을 반영합니다. $p(\alpha_\phi \vert u, i)$는 그 유저가 유저의 선호도 $\alpha_\phi$를 만족하는 정도를 나타내는데, 이를 별도로 정의하는 이유는 같은 장르이더라도, 유저가 특정 아이템을 선호할 수 있고 선호하지 않을 수 있기 때문입니다. 예를 들어서, *밴드 오브 브라더스*는 좋아하지만 *오! 인천*은 그다지 좋아하지 않는 경우가 있습니다. $$ p(\alpha_\phi \vert u, i) = \begin{cases} 0 & \text{아이템의 장르가 다름} \\ \alpha & \text{유저가 그 장르를 좋아하는데, 유저가 클릭하지 않은 경우} \\ \beta & \text{유저가 그 장르를 좋아하고, 유저가 그 아이템을 클릭한 경우} \\ \end{cases} $$ Diversity Term은 유저가 그 아이템을 좋아하거나, 그 장르를 선호하거나에 따라 score에 대해 차등을 주는 식으로 모델링됩니다. 간단히 요약하자면, 기존 nDCG에서는 유저가 실제로 클릭한(relevant) 대해서만 추천을 준다고 가정하는 반면, 유저가 좋아하는 장르에 대한 추천에도 약간이나마 선호도를 부여합니다. $\alpha, \beta$에 대한 정의는 논문에서 자세히 되어있지 않지만, $p(\alpha \vert u), p(\alpha \vert i)$에 따라 적절히 정의될 수 있을 것 같습니다. ### Novelty Consideration $p(\alpha_\phi \vert u, S)$ (Novelty Term)는 유저가 특정 위치 $S\in \{1, 2, \dots, n\}$에 존재하는 추천에 대해 얼마나 만족하는지를 나타내는 지표입니다. 이를 별도로 모델링하는 이유는, 유저가 상위 랭크 $1, 2, \dots, S-1$에서 특정 토픽 $\alpha_\phi$를 봤다면, rank $S$에서 같은 토픽 $\alpha_\phi$인 아이템을 보더라도 만족도가 그리 높지 않을 것이라는 가정을 포함하고 있습니다. $$ p(\alpha_\phi \vert u, S) = p(\alpha_\phi \vert u) \prod_{j = 1}^S [1-p(\alpha_\phi \vert u, i_j)] $$ 유저가 이전에 본 항목에 같은 토픽의 아이템이 많이 들어있을 경우, Novelty Term은 감소한다. 새로운 토픽의 아이템이 추천될 경우, 이 값은 증가한다. 증가폭은 유저가 그 토픽을 선호할 확률 $p(\alpha_\phi \vert u)$에 비례합니다. ### Axioms for Diverse Ranking Evaluation 논문에서 추천 리스트와, 그 추천 리스트에 대한 평가 메트릭에 관한 공리를 정의해놨는데, 논문에서 8가지 공리가 정의되어 있지만, 거칠게 요약하자면 다음과 같습니다. 1. 두 아이템의 토픽이 완전히 같다고 가정하면, 유저는 relevancy가 더 높은 아이템이 추천되는 추천 리스트를 선호한다. 2. 유저가 좋아하는 아이템이 추천 리스트에 포함될 경우, 이 아이템이 더 상위 랭크에 있는 추천 리스트가 더 하위 랭크에 있는 추천 리스트보다 선호된다. 3. 한 추천 리스트에서 같은 토픽이 너무 자주 추천되는 경우, 이 토픽이 유저가 선호하는 토픽이라 할 지라도 유저가 좋아하지 않는 토픽의 아이템을 더 선호할 수 있다. 4. 유저는 본 적 없는 아이템을, 이미 싫어하는 아이템보다 더 선호한다. ## Conclusion - 구현 후, 오프라인 메트릭은 구현이 제대로 되어 있는 지만 확인 한 이후 온라인 평가가 실전이다 이런 느낌으로 온라인에 배포해던가, 혹은 IPS같은 방법으로 온라인 평가를 오프라인으로 가져오는 방법만 알고 있었는데, 유저 행동에 대한 합리적인 가정과 모델링을 통해 더 좋은 offline metric을 만드는 일도 좋은 방향일 수 있구나 하는 생각이 들었습니다. - Novelty가 중요하다는 얘기만 들었었는데, 그럴 듯 한 설명을 들은 것은 처음입니다. ================================================ FILE: paper_review/recsys/recsys2021/Towards Source-Aligned Variational Models for Cross-Domain Recommendation.md ================================================ # Towards Source-Aligned Variational Models for Cross-Domain Recommendation - Paper : - Authors : Aghiles Salah, Thanh Binh Tran, Hady Lauw - Reviewer : andrew.y - Topics - [#Language_and_Knowledge](../../topics/Language%20and%20Knowledge.md) - #Cross-Domain - [#RecSys2021](RecSys2021.md) ## Summary - Cross Domain 추천이란? - 기존 data sparsity로 힘든 콜드 유저의 추천을 위해 다른 서비스에서 해당 유저의 소비 이력을 쓰는 추천입니다. (예. 유저의 영화 소비 이력으로 유저한테 책 추천) - 기존에 있던 방법은 아래와 같습니다. - matrix factorization jointly factorizes rating matrices from various domains with a shared user-latent space - transfer learning: a mapping between the source and target models or infer user representations that are domain-invariant - 이 논문에서 제안하는 방법은 다음과 같습니다. - Variational AutoEncoder (VAE)를 사용하는 기법 - VAE를 source domain에서 학습 시켜서 target domain에 preference modeling을 한다. ## Approach ### VAE? - [참고 링크](https://towardsdatascience.com/understanding-variational-autoencoders-vaes-f70510919f73#:~:text=In%20a%20nutshell%2C%20a%20VAE,to%20generate%20some%20new%20data.) ![image](https://user-images.githubusercontent.com/38134957/165147766-409ac332-6425-456d-bb3c-c002d8ce3ba5.png) ![image](https://user-images.githubusercontent.com/38134957/165147773-912b06b2-8965-4a77-8409-c019279351cd.png) ![image](https://user-images.githubusercontent.com/38134957/165147781-c526bc79-2acb-4a98-97f4-bb862f654f36.png) ### Why VAE? - Matrix Factorization의 limitation인 linear nature가 아닌 non-linear recommendation 모델을 써보기 위해 VAE를 사용할 수 있습니다. - non-linear recommendation 모델은 sparse data에 overfitting 하기 쉬운 문제는 있습니다. - VAE가 다른 논문들에서 성능이 좋은 측면도 있습니다. ### Source Domain - VAE의 디코더랑 상응하는 부분 (theta 학습) - VAE의 인코더랑 상응하는 부분 (phi 학습) - Evidence Lower BOund (ELBO) -> maximize: - a given input x, we want to maximise the probability to have x̂ = x when we sample z from the distribution q*_x(z) and then sample x̂ from the distribution p(x|z) - KL divergence: staying close to the prior distribution ( ) ### Target Domain - Rigidly Aligned VAE (RA-VAE): - source domain data held fixed while training target domain data - Softly Aligned VAE (SA-VAE): ### 논문에서 쓰는 모델들 (baseline 포함) ![image](https://user-images.githubusercontent.com/38134957/165148112-f73f3f06-1b36-435c-b184-e7487a715429.png) ## Results - Amazon, Douban 데이터셋에서 실험하였습니다. - 오프라인 실험: 10%, 20%, 30% 랜덤하게 테스트 셋으로 ndcg, recall 계산 (target domain에서 콜드 유저로 인식) ![image](https://user-images.githubusercontent.com/38134957/165148128-b304551b-8736-48e7-a162-c3cba55b6e91.png) ![image](https://user-images.githubusercontent.com/38134957/165148172-dae9a356-7f06-48d5-a120-0d340e990e05.png) ![image](https://user-images.githubusercontent.com/38134957/165148184-f53e89ab-c1d1-48b2-84d9-7f01bda0904e.png) tldr; RA-VAE, SA-VAE가 베이스라인보다 더 성능이 좋음. baseline에서는 EMCDR이 제일 성능이 좋음. ### 모델의 성능이 유저 활동성에 따라 달라지나? (robustness of the model) 테스트 셋은 10%으로. ![image](https://user-images.githubusercontent.com/38134957/165148349-b9041eb3-ad24-4cf1-b6c3-496c4c10c397.png) tldr; 모든 그룹에 성능 좋아지고, 30회 이하 유저 그룹들에 베이스라인보다 더 성능이 좋아졌다 한다. ## Conclusion - VAE 기반 cross-domain 추천을 할때 모델을 어떻게 짜는지가 중요한걸 볼수 있다. (e.g. 모델 architecture에서 sparsity issue를 줄인다던지) - 기존에 쓰인 deterministic methods과 달리 VAE를 쓴 probabilistic approach도 cross-domain 추천에 잘 쓰일수 있다. ================================================ FILE: paper_review/recsys/recsys2021/Transformers4Rec- Bridging the Gap between NLP and Sequential & Session-Based Recommendation.md ================================================ # Transformers4Rec- Bridging the Gap between NLP and Sequential & Session-Based Recommendation - Paper : - Authors : Gabriel de Souza Pereira Moreira, Sara Rabhi, Jeong Min Lee, Ronay Ak, Even Oldridge - Reviewer : marv.20 - Topics - [#Language_and_Knowledge](../../topics/Language%20and%20Knowledge.md) - #Semi-Supervised_Learning - #Sequential_Recommendation - [#RecSys2021](RecSys2021.md) ## Summary - NLP와 sequential / session 기반 추천 방식이 유사한데, 최근 NLP의 수많은 모델 구조들을 바로 추천에 적용할 수 있게끔 huggingface transformers 라이브러리 기반의 transformer4rec 라이브러리를 공개하였습니다. Huggingface의 모델 구조를 적용, 튜닝하는 것으로 2개의 2021 이커머스 챌린지에서 우승할 수 있었습니다. - casual language modeling에서 자주 쓰였던 학습방법들인 masked LM, permutation LM, replacement token detection 방법론들을 비교하여 보았습니다. - 사이드 정보를 결합하여 추천해보았습니다. ## Approach ### NLP 모델들과 Sequential / Session 기반 추천의 관계 ![image](https://user-images.githubusercontent.com/38134957/165446726-6ebf29d3-91c8-4ddd-a968-8e2dfcb8ff36.png) ### LM 학습기법들 비교 (CLM, MLM, PLM, RTD) ![The possible transformation of MLM and PLM, where w i and p i represent token and position embeddings. [M ] is the special mask token used in MLM. The left side of MLM (a) can be seen as bidirectional AR streams (in blue and yellow, respectively) at the right side. For MLM (b) and PLM (c), the left sides are in original order, and the right sides are in permuted order, which are regarded as a unified view.](https://www.researchgate.net/profile/Rui-Wang-17/publication/341369190/figure/fig4/AS:890933465849856@1589426499052/The-possible-transformation-of-MLM-and-PLM-where-w-i-and-p-i-represent-token-and.png) - causal language model (CLM) : next token prediction - masked language model (MLM) : masked token prediction - permuation languagem model (PLM) : permutation + next token prediction ### Transformer4Rec 구조 ![image](https://user-images.githubusercontent.com/38134957/165446737-bfbd5f4a-619f-46f8-9753-ab0f1c925eb5.png) - 데이터 전처리, 피처 엔지니어링 : NVTabular - sequential reco를 위한 ops : grouping time-sorted interactions, truncating first/last N interactions - Meta architecture - feature processing module : sparse categorical, continuous -> normalized and combined - sequence masking module : CLM, MLM, PLM - prediction head module : tasks (item prediction, sequence-level prediction) ## Results - RQ1. 다양한 모델 아키텍쳐 실험 결과 - RQ2. 다양한 학습 방식 실험 결과 - RQ3. item embedding을 다양한 feature들의 결합으로 변형 ![image](https://user-images.githubusercontent.com/38134957/165446761-2f16c809-ea69-44a5-9169-e6570ba8c84d.png) ## Conclusion - sequential recommendation이 NLP의 발전을 따라가기만 하는 형태여서 비판적이었는데 이를 실용적으로 풀어낸 게 인상깊었습니다. - winning solution은 존재하지 않았습니다. 오히려 그렇기 때문에 데이터셋이나 환경에 따라 다양한 모델을 자유롭게 실험해볼 수 있어야 하고, 그런 의미에서 이 논문의 가치가 있다고 생각합니다. - 사이드 정보를 넣는 방식이 인상 깊었습니다. 상당히 간단해서 어느 구좌 / 메타이던지 사용해볼 수 있을 것 같습니다. ================================================ FILE: paper_review/recsys/recsys2021/Values of Exploration in Recommender Systems.md ================================================ # Values of Exploration in Recommender Systems - Paper : - Authors : Minmin Chen, Yuyan Wang, Can Xu, Ya Le, Mohit Sharma, Lee Richardson, Su-Lin Wu, Ed Chi - Reviewer : andrew.y - Topics - [#Metrics_and_Evaluation](../../topics/Metrics%20and%20Evaluation.md) - [#RecSys2021](RecSys2021.md) ## Summary - 강화학습 기반 추천 시스템에서 exploration이 어떤 영향을 미치는지 알아보고 user exploration을 추가하는 methodology를 소개한 논문입니다. - Accuracy, diversity, novelty, serendipity를 측정하고, 오프라인과 온라인 실험을 통해 exploration의 영향을 분석하였습니다. ## Approach ### 배경 논문은 REINFORCE 추천 시스템을 베이스로 사용합니다. ([참고 논문](https://arxiv.org/abs/1812.02353)) - 용어 정리 - 유저의 히스토리 up to time t, A_t = set of item recommended at time t, a = item user interacted with, r = reward - u_s_t = RNN_theta(H_t) → latent user state (s_t = user state) - v_a = embedding of item a - Softmax Policy over item corpus given the latent user state - 여기서 policy parameters θ가 밑의 수식을 (expected culumative reward) 최대화 하게 학습을 합니다. - 이 학습된 softmax policy를 사용해서 time t에 set of recommendation A_t생성해서 A_t를 유저한테 추천합니다. ### User Exploration 활성화 하는 방법 #### Entropy Regularization policy π_θ (·|s)를 entropy가 높은 output distribution으로 유도해서 유저 관심사 밖 콘텐츠를 추천하는걸 더 활성화 시킵니다. (user exploration 활성화) - entropy는 negative reverse KL divergence of the conditional distribution π_θ (·|s) to the uniform distribution. (uniform distribution과 얼마나 비슷한지) - entropy를 높이면 높일수록 학습된 policy는 uniform distribution이 된다. (선호도와 상관 없이 공평하게 추천된다) #### Intrinsic Motivation and Reward Shaping - 위 policy 수식의 r(s,a) reward function (유저 s에게 a를 추천하는 immediate value)에서 intrinsic reward를 추가합니다. - 유저가 소비한 아이템의 리스트가 있을때 유저가 막 소비한 아이템이 이전 아이템들이랑 많이 다르면 reward를 높게 합니다. - multiplication인 이유는 relevance를 유지하기 위해서 (R_t^e (s_t , a_t ) = 0는 계속 0)입니다. - 유저에게 더 좋은 user experience를 주는 surprising한 (과거 소비 아이템이랑 다른) 아이템에게 reward를 많이 줍니다. - unknown interest는 아이템의 클러스터가 유저가 이미 소비한 클러스터가 아닌 경우를 의미합니다. (i.e. different topic, different provider) #### Actionable Representation for Exploration - 유저가 surprising한 아이템을 소비해서 리워드를 높게 받은 상태면, 다음에는 다르게 interact할수있게 유저 피쳐에 반영을 해야합니다. - 따라서 유저 피쳐 (유저 히스토리)에 surprise랑 relevance를 추가합니다. , i_t = 1 if topic/provider cluster different, r_t (reward) > 0 (relevance) ### 측정 방법 #### Accuracy - mean average precision at K = 50 (밑의 수식에서는 j) ([참고 논문](https://www.cs.cornell.edu/people/tj/publications/yue_etal_07a.pdf)) #### Diversity - 직관적인 수식입니다. uniform에서는 sim(i,j)는 1이니까 diversity는 0, sim(i,j)가 낮으면 낮을수록 diversity가 올라가게 됩니다. #### Novelty - I(a)= − log (# users consumed item a) + const - globally 덜 popular 한 아이템 (모두가 좋아하지 않는 아이템)을 학습해서 추천하면 더 novel하다고 봅니다. #### Serendipity - 위에 언급한 surprise + relevance를 둘다 챙기면 1, 아니면 0로 둡니다. - 유저가 소비하는 주류 아이템이 아닌 관심있는 아이템이 있는지 quanitify 하는 metric입니다. #### Long Term User Experience - 결국엔 exploration이 long term user experience에는 도움이 될것인지 알려면 이거에 대한 측정 방법도 있어야 합니다. - 논문에서는 유저가 다시 서비스를 쓰는지, 그리고 활동량이 적은 유저들이 활동량이 많은 유저로 변하는지를 보고 long term user experience를 판단합니다. ## Results ### 오프라인 실험 결과 및 분석 ![image](https://user-images.githubusercontent.com/38134957/165145163-284be0f7-1b83-4371-9668-5c86004ab50a.png) - 무슨 데이터셋을 썼는지 정확히 언급은 하고 있지 않습니다. ("a billion user trajectories from a commercial recommendation platform") - item space = most popular 10 million items in the past 48 hours on the platform - 99% training, 1% validation #### Entropy Regularization - as α ↑, diversity ↑, novelty ↑ at cost of accuracy ↓ + serendipity ↓ (due to loss of relevance) #### Intrinsic Motivation - 위의 c를 조정 가능하지만 이 페이퍼에서는 | I_t | 를 조정하기로 하였습니다. - baseline 대비 diversity ↑ at cost of accuracy ↓, serendipity ↑, novelty - 의 성능을 보여주었습니다. - d = 1, 7, 365에서는 큰 차이 없었습니다. - In the datasets, the percentage is reduced from 36% → 19% → 12% when the window size is extended from 1 → 7 → 365 days. (서프라이징 한 state-action pair %) #### Actionable Representation - actionable representation만으로는 baseline과 비슷해서 intrinsic motivation이랑 같이 써야합니다. - intrinsic motivation 대비 serendipity ↑ - mean input gate activation value차이 → RNN이 surprising event때 더 큰 업데이트를 합니다. → 유의미한 차이가 있습니다. ### 온라인 실험 결과 및 분석 - 오프라인 실험과 데이터 크기는 비슷합니다. - "a industrial recommendation platform serving billions of users", "a corpus of 10 million" ![image](https://user-images.githubusercontent.com/38134957/165145338-547f5d84-66fc-4269-a0ee-f578160d2662.png) - entropy regularization (red: α = 0.1, blue: α = 0.5) - intrinsic motivation (d = 7, topic, c = 4) - user enjoyment improvement 어떻게 측정 했는지 안나와있습니다. - α = 0.1 → α = 0.5: lower user enjoyment improvement. 따라서 diversity ↑ novelty ↑은 better user experience를 가져오지 못한다고 볼 수 있습니다. - Figure 3b, 3c에서는 user enjoyment이 improve했고 (baseline 대비) 오프라인 분석과 합쳐서 분석하면 serendipity ↑ 이 user experience를 더 좋게 만든다고 볼 수 있습니다. - Returning 유저도 더 많아졌습니다. #### Long Term User Experience ![image](https://user-images.githubusercontent.com/38134957/165145476-f81882da-c0b4-4e45-b800-d63528785fbd.png) - 시간이 지날수록 exploration의 효과 (유저가 새로운 "interest"를 찾는거)가 있었습니다. ![image](https://user-images.githubusercontent.com/38134957/165145485-994383d3-1a05-4d21-973e-001397e57b2e.png) - 실험 시작하기 전과 후를 비교한 a user activity level transition matrix입니다. - 저 %가 어떻게 계산되는지는 불확실합니다. (개인적으로 이해 못함) - casual → core conversion이 많았다 주장하고 있습니다. ## Conclusion - serendipity가 long term user experience에 좋은 영향을 준다는 것을 밝혔습니다. 따라서 long term user experience를 높히기 위해서는 exploration을 해야하고, exploration이 serendipitous recommendation을 잘 해줘야 합니다. ================================================ FILE: paper_review/topics/Algorithmic Advances.md ================================================ # Algorithmic Advances - [Next-item Recommendations in Short Sessions](../recsys/recsys2021/Next-item%20Recommendations%20in%20Short%20Sessions.md) - [Burst-induced Multi-Armed Bandit for Learning Recommendation](../recsys/recsys2021/Burst-induced%20Multi-Armed%20Bandit%20for%20Learning%20Recommendation.md) - [Top-K Contextual Bandits with Equity of Exposure](../recsys/recsys2021/Top-K%20Contextual%20Bandits%20with%20Equity%20of%20Exposure.md) ================================================ FILE: paper_review/topics/Applications-Driven Advances.md ================================================ # Applications-Driven Advances - [Follow the guides- disentangling human and algorithmic curation in online music consumption](../recsys/recsys2021/Follow%20the%20guides-%20disentangling%20human%20and%20algorithmic%20curation%20in%20online%20music%20consumption.md) ================================================ FILE: paper_review/topics/Bandits and Reinforcement Learning.md ================================================ # Bandits and Reinforcement Learning - [Burst-induced Multi-Armed Bandit for Learning Recommendation](../recsys/recsys2021/Burst-induced%20Multi-Armed%20Bandit%20for%20Learning%20Recommendation.md) - [Top-K Contextual Bandits with Equity of Exposure](../recsys/recsys2021/Top-K%20Contextual%20Bandits%20with%20Equity%20of%20Exposure.md) ================================================ FILE: paper_review/topics/Echo Chambers and Filter Bubbles.md ================================================ # Echo Chambers and Filter Bubbles - [I want to break free! Recommending friends from outside the echo chamber](../recsys/recsys2021/I%20want%20to%20break%20free!%20Recommending%20friends%20from%20outside%20the%20echo%20chamber.md) ================================================ FILE: paper_review/topics/Interactive Recommendation.md ================================================ # Interactive Recommendation - [The role of preference consistency, defaults and musical expertise in users’ exploration behavior in a genre exploration recommender](../recsys/recsys2021/The%20role%20of%20preference%20consistency,%20defaults%20and%20musical%20expertise%20in%20users’%20exploration%20behavior%20in%20a%20genre%20exploration%20recommender.md) ================================================ FILE: paper_review/topics/Language and Knowledge.md ================================================ # Language and Knowledge - [Transformers4Rec- Bridging the Gap between NLP and Sequential & Session-Based Recommendation](../recsys/recsys2021/Transformers4Rec-%20Bridging%20the%20Gap%20between%20NLP%20and%20Sequential%20&%20Session-Based%20Recommendation.md) - [Sparse Feature Factorization for Recommender Systems with Knowledge Graphs](../recsys/recsys2021/Sparse%20Feature%20Factorization%20for%20Recommender%20Systems%20with%20Knowledge%20Graphs.md) - [ProtoCF- Prototypical Collaborative Filtering for Few-shot Item Recommendation](../recsys/recsys2021/ProtoCF-%20Prototypical%20Collaborative%20Filtering%20for%20Few-shot%20Item%20Recommendation.md) - [Towards Source-Aligned Variational Models for Cross-Domain Recommendation](../recsys/recsys2021/Towards%20Source-Aligned%20Variational%20Models%20for%20Cross-Domain%20Recommendation.md) - [Together is Better- Hybrid Recommendations Combining Graph Embeddings and Contextualized Word Representations](../recsys/recsys2021/Together%20is%20Better-%20Hybrid%20Recommendations%20Combining%20Graph%20Embeddings%20and%20Contextualized%20Word%20Representations.md) ================================================ FILE: paper_review/topics/Metrics and Evaluation.md ================================================ # Metrics and Evaluation - [Toward Unified Metrics for Accuracy and Diversity for Recommender Systems](../recsys/recsys2021/Toward%20Unified%20Metrics%20for%20Accuracy%20and%20Diversity%20for%20Recommender%20Systems.md) - [Values of Exploration in Recommender Systems](../recsys/recsys2021/Values%20of%20Exploration%20in%20Recommender%20Systems.md) - [Accordion- a Trainable Simulator for Long-Term Interactive Systems](../recsys/recsys2021/Accordion-%20a%20Trainable%20Simulator%20for%20Long-Term%20Interactive%20Systems.md) - [Evaluating Off-Policy Evaluation- Sensitivity and Robustness](../recsys/recsys2021/Evaluating%20Off-Policy%20Evaluation-%20Sensitivity%20and%20Robustness.md) ================================================ FILE: paper_review/topics/Practical Issues.md ================================================ # Practical Issues - [Shared Neural Item Representation for Completely Cold Start Problem](../recsys/recsys2021/Shared%20Neural%20Item%20Representation%20for%20Completely%20Cold%20Start%20Problem.md) ================================================ FILE: paper_review/topics/Privacy, Fairness, Bias.md ================================================ # Privacy, Fairness, Bias - [Debiased Explainable Pairwise Ranking from Implicit Feedback](../recsys/recsys2021/Debiased%20Explainable%20Pairwise%20Ranking%20from%20Implicit%20Feedback.md) - [Mitigating Confounding Bias in Recommendation via Information Bottleneck](../recsys/recsys2021/Mitigating%20Confounding%20Bias%20in%20Recommendation%20via%20Information%20Bottleneck.md) ================================================ FILE: paper_review/topics/Real-World Concerns.md ================================================ # Real-World Concerns - [Cold Start Similar Artists Ranking with Gravity-Inspired Graph Autoencoders](../recsys/recsys2021/Cold%20Start%20Similar%20Artists%20Ranking%20with%20Gravity-Inspired%20Graph%20Autoencoders.md) - [Semi-Supervised Visual Representation Learning for Fashion Compatibility](../recsys/recsys2021/Semi-Supervised%20Visual%20Representation%20Learning%20for%20Fashion%20Compatibility.md) ================================================ FILE: paper_review/topics/Scalable Performance.md ================================================ # Scalable Performance - [Local Factor Models for Large-Scale Inductive Recommendation](../recsys/recsys2021/Local%20Factor%20Models%20for%20Large-Scale%20Inductive%20Recommendation.md) - [Reverse Maximum Inner Product Search- How to efficiently find users who would like to buy my item?](../recsys/recsys2021/Reverse%20Maximum%20Inner%20Product%20Search-%20How%20to%20efficiently%20find%20users%20who%20would%20like%20to%20buy%20my%20item%3F.md) ================================================ FILE: paper_review/topics/Theory and Practice.md ================================================ # Theory and Practice - [Negative Interactions for Improved Collaborative Filtering- Don’t go Deeper, go Higher](../recsys/recsys2021/Negative%20Interactions%20for%20Improved%20Collaborative%20Filtering-%20Don’t%20go%20Deeper,%20go%20Higher.md) - [Matrix Factorization for Collaborative Filtering Is Just Solving an Adjoint Latent Dirichlet Allocation Model After All](../recsys/recsys2021/Matrix%20Factorization%20for%20Collaborative%20Filtering%20Is%20Just%20Solving%20an%20Adjoint%20Latent%20Dirichlet%20Allocation%20Model%20After%20All.md) ================================================ FILE: paper_review/topics/Users in Focus.md ================================================ # Users in Focus - ["Serving Each User"- Supporting Different Eating Goals Through a Multi-List Recommender Interface](../recsys/recsys2021/"Serving%20Each%20User"-%20Supporting%20Different%20Eating%20Goals%20Through%20a%20Multi-List%20Recommender%20Interface.md) ================================================ FILE: presentations/README.md ================================================ # 발표 자료 모음 ================================================ FILE: programming_assignments/beale_ciphers/README.md ================================================ # 빌 암호(Beale Ciphers) 해독 문제 출제 및 검수: 한상덕(leo.han) > 이 문제로 영입을 진행하며 지원자분에게 드렸던 인터뷰 질문은 [interview.md](interview.md)에 있습니다. 문제를 풀어보시고 이 문서도 확인해보세요. ## 문제 사건은 1885년 한 조그마난 팜플렛이 버지니아에서 발견되면서부터 시작된다. 이 팜플렛에는 빌이라는 이름의 한 남자의 이야기와 세 개의 암호 메세지가 담겨있었다. 이야기의 내용은 1820년 빌이라는 남자가 버지니아 베드포드 카운티 한 비밀의 장소에 보물로 가득 찬 수레 두 대를 묻었다는 것이다. 이 남자는 여관 주인에게 작은 열쇠 상자를 맡기고 마을을 떠난 뒤 다시는 나타나지 않았다. 수 년 뒤 여관 주인은 열쇠 상자를 열었고 세 개의 암호화된 메세지를 발견한다. 그는 평생 암호를 해독하지 못하고 1863년 죽기 전에 친구에게 암호를 준다. 그로부터 20년 후 이 이름 모를 친구는 세 개의 암호 중 첫 번째와 두 번째 암호를 해독하는데 성공한다. 해독된 메세지에는 빌이 묻은 금은보화들의 존재와 위치가 담겨있었다. 마지막 메세지에는 세부 위치와 그 보물들이 누구의 소유인지 밝혀져 있다고 한다. 수십 년간 많은 사람이 암호 해독을 시도해보았고 보물을 찾아 나섰지만 모두 실패했다. ![빌의 두번째 암호](https://user-images.githubusercontent.com/38134957/205591146-88a80e11-1dee-4d33-8305-40ef6f13d6f1.png) 빌의 두번째 암호 ![빌의 세번째 암호](https://user-images.githubusercontent.com/38134957/205591160-5b7a7fa5-964f-443b-a5bf-01d9dd093420.png) 빌의 세번째 암호 그러던 중 카카오 추천팀 레오는 빌의 다른 암호문 중에서 세 번째 암호를 해결하기 위한 단서가 첫 번째 암호와 두 번째 암호에 존재한다는 사실을 발견했다. 첫 번째 암호문을 행렬로 표현했을 때 k x k 크기의 정방 블록부분행렬들 중 한 블록부분행렬 X와 X와 같은 크기의 두 번째 암호의 블록부분행렬들 중 한 블록부분행렬 Y가 세 번째 암호를 해독하는데 중요한 역할을 한다는 사실을 발견한 것이다. 레오는 세 번째 암호문의 k x k 크기의 블록부분행렬 집합 Q의 원소 중 의미있는 원소의 집합 S를 다음과 같이 표현하였다. $$\large S = \\{ Z | XZ = Y, Z \in Q \\}$$ 레오는 집합 S의 크기가 클수록 암호를 해독할 가능성이 높아진다고 생각하였지만 모든 경우를 전부 해보는 것은 시간상 힘들기 때문에 X, Y 그리고 세 번째 암호문 n×m 행렬 R이 주어졌을 때 |S|를 구하는 프로그램을 구현하고자 한다. ## 조건 1. 입력제한 - C++, Java : 1 ≤ k ≤ 100, k ≤ n, m ≤ 150 - Python : 1 ≤ k ≤ 40, k ≤ n, m ≤ 60 2. k×k의 두 행렬의 곱 연산은 일반적인 방법으로 O(k^3)에 구현이 가능하고 가장 빠른 방법은 O(k^2.373)에 구하는 방법으로 알려져 있다. 하지만 위 두 가지 방법론으로 위 문제를 해결하기에는 적절하지 않기 때문에 다음 방법론을 이용하여 구현해야 한다. - 링크: 3. Standard Library만 사용해야 한다. (ex Python 2, Python 3 - numpy 모듈 허용하지 않음) 4. 제한시간 C++ 1.5초, Java 2.5초, Python 5초 5. 표준 입출력 사용 6. matrix 연산 과정은 int 범위 안에서 계산할 수 있습니다. ## 입력 첫 번째 줄에 테스트 케이스 T(1 ≤ T ≤ 10)가 입력으로 주어진다. 두 번째 줄부터 테스트케이스가 시작된다. 각 테스트 케이스의 첫 번째 줄에 공백을 기준으로 n, m, k가 주어진다. 그 다음줄부터 k개의 줄에는 X의 원소가 k개씩 주어진다. 이어서 k개의 줄에는 Y의 원소가 k개씩 주어지고 그 다음에 n개의 줄에 R의 원소가 m개씩 주어진다. ## 출력 각 테스트케이스마다 |S| 를 한 줄에 하나씩 출력한다. ## 예제 |입력 예제|출력 예제| |:---|:---| |2
1 4 1
2
6
3 4 3 3
3 4 2
1 0
0 1
1 1
0 1
1 1 1 1
0 1 0 1
1 3 1 -1|3
2











| ================================================ FILE: programming_assignments/beale_ciphers/interview.md ================================================ # 빌 암호(Beale Ciphers) 해독 인터뷰 질문 > [▶︎ 빌 암호(Beale Ciphers) 해독 문제로 돌아가기](README.md) 빌 암호(Beale Ciphers) 해독 문제로 영입을 진행하며 지원자분에게 드렸던 인터뷰 질문과 예시 답변을 모아놓았습니다. ## 질문 1 Freivalds 알고리즘의 목적 및 동작에 대해 설명해주세요.
예시 답변 - N x N 행렬 A, B, C에 대해서, AB = C 인지 여부를 빠르게 계산하기 위한 확률 기반 approximate 알고리즘
## 질문 2 빌 암호 해독 문제를 freivalds 알고리즘을 이용하여 해결 했을 경우 시간 복잡도는? 그리고 시간복잡도 그렇게 되는 이유(증명)를 설명할 수 있겠는가?
예시 답변 - O(kN^2), k는 frealids 알고리즘 반복 횟수 - 간혹 kN^2 이 아니라 반복횟수 k를 상수 취급해서 무시하는 경우가 있는데, 정확하게 집고 넘어가도록 하자. - 문제를 풀 때 증명을 읽지 않고 문제를 해결할 수 있기 때문에 증명 내용에 대해서는 추가 점수 정도로 조정
## 질문 3 Freivalds 알고리즘의 오답률은?
예시 답변 ≤ 1/(2^k)
## 질문 4 Freivalds 알고리즘 반복 횟수 k는 문제에서 몇 번 시도하였는가? 왜 그렇게 값을 정하였는가? 만약 K 값을 더 최적화해보라고 한다면, 어떻게 접근하겠는가? 필요한 가정은 직접 추가해도 무방하다.
예시 답변 - 시스템이 요구하는 정확도가 xx 라면 xx 를 초과하도록 k 를 정하겠다. - 시스템의 수행시간이 허용하는 한도 내에서 가장 높은 k 를 실험적으로 찾겠다. - 정확도와 수행시간 간에 트레이드오프임을 인지하는지 판단
================================================ FILE: programming_assignments/beale_ciphers/solution/solve.cpp ================================================ #include #include #include const int K = 102; const int N = 302; const int M = 302; int X[K][K], Y[K][K], Q[N][M], _C[K][K]; int v[K], t[K], q[K]; bool freivald(int X[][K], int Y[][K], int Q[][M], int x, int y, int n, int m, int k){ int T = 10; while(T--){ for(int i=0; i 0 ) { for(int i=0; i 10: break count = count + 1 return True def solve(): n, m, k = map(int, input().split()) X = [] Y = [] Q = [] v = [0 for i in range(k)] t = [0 for i in range(k)] q = [0 for i in range(k)] for i in range(k): X.append(map(int, input().split())) for i in range(k): Y.append(map(int, input().split())) for i in range(n): Q.append(map(int, input().split())) ans = 0 for i in range(n - k + 1): for j in range(m - k + 1): if freivald(X, Y, Q, i, j, n, m, k, v, t, q): ans = ans + 1 print(ans) def test(): T = map(int, input().split())[0] for i in range(T): solve() if __name__ == '__main__': test() ================================================ FILE: programming_assignments/beale_ciphers/testcase/README.md ================================================ # 테스트 케이스 - Python2, Python3의 경우 small test case까지만 채점 - C++, Java의 경우 small + large test case로 채점 ================================================ FILE: programming_assignments/beale_ciphers/testcase/large/test1.in ================================================ 1 150 150 100 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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9 1 -1 -9 -1 2 2 7 1 9 -3 7 -8 7 -1 8 0 5 9 7 4 5 5 5 -8 4 -7 0 3 -4 -4 2 -1 -2 3 0 -10 8 -2 ================================================ FILE: programming_assignments/beale_ciphers/testcase/small/test8.out ================================================ 1 ================================================ FILE: programming_assignments/jukebox/.gitignore ================================================ *.bundle.* lib/ node_modules/ *.egg-info/ .ipynb_checkpoints *.tsbuildinfo jupyterlab_git/labextension src/version.ts # Integration tests ui-tests/test-results/ ui-tests/playwright-report/ # Created by https://www.gitignore.io/api/python # Edit at https://www.gitignore.io/?templates=python ### Python ### # Byte-compiled / optimized / DLL files __pycache__/ *.py[cod] *$py.class # C extensions *.so # Distribution / packaging .Python build/ develop-eggs/ dist/ downloads/ eggs/ .eggs/ lib/ lib64/ parts/ sdist/ var/ wheels/ pip-wheel-metadata/ share/python-wheels/ .installed.cfg *.egg MANIFEST # PyInstaller # Usually these files are written by a python script from a template # before PyInstaller builds the exe, so as to inject date/other infos into it. *.manifest *.spec # Installer logs pip-log.txt pip-delete-this-directory.txt # Unit test / coverage reports htmlcov/ .tox/ .nox/ .coverage .coverage.* .cache nosetests.xml coverage.xml *.cover .hypothesis/ .pytest_cache/ # Translations *.mo *.pot # Scrapy stuff: .scrapy # Sphinx documentation docs/_build/ # PyBuilder target/ # Jupyter Notebook .ipynb_checkpoints # pyenv .python-version # celery beat schedule file celerybeat-schedule # SageMath parsed files *.sage.py # dotenv .env # virtualenv .venv venv/ ENV/ # Spyder project settings .spyderproject .spyproject # Rope project settings .ropeproject # Mr Developer .mr.developer.cfg .project .pydevproject # mkdocs documentation /site # mypy .mypy_cache/ .dmypy.json dmypy.json # Pyre type checker .pyre/ # End of https://www.gitignore.io/api/python # OSX files .DS_Store # jetbrains ide stuff *.iml .idea/ # vscode ide stuff *.code-workspace .history .vscode # vim stuff *.swp ================================================ FILE: programming_assignments/jukebox/README.md ================================================ # Jukebox - 문제 출제 및 검수: lucas.ii - 해설 작성자: iggy.ll > 이 문서에는 Jukebox 문제의 요약과 간단한 설명이 덧붙여져 있습니다. **문제 원문은 [jukebox.pdf](jukebox.pdf) 문서에 있습니다.** > 문제에 대한 해설과 풀이는 [solution](solution/) 디렉토리를 참고해주세요. ## 1. 문제 설명 사용자의 성향을 고려해 각 사용자가 좋아할 음악을 추천하는 추천 시스템을 만들고자 합니다. 각 사용자가 들었던 음악과 그 음악을 들은 횟수가 입력으로 주어집니다. 임의의 Collaborative Filtering 알고리즘을 구현해, 추천 시스템을 구현하고 이를 오프라인으로 평가하는 것입니다. ## 2. 실험에 필요한 데이터 ### `listen_count.txt` 각 유저가 어떤 음악을 몇 번 들었는가를 표현하는 데이터입니다. ``, ``, ``가 공백을 기준으로 구분되어 있습니다. 예시: ```text 18091 6716 3 15772 1251 1 ... ``` ### `test_data.txt` 평가 데이터는 미리 주어지지 않습니다. 제출하기 이전에, 이 데이터를 임의로 학습 데이터, 테스트 데이터로 나눈 뒤, validation을 수행하기를 권장합니다. 평가 데이터의 형식은 다음과 같습니다. 평가 데이터에서, 각 유저마다 유저가 실제로 들은 아이템의 수는 다를 수 있습니다. ```text $ cat test_data.txt 15772 3663 2151 3759 2554 1151 3399 ... ``` ### 3. 추천 성능 평가 추천 성능의 평가 기준은 NDCG@100입니다. 주어진 데이터에서 가장 청취 회수가 많은 곡 100개를 유저에게 추천했을 때의 NDCG@100는 0.1입니다. 제출한 결과물은 평가 데이터에서 평가했을 때, NDCG@100이 0.2보다 크기를 기대합니다. ### 4. 수행 과정 #### `train` - 주어진 데이터(listen_count.txt)를 이용해 추천 모델을 생성합니다. - 모델을 생성하지 않는 경우, 이 과정을 생락하셔도 좋습니다. 실행 방법: `./train ` e.g., `./train listen_count.txt my_model` #### `recommend` `train`에서 학습한 아웃풋 모델을 이용해, 유저 아이디가 주어졌을 때의 추천을 K개 생성합니다.`train` 과정을 생략한 경우, ``을 여기서 사용해도 좋습니다. 입력에 쓰이는 `user_id.txt`는 각 라인마다 유저 아이디를 담고 있는 파일입니다. user_id.txt의 예시: ```text 15722 2716 3759 ``` 실행 방법: `./recommend user_id.txt ` e.g., `./recommend my_model user_id.txt 100` e.g., `./recommend listen_count.txt user_id.txt 100` ```text $ ./recommend my_model user_id .txt 5 15772 201 200 1819 215 203 2716 514 184 1235 1184 1752 3759 514 534 1249 6341 4623 ``` 결과 형식은: 각 줄의 첫 번째 단어는 유저의 아이디, 이후 K개 단어는 각각 유저에게 추천되는 K개의 아이템 아이디입니다. `15772 201 200 1819 215 203` 이 라인은, 유저 15772가 201 200 1819 215 203를 순서대로 좋아할 것라는 의미입니다. #### `evaluate` `recommend`에서 생성한 추천과, test data를 비교해 추천의 NDCG@100 성능을 평가합니다. test data는 다음과 같은 형태입니다. 각 줄의 첫 번째 단어는 유저의 아이디이며, 각 줄의 나머지 단어는 유저가 실제로 들은 아이템의 리스트입니다. 평가 데이터에서, 각 유저마다 유저가 실제로 들은 아이템의 수는 다를 수 있습니다. ```text $ cat test_data.txt 15772 3663 2151 3759 2554 1151 3399 ... ``` ### 5. 제약 조건 - 8core, 8GB 머신에서 전체 수행 시간 20분 이내에 추천을 생성할 수 있어야 합니다. - 채점의 용이성을 위해 C, C++, Python, C#, Java, Scala 중 하나의 언어를 사용하기를 권장하지만 다른 언어 사용을 원하는 경우 사전에 협의 가능합니다. - 오픈소스로 추천 라이브러리, 혹은 머신 러닝 라이브러리를 사용할 수 있습니다. ### 6. 제출 파일 1. 구현 코드 1. 구현한 방법에 대한 간단한 설명과 실험 결과 리포트 1. 구현 코드를 실행하는 방법에 대한 설명 1. 실험에 사용한 학습/평가 데이터와, 모델을 생성했다면 생성한 모델 ### 7. 평가 기준 - 제약 조건 이내에 컴파일 후 추천을 생성할 수 있는지 - 생성된 추천의 NDCG@100 - 사용한 알고리즘과 그 알고리즘에 대한 이해도 - 코드를 효율적이고 이쁘게 구현하였는지. ### Note - NDCG@100 점수가 유일한 평가 기준은 아닙니다. 어떤 모델을 사용하기로 선택했는지에 따라 NDCG@100이 크게 달라질 수 있기 때문입니다. 추천 시스템에 대한 경험이 많으면 우수한 모델을 쉽게 선택하고, 좋은 오픈 소스 구현체들을 손쉽게 가져올 수 있기도 합니다. - 직접 모델을 구현하는 경우, 추천 알고리즘을 제한 시간 이내에 올바르게 생성하는 코드를 효율적으로 구현하는 것이 오픈 소스를 사용하는 경우 모델 선택을 한 방법과 이유, 그리고 실험 설계와 평가를 얼마나 논리적으로 수행했는가가 채점에서 중요한 요소가 됩니다. ================================================ FILE: programming_assignments/jukebox/listen_count.txt ================================================ 18091 6716 3 15722 1251 1 2716 4394 1 3759 7857 4 11755 5000 1 15712 1776 1 10826 3374 1 5074 4635 1 4068 1755 1 16290 2588 15 7025 3230 1 4902 2668 1 5060 1580 1 5002 4176 1 11882 1768 1 6058 2698 2 10865 3661 1 12947 235 1 10325 755 1 8251 1710 2 9941 7527 1 12499 1251 1 13465 685 1 16914 6031 1 127 915 1 7560 3602 1 13464 8238 1 16384 4967 1 8088 809 3 2156 4472 1 12702 3564 1 16831 1116 1 19989 7085 1 15599 3555 1 7910 6099 1 16645 2689 1 2480 1234 3 16274 5051 8 2204 874 1 13600 3438 1 9954 628 1 778 1356 1 6740 4500 1 5860 23 2 12706 1305 22 8720 1772 1 16359 2352 6 387 1116 1 8737 4944 3 16916 4121 2 6657 1946 2 10736 1388 1 717 496 1 17912 95 4 1847 5302 1 4265 5036 1 1214 6640 1 56 2688 1 13372 698 1 18940 214 4 1148 3206 1 12595 4949 1 5402 2097 5 7387 6180 1 5005 175 4 11533 8148 1 15576 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916 1 1587 679 2 16123 1482 4 5645 1250 1 12592 6793 1 18195 665 1 1246 1250 3 1849 2330 1 2989 1960 1 14493 6231 1 9809 6286 1 9809 6680 6 6943 3980 1 19144 292 1 11370 3233 5 9978 368 3 13864 316 1 8043 201 2 16621 1828 5 14661 1105 11 9503 1747 5 18345 5730 1 2128 4591 1 8525 2678 1 9457 4006 1 7278 221 2 5977 1739 2 2147 1244 1 3651 240 1 48 2404 2 7966 1383 1 10781 2636 2 7778 1784 1 11933 5951 1 10815 6440 1 10381 501 1 6105 4869 3 18814 6925 1 17484 6252 1 760 489 2 9519 964 5 3569 3510 4 13587 443 1 9889 212 1 10080 4290 1 7774 1237 3 15618 4459 4 3705 1729 1 8069 1740 1 10525 2263 4 967 1717 7 6516 3334 1 153 7087 6 16378 498 1 2016 2068 1 6088 3872 3 7148 8119 2 12375 341 1 5815 5390 1 130 5925 2 20019 2677 3 20177 2266 3 5520 4490 2 5421 3015 1 13023 5676 3 17257 744 1 12502 1342 2 14491 7251 1 3385 2632 2 6524 23 1 14964 4196 3 11902 1748 1 2833 1341 3 770 235 1 19787 8141 5 10829 1649 1 12821 4944 1 7769 7466 1 14357 10 2 8889 3991 1 8408 963 5 42 2230 1 13356 4242 1 15657 1304 1 15297 2727 2 5617 2503 1 3050 229 1 18779 1208 2 4436 252 1 3573 6591 3 4599 219 1 15323 6084 2 1770 207 1 3557 6692 3 592 1285 1 4539 541 19 5833 201 1 5505 1237 1 2887 5871 2 15086 2100 43 13 931 1 14900 2352 1 5515 232 3 6205 7554 2 15288 950 1 16626 1779 1 16192 184 3 5174 3167 4 13341 4166 1 2462 6377 4 15827 5677 5 11327 496 4 11928 8200 3 4491 536 1 19428 910 4 1552 4367 1 7597 7210 2 8221 5141 1 10078 2793 3 16789 1505 1 6488 4985 2 12962 1779 1 14684 3382 1 15989 2584 1 2879 6106 4 18623 498 2 9421 1727 1 8468 1788 1 9946 4413 2 11606 2494 1 11050 1827 1 20225 670 1 5335 223 1 17555 883 4 4134 3065 1 7738 1450 2 14892 5020 7 2459 7687 6 9178 385 6 6348 229 1 11306 225 3 18207 7136 1 11672 665 1 14617 7308 2 48 2381 2 5340 1705 1 1870 198 1 8620 922 1 17896 8153 1 9329 1567 16 17416 1760 1 5454 534 1 13601 2626 1 7991 6099 1 6210 1241 1 18017 4698 1 14621 4573 1 17867 1903 4 17504 1729 1 14971 214 2 4055 1762 1 1839 6658 1 4307 1244 3 2341 1757 1 787 834 1 10696 2737 1 1962 6808 2 805 3980 1 10733 2009 1 8329 3414 2 14905 1396 5 13827 536 1 5158 792 2 1653 1816 7 18818 222 6 9341 2661 1 1 73 1 12771 759 6 14203 6408 1 177 215 3 2303 5758 7 6781 173 5 12565 3775 1 6661 4161 1 1787 8139 4 5652 7229 1 2884 3013 2 13233 6526 3 11297 1760 2 13543 917 1 15198 411 1 4147 794 1 529 252 1 2645 3276 1 12514 4436 1 7058 1745 1 16970 1518 17 18158 5907 1 18102 5011 2 8368 779 1 20269 1731 1 1653 229 1 2568 8093 1 16956 2057 2 975 1778 6 5926 533 4 5671 5758 5 20123 7091 1 7994 662 1 9077 517 1 6549 6390 22 15683 1238 1 16636 169 11 17797 532 1 12176 1770 4 11857 6633 1 19455 292 1 19604 6555 1 7643 657 1 4879 7029 1 5542 4595 2 14798 5940 1 9993 3906 1 17725 918 1 2449 1698 3 13607 3431 2 450 5268 1 6669 1190 1 13783 5559 4 10837 1757 3 1825 2683 1 3272 220 1 10980 230 1 11673 541 22 8547 253 1 8051 6920 2 1612 541 1 9224 926 5 7780 3511 1 6765 1740 1 11763 4852 1 14208 411 1 9808 201 6 4259 4977 1 3796 829 1 2778 4902 2 19995 823 1 6983 5301 2 12257 1784 3 4488 221 1 12833 2444 22 13564 353 4 10498 2555 1 11047 1638 2 13017 2964 1 6855 759 5 18033 3922 1 14252 3163 13 17179 3163 7 8458 232 1 3392 8082 15 8242 3471 58 11762 221 3 3574 5911 2 18781 2369 1 13119 1703 3 7780 864 2 18118 667 1 15635 659 1 5952 5302 3 18489 2184 1 11616 597 2 7445 532 4 16554 631 1 3603 2534 5 19486 1205 1 419 3916 1 7809 828 1 9485 13 1 1872 3275 1 14212 2938 1 8438 4306 1 9374 1762 1 5053 292 1 4574 7097 28 4687 2190 1 2045 1363 1 74 3481 3 769 4703 1 6949 2591 1 11851 2704 1 6894 6339 4 15635 612 1 17894 1736 1 5494 1747 2 17743 306 1 6644 2789 1 5995 2661 1 19331 6102 1 7893 3015 6 4371 374 1 17224 1783 1 19763 40 1 636 6897 1 1001 2575 5 12493 507 2 19086 2355 1 8560 3477 1 15468 3511 3 19761 2072 2 530 7122 2 16716 1190 1 7651 7471 1 18893 7969 1 18918 201 14 124 5413 1 7991 3596 3 9787 2968 1 13023 942 1 745 624 1 8229 357 1 15260 5062 2 11367 6341 1 4305 2600 1 20145 1235 2 18657 6106 1 4963 6355 1 10703 1342 2 715 4175 1 3738 8200 6 17695 2369 1 13686 1727 1 12619 1732 3 5862 2653 1 16698 4447 1 12378 413 1 10654 2190 1 19344 5436 1 6510 1248 1 4679 215 4 19053 744 1 2104 3273 1 7295 5439 2 12775 1664 1 20044 7666 4 6457 7073 1 19355 1990 1 19286 2894 1 5479 759 1 873 1996 2 16839 2675 1 484 2058 1 17083 504 1 12152 186 1 1989 3156 2 11327 367 2 4880 7531 1 3485 1464 1 11461 501 1 7022 7227 1 14884 2646 11 9445 471 1 5298 3634 1 2629 1768 2 16831 1775 2 4492 519 1 15686 505 4 8560 597 1 10401 2671 1 10338 2362 2 15707 5420 3 486 2103 3 17738 863 2 2942 2515 1 2319 5120 1 16104 1827 21 9597 2813 2 5318 187 1 4140 6198 7 5882 1206 1 13285 2555 2 34 1842 2 19952 5259 1 8007 1771 4 8021 3516 17 18665 1757 2 13799 200 16 4542 2216 7 17298 1663 2 6183 533 3 14218 1732 2 13645 1335 1 17742 233 3 10452 3748 1 3847 1829 1 14780 222 1 14005 5086 1 15140 200 5 14900 1453 1 6229 3626 1 12913 3399 1 8549 514 2 86 3983 1 1304 6482 1 12200 3848 2 1772 440 1 9192 6705 1 2223 201 2 62 2933 1 6741 206 5 4055 4486 2 19881 498 3 17260 4653 2 2910 3207 18 6809 1241 7 19826 423 1 5320 3714 7 2801 789 1 17357 1366 1 18149 215 8 6687 7772 2 13928 7489 1 1443 2767 3 593 1743 1 2772 201 5 17302 752 1 20180 3631 2 18698 1724 1 12700 2584 4 5684 482 2 5681 184 1 3651 2581 2 20059 7983 2 18347 7554 2 3956 745 5 14490 1788 1 15352 5885 1 19313 1704 4 18293 427 1 14271 4061 10 6687 823 1 11912 5506 1 3996 6542 3 7129 1275 13 6849 5243 1 5408 3262 1 19990 229 3 17361 4009 1 14150 1752 1 94 4241 6 6263 3854 1 10496 7961 5 6509 5738 3 16931 2595 1 1151 7706 5 12812 1734 1 10824 2419 1 19470 1726 1 13624 184 3 11185 6914 2 10733 7801 1 13873 219 2 7028 4992 1 6153 2256 1 8520 7437 10 3175 7840 1 11386 581 1 5438 303 5 8015 200 1 5059 508 1 15566 1539 1 11727 2864 3 19872 881 1 5117 929 2 5834 690 1 6700 206 11 18201 3526 2 1866 215 2 1404 8029 1 129 5772 2 388 3629 4 18257 3391 1 17909 2349 1 6235 7450 1 19351 5330 10 414 366 1 16619 2013 3 2641 2377 1 6332 230 4 15323 220 1 8439 521 1 6140 1363 1 7904 919 1 857 11 1 17328 7294 1 13997 1021 1 ================================================ FILE: programming_assignments/jukebox/solution/1. 데이터 전처리.ipynb ================================================ { "cells": [ { "cell_type": "markdown", "id": "c9a6149a", "metadata": {}, "source": [ "# 데이터 전처리" ] }, { "cell_type": "code", "execution_count": 2, "id": "302a585e", "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "from scipy.sparse import csr_matrix\n", "from sklearn.utils import shuffle\n", "import numpy as np\n", "import os\n", "import shutil" ] }, { "cell_type": "markdown", "id": "6af0cc5f", "metadata": {}, "source": [ "## 데이터 읽기" ] }, { "cell_type": "code", "execution_count": 2, "id": "02eeb334", "metadata": {}, "outputs": [], "source": [ "data = pd.read_csv('listen_count.txt', sep=' ', header=None, dtype=str)\n", "data.columns = ['uid', 'sid', 'cnt']\n", "data['cnt'] = data['cnt'].astype(int)" ] }, { "cell_type": "code", "execution_count": 3, "id": "9f889441", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "folder exist\n" ] } ], "source": [ "try:\n", " os.mkdir('./parsed')\n", "except FileExistsError:\n", " print(\"folder exist\")\n", " shutil.rmtree('./parsed')\n", " os.mkdir('./parsed')" ] }, { "cell_type": "markdown", "id": "d3cb7773", "metadata": {}, "source": [ "## 유저 아이디 저장\n", "\n", "유니크한 유저 아이디를 가져와서 저장합니다." ] }, { "cell_type": "code", "execution_count": 4, "id": "14454e07", "metadata": {}, "outputs": [], "source": [ "uids = sorted(data.uid.unique(), key=lambda x: int(x))" ] }, { "cell_type": "code", "execution_count": 5, "id": "7e8ae522", "metadata": {}, "outputs": [], "source": [ "with open(\"./parsed/all_uids.txt\", 'w') as f:\n", " print('\\n'.join(uids), file=f)" ] }, { "cell_type": "code", "execution_count": 6, "id": "b79ab959", "metadata": {}, "outputs": [], "source": [ "n_user, n_song = len(data.uid.unique()), len(data.sid.unique())\n", "data_len = len(data)" ] }, { "cell_type": "markdown", "id": "cea206d4", "metadata": {}, "source": [ "## 데이터셋 나누기\n", "\n", "전체 데이터를 8:2 비율의 train/validation 데이터로 split합니다." ] }, { "cell_type": "code", "execution_count": 7, "id": "8b89e881", "metadata": {}, "outputs": [], "source": [ "shuffled_data = shuffle(data)" ] }, { "cell_type": "code", "execution_count": 8, "id": "dfc596c4", "metadata": {}, "outputs": [], "source": [ "ratio = 0.8" ] }, { "cell_type": "code", "execution_count": 9, "id": "84f9cfd3", "metadata": {}, "outputs": [], "source": [ "tr, val = shuffled_data[:int(data_len * ratio)], shuffled_data[int(data_len * ratio):]" ] }, { "cell_type": "code", "execution_count": 10, "id": "78faabca", "metadata": {}, "outputs": [], "source": [ "tr_in_uids = set(tr.uid.unique())\n", "tr_in_sids = set(tr.sid.unique())\n", "val_filtered = val[val.uid.isin(tr_in_uids) & val.sid.isin(tr_in_sids)]" ] }, { "cell_type": "markdown", "id": "fabbde30", "metadata": {}, "source": [ "전처리 코드를 두번 작성하는 것을 막기 위해 저장되는 학습 파일은 실제 데이터([`listen_count.txt`](../listen_count.txt))와 같은 형태로 두는 것이 편리합니다." ] }, { "cell_type": "code", "execution_count": 11, "id": "7fbf6130", "metadata": {}, "outputs": [], "source": [ "tr.to_csv('./parsed/listen_count.txt', index=None, header=None, sep=' ')" ] }, { "cell_type": "markdown", "id": "6790c04d", "metadata": {}, "source": [ "validation 파일은 채점용 데이터([`jukebox.pdf`](../jukebox.pdf)에 기술되어 있는 형태)와 같은 형식으로 두는 것이 편리합니다." ] }, { "cell_type": "code", "execution_count": 12, "id": "a0b80e3d", "metadata": {}, "outputs": [], "source": [ "save = val.groupby('uid').sid.apply(list).reset_index()\n", "with open(\"./parsed/TEST_DATA.txt\", 'w') as f:\n", " for uid, sids in zip(save.uid, save.sid):\n", " print(\"%s \" % uid + ' '.join(sids), file=f)" ] }, { "cell_type": "markdown", "id": "9e0afdcf", "metadata": {}, "source": [ "데이터가 적절하게 잘 저장되어 있는지 한 번 더 확인합니다." ] }, { "cell_type": "code", "execution_count": 13, "id": "bdae351e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "listen_count.txt\n", "11377 7184 13\n", "1852 206 3\n", "19145 1692 3\n", "15629 585 2\n", "15821 5003 1\n", "16033 2242 1\n", "13306 2920 1\n", "16734 2488 2\n", "19990 23 5\n", "9208 3913 1\n", "\n", "TEST_DATA.txt\n", "1 96 57 101 65 10 58 97 31 47 37 11 20 44 103 35 94 4 6 33 50 19\n", "10 305 335 259 263 347 292 289 328 307 321 297 311 286 303 294 202 339 99 323 332 315 356 309 277\n", "100 4547 4564 4475 4503 4502 420 4507 4501 1903 4576 4505 4504 4522 4533 4491 4570 4510 4556 4225 4521 4481 4542 4527 4506 4499 4520 4552 890 687 4523 4483 4544\n", "1000 3595 3585 201\n", "10000 1338 7336 5327 5256 1285 2821 4233 2517 545 2369 1172 4882 4299 427 1042 6979 1194 379 2953 433 137 5253 2494 2981 477\n", "10001 4643\n", "10002 200\n", "10004 2966\n", "10005 3723\n", "10006 5826\n", "\n" ] } ], "source": [ "!echo \"listen_count.txt\"\n", "!head ./parsed/listen_count.txt\n", "!echo \"\"\n", "!echo \"TEST_DATA.txt\"\n", "!head ./parsed/TEST_DATA.txt\n", "!echo \"\"" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.10.2 64-bit ('py-3.10.2')", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.2" }, "vscode": { "interpreter": { "hash": "9a43ef12e54cbdce1713efe7092ebffcfb641e943ae67d0e6fe4a12aa1b58da6" } } }, "nbformat": 4, "nbformat_minor": 5 } ================================================ FILE: programming_assignments/jukebox/solution/2-1. Shallow AutoEncoder.ipynb ================================================ { "cells": [ { "cell_type": "markdown", "id": "020c94ee", "metadata": {}, "source": [ "# Shallow AutoEncoder를 이용한 Jukebox 풀이" ] }, { "cell_type": "markdown", "id": "631268aa", "metadata": {}, "source": [ "## Jax 101\n", "\n", "임의의 행렬 연산에 대한 gradient 계산을 하기 위해서, 행렬 계산 라이브러리로 [jax](https://github.com/google/jax)를 사용했습니다. jax를 사용하면, 간단한 gradient 계산을 numpy를 사용할 때와 거의 같은 방법으로 할 수 있습니다." ] }, { "cell_type": "markdown", "id": "6e698215", "metadata": {}, "source": [ "### Super basics of Jax" ] }, { "cell_type": "code", "execution_count": 1, "id": "587f89fb", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from jax import grad, jit, vmap\n", "import jax.numpy as jnp" ] }, { "cell_type": "markdown", "id": "1d289920", "metadata": {}, "source": [ "#### 1. numpy array와 jax.numpy.array는 대체로 compatible하다." ] }, { "cell_type": "code", "execution_count": 2, "id": "4ddaded6", "metadata": {}, "outputs": [], "source": [ "x = 0.001 * np.arange(16)\n", "jx = jnp.array(x)\n", "jy = jnp.array(3.141592 * jnp.sin(jnp.arange(16)))\n", "a = jnp.array([0.01, 0.01, 0.01])" ] }, { "cell_type": "markdown", "id": "7a22c9e3", "metadata": {}, "source": [ "#### 2. jax object/numpy object 등이 포함된 식의 gradient를 계산할 수 있다.\n", "\n", "$\\hat y = a_0 * x + a_1 * x^2 + a_2 * x^3$으로 $sin(\\pi y)$를 근사할 때의 loss를 다음과 같이 계산할 수 있습니다." ] }, { "cell_type": "code", "execution_count": 3, "id": "4868f18f", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray(4.85457, dtype=float32)" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "@jit\n", "def loss(x, y, a):\n", " y_hat = a[0] * x + a[1] * (x ** 2) + a[2] * (x ** 3)\n", " return ((y_hat - y) ** 2).mean()\n", "loss(jx, jy, a)" ] }, { "cell_type": "code", "execution_count": 4, "id": "41b3bb71", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "DeviceArray([ 0. , -0.00331105, -0.0035851 , -0.00055748,\n", " 0.00299592, 0.00380369, 0.00111062, -0.00261639,\n", " -0.00394801, -0.00164779, 0.00217986, 0.00401491,\n", " 0.00215875, -0.00169356, -0.00400113, -0.00263181], dtype=float32)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "grads = grad(loss, argnums=[0,2])(jx ,jy, a) # 0번째 argument인 jx에 대한 grad, 2번째 argument인 a에 대한 gradient\n", "grads[0] # jx의 gradient" ] }, { "cell_type": "markdown", "id": "71110f57", "metadata": {}, "source": [ "따라서 다음 식은, 주어진 loss를 최적화하는 방향의 `jx`, `a`의 gradient descent update가 됩니다." ] }, { "cell_type": "code", "execution_count": 5, "id": "ece92078", "metadata": {}, "outputs": [], "source": [ "lr = 0.5\n", "jx -= lr * grads[0]\n", "a -= lr * grads[1]" ] }, { "cell_type": "markdown", "id": "53cecce1", "metadata": {}, "source": [ "#### 3. 간단한 gradient update iterations" ] }, { "cell_type": "code", "execution_count": 6, "id": "f5095a68", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loss: 4.8544683\n", "loss: 4.854233\n", "loss: 4.8536825\n", "loss: 4.852408\n", "loss: 4.8494987\n", "loss: 4.8429565\n", "loss: 4.8284535\n", "loss: 4.7968144\n", "loss: 4.7290735\n", "loss: 4.587598\n", "loss: 4.303007\n", "loss: 3.7652407\n", "loss: 2.8549566\n", "loss: 1.5948524\n", "loss: 0.4395939\n", "loss: 0.043171447\n", "loss: 0.005146715\n", "loss: 0.0013591682\n", "loss: 0.0004096477\n", "loss: 0.0001331548\n" ] } ], "source": [ "lr = 0.5\n", "for i in range(20):\n", " print(\"loss: \", loss(jx, jy, a))\n", " grads = grad(loss, argnums=[0,2],)(jx, jy, a) #gradient update\n", " jx -= lr * grads[0]\n", " a -= lr * grads[1]\n", " lr *= 0.98 # weight decay" ] }, { "cell_type": "markdown", "id": "2f33a401", "metadata": {}, "source": [ "자세한 소개는 를 참고하세요." ] }, { "cell_type": "code", "execution_count": 7, "id": "fac3c24c", "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "from scipy.sparse import csr_matrix\n", "import numpy as np" ] }, { "cell_type": "markdown", "id": "30ee5738", "metadata": {}, "source": [ "## 전처리한 데이터 읽기" ] }, { "cell_type": "code", "execution_count": 8, "id": "a6876280", "metadata": {}, "outputs": [], "source": [ "tr = pd.read_csv('./parsed/listen_count.txt', sep=' ', header=None, dtype=str)\n", "tr.columns = ['uid', 'sid', 'cnt']\n", "tr['cnt'] = tr['cnt']" ] }, { "cell_type": "markdown", "id": "d4988dcb", "metadata": {}, "source": [ "## user/song id ↔︎ index mapper 생성" ] }, { "cell_type": "code", "execution_count": 9, "id": "98fc1a4f", "metadata": {}, "outputs": [], "source": [ "uid2idx = {_id: i for (i, _id) in enumerate(tr.uid.unique())}\n", "sid2idx = {_id: i for (i, _id) in enumerate(tr.sid.unique())}\n", "idx2uid = {i: _id for (_id, i) in uid2idx.items()}\n", "idx2sid = {i: _id for (_id, i) in sid2idx.items()}" ] }, { "cell_type": "code", "execution_count": 10, "id": "dfabc6be", "metadata": {}, "outputs": [], "source": [ "n_users, n_items = len(uid2idx), len(sid2idx)" ] }, { "cell_type": "code", "execution_count": 11, "id": "827ddd9c", "metadata": {}, "outputs": [], "source": [ "tr['uidx'] = tr.uid.apply(lambda x: uid2idx[x])\n", "tr['sidx'] = tr.sid.apply(lambda x: sid2idx[x])" ] }, { "cell_type": "code", "execution_count": 12, "id": "c8410198", "metadata": {}, "outputs": [], "source": [ "with open('./user_id.txt', 'w') as f:\n", " print('\\n'.join(list(uid2idx)), file=f)" ] }, { "cell_type": "code", "execution_count": 13, "id": "519a6faa", "metadata": {}, "outputs": [], "source": [ "X = csr_matrix((tr.cnt, (tr.uidx, tr.sidx)), shape=(n_users, n_items), dtype=np.float32)\n", "X.data[:] = 1.0 + np.log(1.0 + X.data[:])\n", "jX = jnp.array(X.todense())" ] }, { "cell_type": "markdown", "id": "ad0b2ae1", "metadata": {}, "source": [ "## 모델 패러미터 선언" ] }, { "cell_type": "code", "execution_count": 14, "id": "30e9dcd8", "metadata": {}, "outputs": [], "source": [ "P = jnp.array(np.random.normal(0, 0.001, size=(n_items, n_items)))\n", "P = P.at[jnp.diag_indices(P.shape[0])].set(0)" ] }, { "cell_type": "markdown", "id": "f4e087bc", "metadata": {}, "source": [ "## AutoEncoder Loss function 정의" ] }, { "cell_type": "code", "execution_count": 15, "id": "3bbdccdd", "metadata": {}, "outputs": [], "source": [ "@jit\n", "def loss_fn(X, P):\n", " ret = (((X - X @ P) **2).sum() / X.shape[0])\n", " ret = ret + 0.01 * (P * P).sum()\n", " return ret\n", "\n", "@jit\n", "def loss_fn_with_reg(X, P):\n", " ret = loss_fn(X, P)\n", " ret = ret + 0.01 * (P * P).sum()\n", " return ret " ] }, { "cell_type": "markdown", "id": "b4fe16ee", "metadata": {}, "source": [ "## 모델 학습 iteration" ] }, { "cell_type": "code", "execution_count": 16, "id": "5347798b", "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loss 64.004\n", "loss 66.449\n", "loss 67.097\n", "loss 60.643\n", "loss 59.344\n", "loss 64.691\n", "loss 59.441\n", "loss 63.911\n", "loss 59.402\n", "loss 64.654\n", "loss 62.120\n", "loss 60.031\n", "loss 62.357\n", "loss 61.753\n", "loss 57.506\n", "loss 60.258\n", "loss 58.754\n", "loss 56.311\n", "loss 58.182\n", "loss 62.481\n", "loss 60.810\n", "loss 56.708\n", "loss 57.245\n", "loss 60.673\n", "loss 56.572\n", "loss 59.373\n", "loss 59.507\n", "loss 57.597\n", "loss 59.925\n", "loss 59.495\n", "loss 55.814\n", "loss 55.230\n", "loss 59.792\n", "loss 58.578\n", "loss 58.576\n", "loss 57.569\n", "loss 55.163\n", "loss 58.808\n", "loss 55.075\n", "loss 57.480\n", "loss 56.844\n", "loss 56.501\n", "loss 55.325\n", "loss 58.603\n", "loss 57.383\n", "loss 56.497\n", "loss 55.732\n", "loss 55.738\n", "loss 58.511\n", "loss 60.045\n", "loss 54.302\n", "loss 57.139\n", "loss 57.217\n", "loss 57.407\n", "loss 53.654\n", "loss 55.838\n", "loss 54.236\n", "loss 55.657\n", "loss 56.574\n", "loss 56.752\n", "loss 54.039\n", "loss 53.840\n", "loss 57.588\n", "loss 55.948\n", "loss 56.433\n", "loss 58.417\n", "loss 53.072\n", "loss 57.674\n", "loss 57.769\n", "loss 53.164\n", "loss 55.655\n", "loss 56.704\n", "loss 59.374\n", "loss 55.299\n", "loss 53.946\n", "loss 57.615\n", "loss 58.426\n", "loss 53.965\n", "loss 56.668\n", "loss 58.578\n", "loss 59.542\n", "loss 58.564\n", "loss 57.424\n", "loss 57.376\n", "loss 57.319\n", "loss 56.014\n", "loss 56.321\n", "loss 56.480\n", "loss 55.599\n", "loss 54.096\n", "loss 56.425\n", "loss 54.798\n", "loss 55.761\n", "loss 55.811\n", "loss 52.461\n", "loss 59.287\n", "loss 53.293\n", "loss 55.951\n", "loss 54.867\n", "loss 54.828\n" ] } ], "source": [ "lr = 0.05\n", "for i in range(100):\n", " batch = np.random.choice(X.shape[0], 1024)\n", " l = loss_fn(jX[batch], P)\n", " print(\"loss %.3f\" % l)\n", " r = grad(loss_fn_with_reg, argnums=1)(jX[batch], P)\n", " P -= lr * r\n", " P = P.at[jnp.diag_indices(P.shape[0])].set(0)\n", " lr *= 0.99" ] }, { "cell_type": "code", "execution_count": 17, "id": "cb170b21", "metadata": {}, "outputs": [], "source": [ "scores = np.asarray(X @ P)\n", "\n", "# 유저가 들은 적이 있는 아이템을 추천에서 제외해 줍니다.\n", "scores = np.asarray((scores - X.astype(bool).astype(int) * 10000))" ] }, { "cell_type": "markdown", "id": "9855859e", "metadata": {}, "source": [ "## 아이템 선택\n", "\n", "score가 높은 top 100개 아이템을 선택해줍니다." ] }, { "cell_type": "code", "execution_count": 18, "id": "1d218c77", "metadata": {}, "outputs": [], "source": [ "top_reco = (-scores).argsort(-1)[:, :100]" ] }, { "cell_type": "markdown", "id": "6429b6d2", "metadata": {}, "source": [ "## 추천 생성 후 저장" ] }, { "cell_type": "code", "execution_count": 19, "id": "fb7fdf46", "metadata": {}, "outputs": [], "source": [ "ret = []\n", "for idx, rec_list in enumerate(top_reco):\n", " uid = idx2uid[idx]\n", " rec_sids = [str(idx2sid[sidx]) for sidx in rec_list]\n", " ret.append(\"%s \" % uid + ' '.join(rec_sids))\n", "with open('./parsed/rec_result.txt', 'w') as f:\n", " for w in ret:\n", " print(w, file=f)" ] }, { "cell_type": "markdown", "id": "7bec8d62", "metadata": {}, "source": [ "저장된 추천 결과, 그리고 테스트 데이터를 dictionary 형태로 읽어옵니다." ] }, { "cell_type": "code", "execution_count": 20, "id": "4980fcdb", "metadata": {}, "outputs": [], "source": [ "def load_res(fname):\n", " ret = {}\n", " with open(fname, 'r') as f:\n", " for l in f:\n", " l = l.strip().split()\n", " uid, sids = l[0], l[1:]\n", " ret[uid] = sids\n", " return ret\n", "\n", "recs = load_res('./parsed/rec_result.txt')\n", "gt = load_res('./parsed/TEST_DATA.txt')" ] }, { "cell_type": "code", "execution_count": 21, "id": "bc1cc380", "metadata": {}, "outputs": [], "source": [ "import math\n", "def ndcg(recs, gt):\n", " Q, S = 0.0, 0.0\n", " for u, vs in gt.items():\n", " rec = recs.get(u, [])\n", " if not rec:\n", " continue\n", "\n", " idcg = sum([1.0 / math.log(i + 2, 2) for i in range(len(vs))])\n", " dcg = 0.0\n", " for i, r in enumerate(rec):\n", " if r not in vs:\n", " continue\n", " rank = i + 1\n", " dcg += 1.0 / math.log(rank + 1, 2)\n", " ndcg = dcg / idcg\n", " S += ndcg\n", " Q += 1\n", " return S / Q\n" ] }, { "cell_type": "code", "execution_count": 22, "id": "f8c20670", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.25222175220674803" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ndcg(recs, gt)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "vscode": { "interpreter": { "hash": "1c0b93efeafdf3e6d99eb605273d97a0510dd9f2bbdf91a9dec5466ed68b0be9" } } }, "nbformat": 4, "nbformat_minor": 5 } ================================================ FILE: programming_assignments/jukebox/solution/2-2. EASE^R.ipynb ================================================ { "cells": [ { "cell_type": "code", "execution_count": 24, "id": "3c0dbaaf", "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "from scipy.sparse import csr_matrix\n", "from sklearn.utils import shuffle\n", "import numpy as np" ] }, { "cell_type": "code", "execution_count": 26, "id": "a6876280", "metadata": {}, "outputs": [], "source": [ "tr = pd.read_csv('./parsed/listen_count.txt', sep=' ', header=None, dtype=str)\n", "tr.columns = ['uid', 'sid', 'cnt']\n", "tr['cnt'] = tr['cnt']" ] }, { "cell_type": "code", "execution_count": 27, "id": "98fc1a4f", "metadata": {}, "outputs": [], "source": [ "uid2idx = {_id: i for (i, _id) in enumerate(tr.uid.unique())}\n", "sid2idx = {_id: i for (i, _id) in enumerate(tr.sid.unique())}\n", "idx2uid = {i: _id for (_id, i) in uid2idx.items()}\n", "idx2sid = {i: _id for (_id, i) in sid2idx.items()}" ] }, { "cell_type": "code", "execution_count": 28, "id": "dfabc6be", "metadata": {}, "outputs": [], "source": [ "n_user, n_item = len(uid2idx), len(sid2idx)" ] }, { "cell_type": "code", "execution_count": 29, "id": "827ddd9c", "metadata": {}, "outputs": [], "source": [ "tr['uidx'] = tr.uid.apply(lambda x: uid2idx[x])\n", "tr['sidx'] = tr.sid.apply(lambda x: sid2idx[x])" ] }, { "cell_type": "code", "execution_count": 59, "id": "c8410198", "metadata": {}, "outputs": [], "source": [ "with open('./user_id.txt', 'w') as f:\n", " print('\\n'.join(tr.uid.tolist()), file=f)" ] }, { "cell_type": "code", "execution_count": 30, "id": "8486d1ea", "metadata": {}, "outputs": [], "source": [ "vali_list = val.groupby('uidx').sidx.apply(list).reset_index()" ] }, { "cell_type": "code", "execution_count": 31, "id": "519a6faa", "metadata": {}, "outputs": [], "source": [ "X = csr_matrix((tr.cnt, (tr.uidx, tr.sidx)), shape=(n_user, n_item), dtype=np.float32)" ] }, { "cell_type": "code", "execution_count": 32, "id": "1750a1b5", "metadata": {}, "outputs": [], "source": [ "X.data[:] = 1.0 + np.log(1.0 + X.data[:])" ] }, { "cell_type": "code", "execution_count": 33, "id": "bb224ab9", "metadata": {}, "outputs": [], "source": [ "def gen_top_reco(X, lamb=10.0):\n", " G = (X.T @ X).toarray()\n", " diags = np.diag_indices(G.shape[0])\n", " G[diags] += lamb\n", " P = np.linalg.inv(G)\n", " B = P / -np.diag(P)\n", " scores = X @ B\n", " scores = np.asarray((scores - X.astype(bool).astype(int) * 10000))\n", " top_reco = (-scores).argsort(-1)[:, :100]\n", " return top_reco" ] }, { "cell_type": "code", "execution_count": 44, "id": "287e0468", "metadata": {}, "outputs": [], "source": [ "top_reco = gen_top_reco(X, lamb=30.0)" ] }, { "cell_type": "code", "execution_count": 45, "id": "fb7fdf46", "metadata": {}, "outputs": [], "source": [ "ret = []\n", "for idx, rec_list in enumerate(top_reco):\n", " uid = idx2uid[idx]\n", " rec_sids = [str(idx2sid[sidx]) for sidx in rec_list]\n", " ret.append(\"%s \" % uid + ' '.join(rec_sids))" ] }, { "cell_type": "code", "execution_count": 46, "id": "b4db5269", "metadata": {}, "outputs": [], "source": [ "with open('./parsed/rec_result.txt', 'w') as f:\n", " for w in ret:\n", " print(w, file=f)" ] }, { "cell_type": "code", "execution_count": 48, "id": "4980fcdb", "metadata": {}, "outputs": [], "source": [ "def load_res(fname):\n", " ret = {}\n", " with open(fname, 'r') as f:\n", " for l in f:\n", " l = l.strip().split()\n", " uid, sids = l[0], l[1:]\n", " ret[uid] = sids\n", " return ret" ] }, { "cell_type": "code", "execution_count": 49, "id": "785afcd8", "metadata": {}, "outputs": [], "source": [ "recs = load_res('./parsed/rec_result.txt')" ] }, { "cell_type": "code", "execution_count": 50, "id": "63582e44", "metadata": {}, "outputs": [], "source": [ "gt = load_res('./parsed/TEST_DATA.txt')" ] }, { "cell_type": "code", "execution_count": 51, "id": "bc1cc380", "metadata": {}, "outputs": [], "source": [ "import math\n", "def ndcg(recs, gt):\n", " Q, S = 0.0, 0.0\n", " for u, vs in gt.items():\n", " rec = recs.get(u, [])\n", " if not rec:\n", " continue\n", "\n", " idcg = sum([1.0 / math.log(i + 2, 2) for i in range(len(vs))])\n", " dcg = 0.0\n", " for i, r in enumerate(rec):\n", " if r not in vs:\n", " continue\n", " rank = i + 1\n", " dcg += 1.0 / math.log(rank + 1, 2)\n", " ndcg = dcg / idcg\n", " S += ndcg\n", " Q += 1\n", " return S / Q\n" ] }, { "cell_type": "code", "execution_count": 52, "id": "f8c20670", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.2559553152855044" ] }, "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ndcg(recs, gt)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" }, "vscode": { "interpreter": { "hash": "1c0b93efeafdf3e6d99eb605273d97a0510dd9f2bbdf91a9dec5466ed68b0be9" } } }, "nbformat": 4, "nbformat_minor": 5 } ================================================ FILE: programming_assignments/jukebox/solution/3. (optional) Implicit을 이용한 Jukebox 풀이.ipynb ================================================ { "cells": [ { "cell_type": "markdown", "id": "4c1dbc84", "metadata": {}, "source": [ "# Matrix Factorization 라이브러리인 Implicit을 이용한 Jukebox 풀이" ] }, { "cell_type": "code", "execution_count": 1, "id": "92eb00a1", "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "from scipy.sparse import csr_matrix\n", "import numpy as np\n", "from implicit.als import AlternatingLeastSquares as ALS" ] }, { "cell_type": "code", "execution_count": 2, "id": "a6876280", "metadata": {}, "outputs": [], "source": [ "tr = pd.read_csv('./parsed/listen_count.txt', sep=' ', header=None, dtype=str)\n", "tr.columns = ['uid', 'sid', 'cnt']\n", "tr['cnt'] = tr['cnt']" ] }, { "cell_type": "markdown", "id": "81bd8e98", "metadata": {}, "source": [ "## user/song id ↔︎ index mapper 생성" ] }, { "cell_type": "code", "execution_count": 3, "id": "98fc1a4f", "metadata": {}, "outputs": [], "source": [ "uid2idx = {_id: i for (i, _id) in enumerate(tr.uid.unique())}\n", "sid2idx = {_id: i for (i, _id) in enumerate(tr.sid.unique())}\n", "idx2uid = {i: _id for (_id, i) in uid2idx.items()}\n", "idx2sid = {i: _id for (_id, i) in sid2idx.items()}" ] }, { "cell_type": "code", "execution_count": 4, "id": "dfabc6be", "metadata": {}, "outputs": [], "source": [ "n_users, n_items = len(uid2idx), len(sid2idx)" ] }, { "cell_type": "code", "execution_count": 5, "id": "827ddd9c", "metadata": {}, "outputs": [], "source": [ "tr['uidx'] = tr.uid.apply(lambda x: uid2idx[x])\n", "tr['sidx'] = tr.sid.apply(lambda x: sid2idx[x])" ] }, { "cell_type": "code", "execution_count": 6, "id": "c8410198", "metadata": {}, "outputs": [], "source": [ "with open('./user_id.txt', 'w') as f:\n", " print('\\n'.join(list(uid2idx)), file=f)" ] }, { "cell_type": "code", "execution_count": 7, "id": "519a6faa", "metadata": {}, "outputs": [], "source": [ "X = csr_matrix((tr.cnt, (tr.uidx, tr.sidx)), shape=(n_users, n_items), dtype=np.float32)\n", "X.data[:] = 1.0 + np.log(1.0 + X.data[:])" ] }, { "cell_type": "code", "execution_count": 8, "id": "b6b436f8", "metadata": {}, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "75e14414e65e4ac38a52f4df4632ac15", "version_major": 2, "version_minor": 0 }, "text/plain": [ " 0%| | 0/15 [00:00 0: S += 1.0 / min_rank if Q > 0: # print 'S=%f' % S # print 'Q=%f' % Q # print '%.10f' % (S / Q) return S / Q @staticmethod def map(recs, db): Q = 0 S = 0 for u, vs in db.items(): N = len(vs) Hit = 0 SS = 0 set_v = set(vs.keys()) rec = recs.get(u, []) for idx, r in enumerate(rec): if r[0] in set_v: Hit += 1 SS += (Hit / float(idx + 1)) SS = SS / float(N) S += SS Q += 1 if Q > 0: # print 'S=%f' % S # print 'Q=%f' % Q # print '%.10f' % (S / Q) return S / Q @staticmethod def auc(recs, db, num_total_cand): Q = 0.0 S = 0.0 for u, vs in db.items(): Q += 1 rec = recs.get(u, []) num_dropped_items = num_total_cand - len(rec) num_rel_items = len([1 for r in rec if r[0] in vs]) num_eval_items = num_total_cand num_eval_pairs = (num_eval_items - num_rel_items) * num_rel_items if num_eval_pairs == 0: S += 0.5 continue num_correct_pairs = 0 hit_count = 0 for r in rec: if r[0] not in vs: num_correct_pairs += hit_count else: hit_count += 1 num_missing_rel_items = len(vs) - num_rel_items num_correct_pairs += (hit_count * (num_dropped_items - num_missing_rel_items)) S += float(num_correct_pairs) / float(num_eval_pairs) return S / Q @staticmethod def ndcg(recs, db): Q = 0.0 S = 0.0 for u, vs in db.items(): rec = recs.get(u, []) if not rec: continue idcg = sum([1.0 / math.log(i + 2, 2) for i in range(len(vs))]) dcg = 0.0 for i, r in enumerate(rec): if r not in vs: continue rank = i + 1 dcg += 1.0 / math.log(rank + 1, 2) ndcg = dcg / idcg S += ndcg Q += 1 return S / Q class Evaluation: def __init__(self): self.logger = logging.getLogger(self.__class__.__name__) self.logger.setLevel(logging.DEBUG) sh = logging.StreamHandler() sh.setLevel(logging.DEBUG) formatter = logging.Formatter('[%(levelname)-8s] %(asctime)s [%(filename)s] [%(funcName)s:%(lineno)d] %(message)s', '%Y-%m-%d %H:%M:%S') sh.setFormatter(formatter) self.logger.addHandler(sh) fh = logging.FileHandler(self.__class__.__name__ + '.log') fh.setLevel(logging.DEBUG) formatter = logging.Formatter('[%(levelname)-8s] %(asctime)s [%(filename)s] [%(funcName)s:%(lineno)d] %(message)s', '%Y-%m-%d %H:%M:%S') fh.setFormatter(formatter) self.logger.addHandler(fh) def load_database(self, fname_target_users, fname_database, has_header=False): self.logger.info('Loading database -> %s' % fname_database) self.target_users = None if fname_target_users: self.target_users = set(map(int, open(fname_target_users))) data = '' fin = open(fname_database) while True: line = fin.readline() if line[0] == '#': continue data += line break if has_header: fin.readline() data += fin.read() tokenizer = re.compile('([^ \n]+)') self.db = {} tokens = tokenizer.findall(data) it = iter(tokens) for u, i, s in zip(it, it, it): u, i, s = int(u), int(i), float(s) if self.target_users and u not in self.target_users: continue if u not in self.db: self.db[u] = {} self.db[u][i] = s def load_test_file(self, fpath, has_header=True): self.logger.info('Loading database -> %s' % fpath) with open(fpath) as f: if has_header: f.readline() header = f.readline().rstrip().split(" ") max_uid, max_iid, num_line = map(int, header) td = {} for line in f: uid, iid, r = line.split(" ") r = float(r) if r > 3.0: td.setdefault(uid, set()).add(iid) return td def load_topk_file(self, fpath): self.logger.info('Loading topk file -> %s' % fpath) with open(fpath) as f: topk = {} num_line = 0 for line in f: num_line += 1 item = line.strip().split(" ") if len(item) == 0 or not item[0].isdigit(): print("error %d" % num_line) # item = map(int, item) topk[item[0]] = item[1:] return topk def eval_topk(self, topk, td, metrics=[]): self.logger.info('Start evalution') scores = [] if 'mrr' in metrics: self.logger.info('[MRR]') mrr = Metric.mrr(topk, td) self.logger.info('MRR: %.10f' % mrr) scores.append(mrr) if 'map' in metrics: self.logger.info('[MAP]') _map = Metric.map(topk, td) self.logger.info('MAP: %.10f' % _map) scores.append(_map) if 'auc' in metrics: self.logger.info('[AUC]') self.logger.info('NUM_RECOMMENDATION_CANDIDATES: %d' % NUM_ITEMS) auc = Metric.auc(topk, td, NUM_ITEMS) self.logger.info('AUC: %.10f' % auc) scores.append(auc) if 'ndcg' in metrics: self.logger.info('[NDCG]') ndcg = Metric.ndcg(topk, td) self.logger.info('NDCG: %.10f' % ndcg) scores.append(ndcg) self.logger.info('| ' + (' | '.join(['%.10f' % s for s in scores])) + ' |') if __name__ == '__main__': if len(sys.argv) != 3: print('python', sys.argv[0], '', '') sys.exit() test_fname = sys.argv[1] topk_fname = sys.argv[2] e = Evaluation() test_data = e.load_test_file(test_fname, has_header=False) print(len(test_data)) topk = e.load_topk_file(topk_fname) e.eval_topk(topk, test_data, ['ndcg']) ================================================ FILE: programming_assignments/jukebox/solution/code_using_ease/evaluation/user_id.txt ================================================ 10111 10139 1014 10151 10153 102 1029 103 10300 10349 10393 10396 10450 10458 10459 1047 10715 10811 10828 1087 10896 1090 10901 10955 1109 11121 11124 11141 11155 11200 11227 11268 11278 1128 11281 11310 11325 11326 11364 11432 11459 11498 11529 11536 11547 11590 11632 11660 11702 11796 11918 11929 12023 12026 1207 12157 12167 12215 12224 12296 12339 12355 12447 12494 12499 12534 12558 12599 12632 12639 12717 12751 12762 12814 1289 129 12906 12921 12945 13003 13012 1302 13021 13024 1303 1305 13077 13091 13112 13147 13190 13204 13234 13350 13353 13421 1359 13620 13630 13657 13710 13792 1385 13864 13885 1399 14000 14104 14109 14127 1414 14183 14213 14236 14361 14385 14469 14504 14519 14540 14604 14720 14755 14768 14816 14832 14838 14870 14913 15022 15100 15152 15169 1518 15241 1525 15282 15301 15379 15438 15463 1549 15495 15539 15564 15581 15604 15618 15725 15781 15791 15814 15904 15913 16033 16041 1606 16081 16089 1611 16132 16135 16183 1623 16258 16269 16289 16322 16364 16377 16468 16480 16506 16568 16624 16637 1665 1676 16922 16926 16959 16960 16964 16995 17023 17112 17206 17246 17289 17311 17381 17448 17449 17459 1746 17536 17540 17575 1765 17738 17768 17778 17833 17911 17922 17955 17957 17959 17987 18070 18189 18215 1822 18262 18273 18313 18323 18374 18411 18416 18441 1850 18561 18563 18582 18654 18656 18705 18788 18919 18931 19007 1905 19071 19111 19118 19127 19145 19151 19199 19205 19207 19208 19228 19273 19323 19384 19407 19527 19530 19577 19606 19621 19630 19685 1970 19751 19763 19839 19878 19892 19941 19961 20056 20064 20110 20112 20154 20193 20236 20241 20272 2084 2149 2183 2209 2271 2278 2383 2387 2401 2419 2463 2473 2495 2499 2544 2578 2580 2585 2589 2629 2691 2697 2725 2754 2756 283 2833 2852 2918 2936 3025 3027 3046 306 3082 3116 3153 3176 3185 3214 3220 3229 330 3353 342 3445 3486 352 3542 3573 3617 3625 3635 3646 365 37 372 3752 3761 3766 3775 3852 3875 3899 3913 3940 4061 409 4124 4131 4139 4180 4193 4241 4345 438 4383 4419 4505 4509 4568 4615 4650 467 4671 4734 4747 4769 4787 4859 4860 4875 4899 4905 4964 501 509 5125 5128 5149 52 523 5282 5288 5348 5383 542 5543 5552 5579 5596 5606 5618 5640 5655 566 5721 5730 5731 576 5963 6006 6033 6036 6205 6219 6221 6240 6261 6290 6304 6307 6323 6334 634 6342 6349 6360 6385 6442 6477 6486 6498 6502 6511 6561 6585 6613 6654 6699 6749 69 6925 6974 6995 7 7011 7015 705 7195 7199 7211 7219 7307 7351 7399 7414 7427 7458 7484 75 7523 7543 7708 7721 7742 7785 7802 7838 7908 792 7966 8035 8046 8052 8074 8092 8105 8208 832 8375 8377 8552 8561 8586 8623 863 8654 8669 8689 8699 8719 8763 8801 8844 8848 8884 8944 9011 910 914 9146 9219 9240 9278 9359 936 9450 9469 9497 9581 9594 9602 9654 9670 9749 978 9904 ================================================ FILE: programming_assignments/jukebox/solution/code_using_ease/evaluation/validation_data.txt ================================================ 1303 103 11 5618 1249 9 4193 2352 1 18215 6150 1 8848 1734 1 11929 505 1 6342 6546 1 8375 4245 1 1765 5820 1 19127 1740 1 8052 7089 1 8623 1251 6 4615 520 1 10396 6541 4 13864 665 1 10151 2668 1 19228 6184 1 1047 1740 1 2629 1771 2 2495 3511 1 12717 518 3 863 6029 1 4859 1146 2 352 3445 1 17833 643 1 467 3798 2 17911 706 3 8801 3216 1 19606 1475 1 1746 601 1 14104 1755 1 18070 390 1 1029 2352 1 18919 2488 1 1289 3698 1 18262 6150 1 12534 5291 1 4734 1282 1 1305 834 1 11325 221 3 15495 1764 1 4345 8029 2 566 1695 4 3153 534 1 6477 229 6 14236 4665 1 5606 167 1 1518 910 2 7484 3414 4 18070 526 5 1765 132 1 11281 1762 2 3775 206 1 11702 1116 1 20193 5306 1 5963 193 4 9011 6758 12 16364 5144 3 4061 1548 1 3220 6069 1 2629 2662 1 10139 4314 1 13234 1312 1 1665 5048 1 11121 1328 1 910 2093 6 13024 3411 3 14183 23 1 12026 526 1 9011 1399 8 14913 1312 6 14385 2722 2 409 840 5 13190 6470 1 14832 3239 1 20110 510 1 634 4279 1 17449 1724 1 20112 6355 4 3486 1302 2 8654 6537 1 7966 6627 2 18788 3464 5 7011 1250 13 17246 1241 1 15438 23 1 14504 6342 5 18323 6588 1 1090 7621 5 5606 203 14 3025 4623 5 4615 5436 1 12023 1739 6 6502 8102 1 4650 2459 1 14385 1825 1 4061 6368 1 17778 499 1 6749 4387 1 18561 8096 3 8654 5417 1 13012 1356 1 7399 716 1 10828 1334 1 6342 235 1 11278 1395 2 19228 554 1 3542 1518 1 1090 4404 6 14469 310 3 542 4302 1 2473 742 2 6502 4996 1 18919 1277 1 11155 2169 8 1029 5018 2 2419 897 1 2629 1748 2 8699 769 12 14870 4355 1 542 6680 1 10955 498 2 4241 982 1 13792 200 1 8552 508 1 15791 1730 1 2544 1417 1 17246 719 5 3852 4345 1 15100 901 2 17778 1721 1 18563 4400 16 8884 5863 1 1359 207 10 18931 2317 2 9581 520 5 19527 722 1 10393 518 1 12632 2528 1 14838 6711 2 17778 177 15 17738 5331 1 9240 425 1 5552 840 5 4131 8238 6 14755 3631 1 1128 2646 27 2691 229 3 13630 13 2 7307 758 2 15100 665 6 6925 3698 1 16468 2746 1 2629 1722 1 16568 3731 1 17778 1657 1 17738 5290 1 8074 519 1 16624 4411 2 4509 7819 2 6699 223 3 2936 7823 1 15438 7980 3 1385 4283 1 15814 7699 1 342 475 1 4345 3892 2 19205 2747 5 3025 203 11 16468 5517 1 4734 1369 1 4124 3911 1 17311 6345 2 467 5253 2 5731 225 1 4124 4427 6 9146 5904 3 18563 1695 1 10111 890 1 283 1736 5 10349 4435 1 17112 3684 3 2580 156 11 17449 84 1 16377 3624 1 18262 1751 1 14519 3987 6 8561 214 1 19530 752 1 17955 1334 1 16995 3806 3 20272 3460 1 8375 8238 1 5655 5532 1 7721 1621 1 18705 903 1 4769 4204 2 1302 148 1 5128 8194 3 19685 5518 5 8763 4008 1 18705 2363 1 9497 2352 1 3940 7030 2 12558 5950 1 16041 1946 1 8654 3595 3 16468 499 1 3940 706 1 2473 617 1 7838 214 14 16183 519 16 1746 676 1 19273 7920 1 6442 6714 1 6561 1282 1 2387 207 16 13091 1703 1 16132 839 1 4061 2027 1 8699 7965 2 18561 3775 1 7721 2175 1 102 2511 2 11227 5077 2 1414 2727 3 18323 499 1 7802 1779 1 15463 3747 3 1822 1354 1 11702 2012 2 9749 431 2 15618 7450 1 11529 1453 1 8105 4174 1 19606 220 2 863 2964 1 6307 292 5 14838 3586 1 18705 1686 1 7195 5031 7 17778 491 1 542 554 1 19145 495 1 17246 3625 5 6654 5019 1 3185 5186 1 14385 1707 2 9278 1235 1 1606 261 1 3025 532 1 6261 724 1 1090 7672 1 9146 5922 1 4615 1253 1 16568 7292 1 18273 6484 2 7484 1685 1 9146 6435 1 2697 51 1 4860 1332 2 705 1736 5 1611 197 1 15791 638 2 5618 1747 14 863 6041 6 6349 206 15 10459 3073 4 15791 1248 3 15282 219 20 914 5686 1 10396 3257 3 14236 5385 1 13234 861 1 12296 675 1 5963 1718 4 19118 7232 2 3852 3596 2 1385 6098 1 15618 2184 1 7742 6400 6 14236 2424 1 12558 5023 1 3025 471 1 6749 945 1 863 3349 1 11325 1464 1 14913 1698 5 4509 7417 1 16089 910 1 11529 1244 2 4509 4253 2 17738 759 1 566 1748 7 16960 6007 1 8884 1705 1 16089 3911 1 17459 705 1 2271 5879 1 12215 6346 2 8586 1342 1 8763 3285 1 1029 502 1 19145 1374 1 14870 6000 2 6219 4789 9 37 367 1 4859 1748 1 16135 221 1 11796 243 1 4509 1990 2 20110 3671 1 19407 470 2 15495 7850 1 17459 840 1 2629 1729 1 6477 215 1 15791 594 5 13204 57 5 5963 1703 2 576 1363 2 18654 745 1 16135 200 3 1087 7621 2 5721 2295 4 7543 4827 1 2629 1726 2 1090 4490 1 4734 5438 2 6699 220 1 16183 5115 16 3940 3734 1 1302 1367 4 15564 7120 5 10828 347 2 17023 4612 1 15169 4988 1 19199 1761 1 19384 4122 5 7908 2555 7 16624 3979 1 509 215 1 13003 1768 11 14519 2737 2 16468 6993 8 16258 3464 7 12906 3556 2 13190 6487 1 16089 3230 1 509 1295 1 8105 7477 1 19530 3558 1 1385 6421 1 15241 2651 2 16089 1776 1 17833 7716 1 11326 318 5 6749 5131 2 6749 4616 1 15791 95 1 12814 1721 1 12762 7259 17 17449 1775 1 17922 2955 20 6995 3911 1 6749 2938 1 7211 5018 9 1029 4403 1 9904 1234 2 18189 2109 1 12751 7719 36 7742 6557 2 9497 1739 3 4193 2118 1 2629 1707 2 19606 1764 1 1623 3798 1 4734 5402 2 13112 5082 1 3025 411 1 15152 1949 1 7802 3485 1 18656 829 2 19007 3081 1 19878 861 1 12945 3950 4 13190 1784 1 3940 1208 2 15100 622 1 10458 4027 1 16964 411 1 15618 2151 2 16089 229 1 11325 206 3 17246 10 1 18561 6609 1 4061 150 1 15791 4067 1 7838 3617 2 18561 4299 1 13353 1146 1 16468 3278 4 19751 1730 1 6974 2008 1 5730 431 1 1029 471 1 4875 942 3 8884 5737 1 7351 84 1 8092 6375 1 3775 4976 1 7199 7902 2 1014 71 1 18705 1781 1 3646 518 1 15100 879 2 3752 6121 1 10153 5649 11 20193 5288 1 542 379 1 6498 201 3 2183 232 2 7523 198 1 1606 933 1 4769 5290 4 863 8026 1 7966 667 1 13012 1748 1 11529 200 1 4061 5762 1 17833 2367 1 17768 524 2 10396 1737 2 13091 541 3 330 2675 1 19606 1776 1 11547 3571 3 17959 1770 2 19751 2255 5 20154 3216 2 15539 2296 2 4568 3834 1 8763 723 1 12814 1747 1 2499 232 1 283 1250 21 17381 4256 4 13710 221 4 15618 6035 1 19763 452 1 10111 2499 1 4345 7886 5 4615 94 1 8719 2009 1 12639 524 1 9749 687 2 18705 536 1 18262 1249 1 14109 692 2 372 207 77 16959 2363 1 3635 7085 1 3761 5461 1 12494 379 1 11432 1366 1 3082 221 4 14519 3228 6 10300 1266 1 8763 361 1 9654 2029 2 17023 5234 2 15022 3539 1 3116 1705 1 7966 4011 1 8763 1720 1 15781 5133 5 2585 2885 8 13024 3460 1 13353 4501 1 15438 864 1 17449 2354 1 15791 3685 1 4859 2675 1 17957 4489 6 9602 7419 1 16468 7013 1 11632 1820 16 1128 244 1 2697 5315 1 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13234 1907 2 7 225 3 11536 2254 2 19941 207 2 19878 2737 1 3899 525 1 14469 4760 7 16568 4479 1 15169 6368 1 9469 1247 3 4671 1969 1 3542 8141 5 2918 7719 2 14816 23 11 17540 23 2 6585 7853 3 10901 7531 1 910 12 1 10459 5855 1 14127 1118 1 19273 5734 2 12224 2671 1 103 4655 1 10151 2027 1 8074 244 1 18705 1721 1 13091 8141 5 2629 244 2 5128 3666 17 3025 1718 1 6219 2354 1 6477 232 3 15791 7706 12 330 3072 1 6360 3778 5 10111 416 1 1414 214 1 5282 4275 1 7523 1104 1 14385 2584 1 13353 392 1 501 5515 1 18416 6139 5 11326 7213 4 15100 624 1 6654 4039 5 7195 4623 1 3046 1909 1 3445 5090 17 14385 4413 1 18705 853 3 8105 1 1 3761 4460 1 17738 3352 1 7838 877 1 10393 7407 27 10153 3464 3 4615 205 2 16183 1775 17 283 6322 8 12534 364 7 7966 7791 1 6036 7466 1 3940 764 1 6307 1395 9 1850 35 1 18705 1778 1 3940 177 2 2756 1211 1 3153 252 1 8375 709 1 6307 7427 1 11702 2494 1 18582 2353 2 16926 956 1 4241 5649 1 6261 1421 1 4615 1825 29 306 2353 3 8377 385 4 3573 2556 14 467 7259 3 6995 1825 1 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3 20154 7878 10 542 6622 2 7838 575 1 13234 1732 2 16964 3142 1 3176 4849 13 12499 1721 1 1207 7895 1 9654 1305 7 1822 7674 1 566 397 6 19007 2662 1 18656 4337 1 342 200 1 11155 34 2 863 3840 3 16506 1829 15 6974 1395 1 8844 1276 1 17911 550 1 13091 3012 8 11310 6536 3 15725 3889 6 6033 1695 2 1029 2662 1 10828 1909 4 1905 5887 1 14755 7022 1 17738 310 1 16995 2795 1 14720 2646 2 1518 506 5 4734 5526 1 8654 541 3 20154 1184 97 15495 506 1 542 5502 1 5640 1768 2 15791 888 1 17738 304 4 16089 303 1 5282 1688 1 6036 3138 1 17738 2912 1 14504 1819 9 16377 3252 4 3025 244 1 863 873 1 9581 4204 18 6749 7054 1 17448 4517 1 10111 659 1 8884 1247 1 15791 579 5 1970 1464 1 11632 3311 1 15791 1251 1 15781 952 1 12717 7245 6 4615 229 2 12296 57 1 11929 1332 1 12296 7716 1 3353 6888 1 936 1706 5 2473 1285 1 5596 220 6 914 232 1 13864 263 3 18705 520 1 7199 3686 9 11529 1703 1 129 1164 2 1090 2562 2 18416 46 2 8105 5860 1 1109 6638 1 17911 4511 4 8074 1732 1 16132 665 1 10393 497 1 6261 99 1 1665 5129 2 7219 6527 1 6290 214 7 3025 496 1 16041 1718 1 8884 926 1 5606 23 2 16926 4015 1 1090 422 2 7 226 11 3940 967 1 6749 7112 1 19878 222 7 5640 1738 1 10458 3595 1 37 2016 1 7838 642 1 17575 611 1 5552 215 1 542 545 1 2271 379 1 8092 2021 1 17448 4514 5 2387 215 8 4124 162 5 7523 5413 1 5383 274 1 11702 8036 1 8654 214 3 576 1734 1 10393 3593 1 4061 1772 1 6307 1245 1 15100 3530 5 1109 1924 1 16089 200 6 14385 3643 21 15495 1253 4 6561 2649 1 12499 3973 1 5543 5018 1 3852 3591 2 705 2261 1 17833 5312 1 75 3493 3 69 3273 1 15379 673 2 910 2087 1 4139 878 1 6995 411 1 1029 1775 1 19961 2176 1 2585 4963 1 6205 200 1 6261 1401 1 1047 1251 1 1090 823 3 16033 6748 1 19630 3671 3 7195 5052 1 10111 6430 1 103 4640 7 17459 646 1 409 3445 1 13792 5017 15 3220 1655 1 2918 4967 1 15791 3626 1 6385 3697 3 8208 2499 2 12339 943 2 17778 1380 1 6654 5442 3 13792 4833 1 2495 103 1 1087 3596 2 4505 5903 1 2271 1042 1 15379 3576 3 8552 1763 1 16183 1342 17 2401 23 1 ================================================ FILE: programming_assignments/jukebox/solution/code_using_ease/recommend_with_ease.py ================================================ import pandas as pd from scipy.sparse import csr_matrix import numpy as np import sys def gen_top_reco(X, lamb=10.0, K=100, target_user_inds=None): G = (X.T @ X).toarray() diags = np.diag_indices(G.shape[0]) G[diags] += lamb P = np.linalg.inv(G) B = P / -np.diag(P) _X = X if target_user_inds is not None: _X = X[target_user_inds, :] scores = _X @ B scores = np.asarray((scores - _X.astype(bool).astype(int) * 10000)) top_reco = (-scores).argsort(-1)[:, :K] return top_reco listen_count_fname, user_ids_fname, K = sys.argv[1], sys.argv[2], int(sys.argv[3]) with open(user_ids_fname, 'r') as f: target_user_ids = f.read().strip().split() tr = pd.read_csv(listen_count_fname, sep=' ', header=None, dtype=str) tr.columns = ['uid', 'sid', 'cnt'] tr['cnt'] = tr['cnt'] uid2idx = {_id: i for (i, _id) in enumerate(tr.uid.unique())} sid2idx = {_id: i for (i, _id) in enumerate(tr.sid.unique())} idx2uid = {i: _id for (_id, i) in uid2idx.items()} idx2sid = {i: _id for (_id, i) in sid2idx.items()} tr['uidx'] = tr.uid.apply(lambda x: uid2idx[x]) tr['sidx'] = tr.sid.apply(lambda x: sid2idx[x]) n_user, n_item = len(uid2idx), len(sid2idx) with open('./user_id.txt', 'w') as f: print('\n'.join(tr.uid.tolist()), file=f) X = csr_matrix((tr.cnt, (tr.uidx, tr.sidx)), shape=(n_user, n_item), dtype=np.float32) X.data[:] = 1.0 + np.log(1.0 + X.data[:]) target_user_inds = [uid2idx[uid] for uid in target_user_ids] top_reco = gen_top_reco(X, lamb=30.0, K=K, target_user_inds=target_user_inds) for uid, rec_list in zip(target_user_ids, top_reco): rec_sids = [str(idx2sid[sidx]) for sidx in rec_list] print(uid, ' '.join(rec_sids)) ================================================ FILE: programming_assignments/jukebox/solution/code_using_ease/recommend_with_sgd.py ================================================ import pandas as pd from scipy.sparse import csr_matrix import numpy as np from jax import grad, jit import jax.numpy as jnp import sys listen_count_fname, user_ids_fname, K = sys.argv[1], sys.argv[2], int(sys.argv[3]) with open(user_ids_fname, 'r') as f: target_user_ids = f.read().strip().split() tr = pd.read_csv(listen_count_fname, sep=' ', header=None, dtype=str) tr.columns = ['uid', 'sid', 'cnt'] tr['cnt'] = tr['cnt'] uid2idx = {_id: i for (i, _id) in enumerate(tr.uid.unique())} sid2idx = {_id: i for (i, _id) in enumerate(tr.sid.unique())} idx2uid = {i: _id for (_id, i) in uid2idx.items()} idx2sid = {i: _id for (_id, i) in sid2idx.items()} tr['uidx'] = tr.uid.apply(lambda x: uid2idx[x]) tr['sidx'] = tr.sid.apply(lambda x: sid2idx[x]) n_user, n_item = len(uid2idx), len(sid2idx) with open('./user_id.txt', 'w') as f: print('\n'.join(tr.uid.unique()), file=f) X = csr_matrix((tr.cnt, (tr.uidx, tr.sidx)), shape=(n_user, n_item), dtype=np.float32) X.data[:] = 1.0 + np.log(1.0 + X.data[:]) jX = jnp.array(X.todense()) P = jnp.array(np.random.normal(0, 0.001, size=(n_item, n_item))) P = P.at[jnp.diag_indices(P.shape[0])].set(0) @jit def loss_fn(X, P): ret = (((X - X @ P) **2).sum() / X.shape[0]) ret = ret return ret @jit def loss_fn_with_reg(X, P): ret = loss_fn(X, P) ret = ret + 0.01 * (P * P).sum() return ret grad_fn = grad(loss_fn_with_reg, argnums=1) lr = 0.06 for i in range(100): batch = np.random.choice(X.shape[0], 512) r = grad_fn(jX[batch], P) P -= lr * r P = P.at[jnp.diag_indices(P.shape[0])].set(0) lr *= 0.99 target_user_inds = [uid2idx[uid] for uid in target_user_ids] scores = X[target_user_inds] @ np.array(P) scores = np.asarray(scores - X[target_user_inds].astype(bool).astype(int) * 10000) top_reco = (-scores).argsort(-1)[:, :K] for uid, rec_list in zip(target_user_ids, top_reco): rec_sids = [str(idx2sid[sidx]) for sidx in rec_list] print(uid, ' '.join(rec_sids)) ================================================ FILE: programming_assignments/mini_reco/README.md ================================================ # Mini Reco 문제 출제 및 검수: [김성진(nick.kim)](https://github.com/lancifollia), [양세현(dan.ce)](https://github.com/yangsehyun) > 이 문제로 영입을 진행하며 지원자분에게 드렸던 인터뷰 질문은 [interview.md](interview.md)에 있습니다. 문제를 풀어보시고 이 문서도 확인해보세요. ## 목차 - [소개](#소개) - [User-based Collaborative Filtering](#user-based-collaborative-filtering) - [문제](#문제) - [참고 사항](#참고-사항) - [입력 데이터](#입력-데이터) - [제한 사항](#제한-사항) - [평가](#평가) - [예시](#예시) - [예제 테스트 케이스](#예제-테스트-케이스) - [예제 입력](#예제-입력) - [예제 출력](#예제-출력) - [설명](#설명) ## 소개 이 문제의 목표는 Memory-based Collaborative Filtering 기법 중 하나인 User-based Collaborative filtering 알고리즘을 사용해 추천 시스템을 만드는 것입니다. 아래 알고리즘을 구현하여 Task를 수행하세요. ## User-based Collaborative Filtering The [memory-based](https://en.wikipedia.org/wiki/Collaborative_filtering#Memory-based) approach uses user rating data to compute the similarity between users or items. Typical examples of this approach are neighbourhood-based CF and item-based/user-based top-N recommendations. For example, in user based approaches, the value of ratings user $\large u$ gives to item $\large i$ is calculated as an aggregation of some similar users' rating of the item: $$\large r_{u,i} = \mathop{\mathrm{aggr}}\limits_{u^\prime \in U} r_{u^\prime, i}$$ where $\large U$ denotes the set of top N users that are most similar to user $\large u$ who rated item $\large i$. Some examples of the aggregation function includes: $$\large \displaylines{ r_{u,i} =& \frac{1}{N}\sum\limits_{u^\prime \in U}r_{u^\prime, i}\\ r_{u,i} =& k\sum\limits_{u^\prime \in U}\mathop{\mathrm{simil}}(u,u^\prime)r_{u^\prime, i} }$$ where $\large k$ is a normalizing factor defined as $\large k = 1/\sum_{u^\prime \in U}|\mathop{\mathrm{simil}}(u,u^\prime)|$, and $$\large \textbf{(1)} \qquad r_{u,i} = \bar{r_u} + k\sum\limits_{u^\prime \in U}\mathop{\mathrm{simil}}(u,u^\prime)(r_{u^\prime, i}-\bar{r_{u^\prime}})$$ where $\large \bar{r_u}$ is the average rating of user $\large u$ for all the items rated by $\large u$. The neighborhood-based algorithm calculates the similarity between two users or items, and produces a prediction for the user by taking the [weighted average](https://en.wikipedia.org/wiki/Weighted_average) of all the ratings. Similarity computation between items or users is an important part of this approach. Multiple measures, such as [Pearson correlation](https://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient) and [vector cosine](https://en.wikipedia.org/wiki/Cosine_similarity) based similarity are used for this. The cosine similarity of two users $\large x$, $\large y$ is defined as: $$\large \textbf{(2)} \qquad \mathop{\mathrm{simil}}(x,y) = \cos(\vec x,\vec y) = \frac{\vec x \cdot \vec y}{||\vec x|| \times ||\vec y||} = \frac{\sum\limits_{i \in I_{xy}}r_{x,i}r_{y,i}}{\sqrt{\sum\limits_{i \in I_{x}}r_{x,i}^2}\sqrt{\sum\limits_{i \in I_{y}}r_{y,i}^2}}$$ where $\large I_{xy}$ is the set of items that rated by both user $\large x$ and user $\large y$. The user based top-N recommendation algorithm uses a similarity-based vector model to identify the $\large k$ most similar users to an active user. After the $\large k$ most similar users are found, their corresponding user-item matrices are aggregated to identify the set of items to be recommended. ## 문제 `num_reco_users`명의 사용자를 위해 User-based Collaborative Filtering 알고리즘으로 추천 결과를 만들어야 합니다. 추천 결과를 만드는 방법은 다음과 같습니다. 1. 식 (2)를 활용하여 최근접 이웃 집합 $\large U$를 계산합니다. - $\large U$는 사용자와 유사도가 가장 높은 `num_sim_user_top_N`명의 최근접 이웃 사용자로 구성됩니다. 1. 식 (1)로 생성한 `num_item_rec_top_M` 개의 추천 결과를 한 줄로 출력합니다. - 추천 결과의 각 아이템 ID는 공백으로 구분되어야 합니다. - 사용자에게 추천할 수 있는 아이템은 전체 아이템 집합 $\large I$가 아닌 최근접 이웃 $\large U$가 평가한 아이템 집합 $\large I^\prime$입니다. ### 참고 사항 문제를 해결할 때 아래 내용을 참고하시기 바랍니다. 1. 사용자가 이미 평가한 아이템은 추천 결과에 포함하지 않습니다. 1. 추천할 수 있는 아이템의 수(n)가 `num_item_rec_top_M` 보다 작은 경우, 그 n개에 대해서만 추천합니다. 1. 한 사용자가 같은 아이템을 중복해서 평가한 경우는 없습니다. 1. 데이터는 희소 행렬 데이터입니다. 그러므로 모든 사용자와 아이템 쌍에 대한 평가가 존재하는 것은 아닙니다. 1. Cosine similarity 계산이 정의되지 않는 경우에는 0으로 정의합니다. 1. 식 (1)에서 normalizing factor $\large k$ 값이 정의되지 않는 경우에는 0으로 정의합니다. ## 입력 데이터 데이터는 알고리즘 구현에 필요한 변숫값과 사용자가 아이템에 평가한 점수 그리고 추천 결과를 출력할 사용자 ID로 구성됩니다. - Line 1에는 `num_sim_user_top_N` 값이 있습니다. 평점 예측 시 사용할 최근접 이웃 사용자 수입니다. - Line 2에는 `num_item_rec_top_M` 값이 있습니다. 사용자별로 추천해야 하는 아이템 개수입니다. - Line 3, 4에는 각각 `num_users`, `num_items` 값이 있습니다. 해당 테스트 케이스에서 제공되는 데이터에 있는 사용자, 아이템 수입니다. - Line 5에는 `num_rows` 값이 있습니다. 데이터로 제공될 (`user_id`, `item_id`, `rating`) triplet의 개수입니다. - Line 6부터 `num_rows`개의 Line에는 (`user_id`, `item_id`, `rating`) triplet이 있으며 각 값은 공백으로 구분되어 있습니다. - Line (6 + `num_rows`)에는 `num_reco_users` 값이 있습니다. 추천 결과를 만들어야 할 사용자의 수입니다. - Line (6 + `num_rows` + 1)부터 `num_reco_users`개의 Line에는 추천 결과를 만들어야 할 사용자 ID가 있습니다. 아래는 예시입니다. _(**주의**: `//` 이하는 데이터에 대한 설명이며 실제 데이터에는 존재하지 않습니다.)_ ```C 2 // num_sim_user_top_N 2 // num_item_rec_top_M 5 // num_users 10 // num_items 15 // num_rows 1 1 2.34 // 사용자 1이 아이템 1에 2.34점 부여 1 2 6.21 // 사용자 1이 아이템 2에 6.21점 부여 2 3 1.1 // 사용자 2가 아이템 3에 1.1점 부여 ... ... // Line 20 (= 5 + num_rows) 2 // num_reco_users 1 // print num_item_rec_top_M items for user 1 2 // print num_item_rec_top_M items for user 2 ``` ### 제한 사항 - 1 <= `num_sim_user_top_N` <= 100 (integer) - 1 <= `num_item_rec_top_M` <= 30 (integer) - 1 <= `num_users` <= 300 (integer) - 1 <= `num_items` <= 70 (integer) - 1 <= `num_rows` <= 21,000 (integer) - 1 <= `num_reco_users` <= 100 (integer) - 1 <= `user_id` <= 300 (integer) - 1 <= `item_id` <= 70 (integer) - 1.0 <= `rating` <= 10.0 (real number) ## 평가 채점은 추천 결과와 정답 데이터의 유사성으로 평가합니다. _(nDCG: )_ 채점 코드에서는 정답에서 추천 결과 위치와 제출한 추천 결과 위치가 동일하면 1.0, 다르면 0.7을 부여하는 방식을 사용합니다. 간단하게 아래 두 가지 특징을 참고하시기 바랍니다. 1. 정답 추천 결과와 최대한 같은 순서로 추천해야 높은 nDCG 값을 얻을 수 있습니다. (이 문제의 목적은 Memory-based CF 알고리즘 로직을 정확하게 구현하는 것이지, 더 좋은 추천 결과를 생성하는 것이 아니라는 점을 유념해주시기 바랍니다.) 1. 높은 순위의 추천 결과를 틀릴수록 페널티가 큽니다. 이렇게 계산한 nDCG가 0.9를 넘으면 해당 테스트 케이스는 정답으로 채점하며, 0.9를 넘지 못하면 해당 테스트 케이스는 오답으로 채점합니다. 참고로 Python으로 작성된 nDCG 계산 코드는 아래와 같습니다. ```python # evaluation.py import math def ndcg(gt, rec): idcg = sum([1.0 / math.log(i + 2, 2) for i in range(len(gt))]) dcg = 0.0 for i, r in enumerate(rec): if r not in gt: continue gt_index = gt.index(r) if i != gt_index: rel = 0.7 else: rel = 1.0 dcg += rel / math.log(i + 2, 2) ndcg = dcg / idcg return ndcg ``` 위 코드에서 변수 `gt`는 정답 추천 결과이며, 변수 `rec`는 제출된 추천 결과를 의미합니다. ### 예시 ```python # 예시 1 >>> gt = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] >>> rec = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] >>> ndcg(gt, rec) 1.0 ``` 예시 1은 정답과 완전히 동일한 경우이며, nDCG는 1.0입니다. ```python # 예시 2 >>> gt = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] >>> rec = [1, 2, 3, 11, 5, 6, 7, 8, 9, 10] >>> ndcg(gt, rec) 0.9052116356304495 ``` 예시 2는 네 번째 추천 결과를 틀린 경우입니다. ```python # 예시 3 >>> gt = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] >>> rec = [1, 2, 3, 4, 5, 6, 7, 11, 9, 10] >>> ndcg(gt, rec) 0.9305687780632229 ``` 예시 3은 여덟 번째 추천 결과를 틀린 경우입니다. 네 번째 추천 결과를 틀린 예시 2보다는 여덟 번째 추천 결과를 틀린 예시 3의 nDCG가 높습니다. 즉, 높은 순위의 추천 결과를 틀릴수록 nDCG 페널티가 큽니다. ## 예제 테스트 케이스 ### 예제 입력 ```text 2 2 5 10 15 1 1 1.0 1 2 2.0 1 5 1.2 2 2 1.5 2 3 3.0 3 1 2.2 3 2 6.2 3 7 1.5 4 6 1.2 4 3 1.5 4 1 3.1 4 2 4.0 5 4 8.2 5 2 6.5 5 7 8.0 2 1 2 ``` ### 예제 출력 ```text 3 6 1 6 ``` ### 설명 위 입력으로부터 얻은 값들은 아래와 같습니다. - Line 1: `num_sim_user_top_N` = 2 (집합 U는 최고 유사 사용자 2명으로 만들어야 함) - Line 2: `num_item_rec_top_M` = 2 (사용자별 추천 결과는 2개를 만들어야 함) - Line 3: `num_users` = 5 (평점 데이터의 사용자 수는 총 5명) - Line 4: `num_items` = 10 (평점 데이터의 아이템 수는 총 10개) - Line 5: `num_rows` = 15 (평점 데이터의 row 개수는 15개) - Line 6~20: 평점 데이터의 triplet (`user_id`, `item_id`, `rating`) - Line 21: `num_reco_users` = 2 (추천 결과를 만들어야 할 사용자 수는 2명) - Line 22~23: 추천 결과를 만들어야 할 사용자의 ID 리스트 (`user_id`= 1, 2에 해당하는 사용자의 추천 결과를 만들어서 출력해야 함) 정리하면, 주어진 평점 데이터를 이용해서 사용자 1, 사용자 2에게 각각 추천 결과를 2개씩 만들어주면 됩니다. 식(1)을 이용해 추천 결과를 계산할 때 사용하는 집합 $\large U$는 추천 결과를 만들어야 할 사용자와 가장 유사한 사용자 2명으로 구성합니다. 사용자 1의 경우, 최고 유사 사용자는 사용자 3, 사용자 4이고, 사용자 1과의 유사도는 각각 0.85263, 0.80806입니다. 이렇게 구한 집합 U를 이용해서 식(1)을 계산해서 예측 평점이 가장 높은 아이템 2개를 예측 평점 순으로 내림차순 정렬해서 출력하면 됩니다. 단, 추천 결과를 만들 때는 사용자 1이 기존에 평가한 아이템(샘플에서는 아이템 1, 아이템 2, 아이템 5)은 추천 결과에서 빠져야 하는 점을 유의해주시기 바랍니다. 위 출력 예시의 첫 번째 줄에 있는 `3 6`은 정답 소스 코드로 계산한 사용자 1의 추천 결과 1순위는 아이템 3이며, 2순위는 아이템 6이라는 뜻입니다. 사용자 1, 사용자 2의 정답 추천 결과와 제출된 추천 결과 간 nDCG 계산 후, 0.9 이상이면 정답 처리합니다. ================================================ FILE: programming_assignments/mini_reco/evaluation.py ================================================ import math def ndcg(gt, rec): idcg = sum([1.0 / math.log(i + 2, 2) for i in range(len(gt))]) dcg = 0.0 for i, r in enumerate(rec): if r not in gt: continue gt_index = gt.index(r) if i != gt_index: rel = 0.7 else: rel = 1.0 dcg += rel / math.log(i + 2, 2) ndcg = dcg / idcg return ndcg ================================================ FILE: programming_assignments/mini_reco/interview.md ================================================ # Mini Reco 인터뷰 질문 > [▶︎ Mini Reco 문제로 돌아가기](README.md) Mini Reco 문제로 영입을 진행하며 지원자분에게 드렸던 인터뷰 질문과 예시 답변을 모아놓았습니다. ## 질문 1 [User-based Collaborative Filtering 설명](README.md#user-based-collaborative-filtering)의 식 (1)을 보고 추천 결과가 어떻게 생성되는지 설명해주세요. $$\large \textbf{(1)} \qquad r_{u,i} = \bar{r_u} + k\sum\limits_{u^\prime \in U}\mathop{\mathrm{simil}}(u,u^\prime)(r_{u^\prime, i}-\bar{r_{u^\prime}})$$
예시 답변 - 유저의 특정 아이템에 대한 예측 평점은 아래 두 항을 더해서 구한다. - 우변 첫번째 항은 해당 유저의 평점 평균을 의미하고, - 우변 두번째 항은 유사 이웃들의 평점 편차의 가중 평균을 의미한다.
## 질문 2 [User-based Collaborative Filtering 설명](README.md#user-based-collaborative-filtering)의 식 (1)이 다음과 같이 바뀐다면( $\large\bar{r_u}$, $\large\bar{r_{u^\prime}}$ 항이 사라진다면) 추천 결과가 어떻게 달라질까요? $$\large \textbf{(1-1)} \qquad r_{u,i} = k\sum\limits_{u^\prime \in U}\mathop{\mathrm{simil}}(u,u^\prime)(r_{u^\prime, i})$$
힌트 - 만약 특정 유저의 점수가 굉장히 짠 편이라면(모든 아이템에 대해서 낮은 점수를 부여한다면) 어떤 상황이 발생할까요?
예시 답변 - 식 (1)에서 (1-1)로 바뀌는 것은 bias 텀 없이 이웃들의 평점 평균으로만 해당 유저의 평점을 계산하는 것을 의미한다. - 하지만 유저의 평점 bias가 서로 다르고 그 점이 반영되지 않는다면, 제대로 된 추천 결과(예상 평점)가 계산되지 않을 수 있다. (극단적으로) 예를 들면, 유저 A의 평점 평균은 2점이고 유저 A의 최근접 이웃들의 평점 평균은 4.5점인 상황을 가정해보자. 유저 A의 최근접 이웃들이 특정 아이템 B에 대해서 평균 3점 정도의 평가를 내렸다고 할 때, (bias를 반영하지 않는 식 (1-1)의 경우) 최근접 이웃들의 기준으로 보았을 때 아이템 B는 비추천할만한 아이템이지만 유저 A의 평점 평균과 비교해보았을때는 추천 작품이 될 수 있다. 따라서 각 유저의 평점 bias를 반영하여 추천 결과(예상 평점)를 계산하는 것이 더 좋은 결과를 낼 수 있을 것이다.
## 질문 3 [User-based Collaborative Filtering 설명](README.md#user-based-collaborative-filtering)의 식 (1)이 다음과 같이 바꾸려고 한다면( $\large\mathop{\mathrm{simil}}(u,u^\prime)$ 항이 사라진다면) 식을 어떻게 수정해야할까요? $$\large \textbf{(1-2)} \qquad r_{u,i} = \bar{r_u} + k\sum\limits_{u^\prime \in U}(r_{u^\prime, i}-\bar{r_{u^\prime}})$$
예시 답변 - 식 (1)에서 우변의 마지막 항은 최근접 이웃이 해당 아이템에 매긴 평점의 가중 평균이었으나, 식 (1-2)에서는 가중 평균이 아닌 산술 평균으로 변경하려는 것으로 볼 수 있다. - 따라서 $\large k=\frac{1}{|U|}$로 수정하면 최근접 이웃의 평점의 산술 평균으로 계산한 추천 결과(예상 평점)를 얻을 수 있을 것이다.
================================================ FILE: programming_assignments/mini_reco/solution/solution.py ================================================ import sys # 데이터 입력 num_sim_user_top_N = int(sys.stdin.readline()) # 유사도 top N 사용자에 대하여 예측 평점 계산 num_item_rec_top_M = int(sys.stdin.readline()) # 예측 평점 top M 아이템 출력 num_users = int(sys.stdin.readline()) # 전체 사용자 수 num_items = int(sys.stdin.readline()) # 전체 아이템 수 num_rows = int(sys.stdin.readline()) # 입력 row 개수 rating_data = {} # {사용자 ID: {아이템 ID: 평점}} 형태로 저장 items = set() # 모든 아이템을 모아놓은 set # row 입력 for _ in range(num_rows): user, item, rating = sys.stdin.readline().split(' ') user = int(user) item = int(item) rating = float(rating) if user not in rating_data: rating_data[user] = {} rating_data[user][item] = rating items.add(item) # 사용자 별 평균 평점 계산 user_average_rating = dict() # {사용자 ID: 평균 평점} 형태로 저장 for user, item_ratings in rating_data.items(): user_average_rating[user] = sum(item_ratings.values()) / len(item_ratings) num_reco_users = int(sys.stdin.readline()) # 추천할 사용자 수 for _ in range(num_reco_users): query_user = int(sys.stdin.readline()) # 추천할 사용자 ID user_sim = dict() # {사용자 ID: 유사도} 형태로 저장 # 사용자 별 유사도(cosine similarity) 계산 (query_user 자신과는 계산 안함) for user in rating_data.keys() - {query_user}: user_ratings = rating_data[user] query_user_ratings = rating_data[query_user] intersection_items = rating_data[query_user].keys() & rating_data[user].keys() numerator = sum(user_ratings[item] * query_user_ratings[item] for item in intersection_items) denominator = sum(rating ** 2 for rating in user_ratings.values()) ** 0.5 denominator *= sum(rating ** 2 for rating in query_user_ratings.values()) ** 0.5 # 유사도 계산해서 저장 (계산되지 않는 경우 0으로 정의) user_sim[user] = numerator / denominator if denominator > 0.0 else 0.0 # 유사도 기준으로 정렬. [(사용자 ID, 유사도), ...] 형태의 list of tuple로 저장 nearest = sorted(user_sim.items(), key=lambda x: x[1], reverse=True) predicted_rating = list() # 예측 평점 (높은 순서에 따라 추천됨). [(아이템 ID, 예측 평점), ...] 형태의 list of tuple로 저장 # 이미 평가한 정보가 있으면 예측 평점을 계산하지 않음 for item in items - rating_data[query_user].keys(): sum_k = 0 # normalizing factor k 계산을 위한 sum. k = 1 / sum_k sum_u = 0 # SUM for u' in U [simil(u, u') * (r_u'i - r_u')] # 유사도 top N 사용자에 대해 계산 for user, similarity in nearest[:num_sim_user_top_N]: # 사용자가 아이템을 평가하지 않았으면 계산하지 않음 if item not in rating_data[user]: continue sum_u += similarity * (rating_data[user][item] - user_average_rating[user]) sum_k += abs(similarity) # 아이템의 예측 평점 (r_ui) # 유사도 top N 사용자가 모두 아이템을 평가하지 않았으면 이 아이템에 대해 예측할 수 없음 (0으로 정의) r_ui = user_average_rating[query_user] + (1 / sum_k) * sum_u if sum_k > 0.0 else 0.0 predicted_rating += [(item, r_ui)] # 예측 평점 list에 저장 predicted_rating.sort(key=lambda x: x[1], reverse=True) # 예측 평점 list 정렬 print(' '.join(str(item_rating[0]) for item_rating in predicted_rating[:num_item_rec_top_M])) # 추천 리스트 출력 ================================================ FILE: programming_assignments/mini_reco/testcase/input/input000.txt ================================================ 2 2 5 10 15 1 1 1.0 1 2 2.0 1 5 1.2 2 2 1.5 2 3 3.0 3 1 2.2 3 2 6.2 3 7 1.5 4 6 1.2 4 3 1.5 4 1 3.1 4 2 4.0 5 4 8.2 5 2 6.5 5 7 8.0 2 1 2 ================================================ FILE: programming_assignments/mini_reco/testcase/input/input001.txt ================================================ 32 7 200 50 3454 1 1 4.989 1 2 1.000 1 3 4.989 1 4 1.000 1 5 1.000 1 6 6.338 1 7 1.000 1 8 2.543 1 9 1.000 1 10 1.000 1 11 2.543 1 12 4.989 1 13 1.000 1 14 4.086 1 15 4.989 1 16 1.000 1 17 1.000 1 18 1.000 1 19 2.543 1 20 5.332 1 21 4.989 1 22 1.000 1 23 1.000 1 24 5.332 1 25 4.583 1 26 1.000 1 27 1.000 1 28 5.332 1 29 4.583 2 21 1.000 2 26 1.000 2 2 1.000 2 8 5.332 2 27 4.583 2 15 5.332 2 17 1.000 2 30 1.000 2 31 1.000 2 24 3.446 2 25 1.000 2 29 1.000 3 18 1.000 3 2 3.446 3 4 4.583 3 23 1.000 3 31 3.446 3 15 5.629 3 11 4.989 3 5 5.332 3 19 3.446 3 32 3.446 3 30 4.989 3 20 4.989 3 21 4.086 3 22 1.000 3 24 5.332 3 14 5.332 3 33 5.332 3 26 4.086 3 34 4.989 3 27 2.543 3 10 1.000 3 35 4.583 3 28 5.332 3 29 5.332 4 21 5.332 4 2 4.989 4 4 4.583 4 10 4.989 4 9 4.583 4 15 5.332 4 32 4.583 4 36 4.989 4 19 4.989 4 37 4.583 4 31 4.583 4 22 2.543 4 33 4.583 4 28 4.583 4 29 5.332 4 11 4.086 5 21 2.543 5 31 4.086 5 2 2.543 5 38 5.629 5 7 1.000 5 19 5.629 5 16 5.629 5 13 5.629 5 5 4.989 5 18 1.000 5 20 6.126 5 39 5.891 5 22 1.000 5 23 3.446 5 33 5.891 5 34 5.891 5 10 1.000 5 35 6.338 6 14 1.000 6 6 5.332 6 17 1.000 6 8 4.086 6 40 1.000 6 41 1.000 6 42 2.543 6 30 2.543 6 31 4.086 6 38 4.583 6 26 4.086 6 34 1.000 6 27 2.543 6 24 4.583 6 28 3.446 7 12 4.989 7 2 4.086 7 3 6.126 7 4 5.891 7 33 1.000 7 7 4.583 7 26 2.543 7 10 2.543 7 15 6.710 7 5 3.446 7 37 1.000 7 20 1.000 7 38 4.086 7 34 4.989 7 24 5.332 7 28 5.332 7 18 3.446 7 14 5.332 8 16 4.086 8 5 3.446 8 32 4.583 8 20 1.000 8 9 1.000 8 29 4.583 8 22 1.000 8 24 3.446 8 33 4.583 8 38 2.543 8 26 3.446 8 18 6.532 9 1 5.332 9 3 5.891 9 4 2.543 9 6 7.028 9 43 4.989 9 8 1.000 9 44 5.891 9 9 1.000 9 12 4.989 9 19 1.000 9 15 3.446 9 17 5.332 9 31 4.583 9 25 5.629 9 34 2.543 9 45 5.332 9 46 5.332 9 18 3.446 10 21 4.989 10 6 3.446 10 7 2.543 10 23 1.000 10 16 4.583 10 17 4.583 10 37 3.446 10 31 4.086 10 39 4.583 10 13 2.543 10 35 5.332 11 2 2.543 11 4 6.532 11 6 6.338 11 7 1.000 11 36 4.086 11 23 4.989 11 10 6.126 11 11 5.891 11 5 6.338 11 19 6.532 11 32 6.338 11 17 4.086 11 20 6.710 11 21 5.891 11 18 7.669 11 33 6.338 11 35 7.028 11 29 4.086 12 21 7.307 12 31 7.172 12 2 5.332 12 4 8.253 12 6 4.989 12 43 1.000 12 5 7.434 12 23 9.267 12 10 7.172 12 11 1.000 12 36 1.000 12 19 7.777 12 20 7.777 12 22 2.543 12 18 8.571 12 28 4.583 13 1 4.583 13 4 5.891 13 43 1.000 13 9 3.446 13 10 4.583 13 12 3.446 13 15 4.086 13 3 1.000 13 36 3.446 13 5 4.086 13 20 4.989 13 21 3.446 13 31 4.989 13 18 4.086 13 25 2.543 13 34 2.543 13 24 3.446 14 44 4.086 14 43 1.000 14 36 6.126 14 47 1.000 14 22 1.000 14 14 5.332 14 28 6.338 14 11 4.086 15 3 1.000 15 6 5.891 15 8 4.583 15 32 4.989 15 17 3.446 15 37 4.583 15 20 1.000 15 31 6.875 15 25 7.554 15 27 1.000 15 35 3.446 15 24 3.446 16 25 6.338 16 1 5.629 16 44 5.629 16 2 3.446 16 36 6.338 16 12 3.446 16 27 4.583 16 15 1.000 16 17 4.086 16 31 5.332 16 22 3.446 16 24 5.332 16 14 6.875 16 33 6.532 16 38 4.989 16 26 5.332 16 34 3.446 16 10 1.000 16 45 5.332 16 28 5.332 17 4 2.543 17 22 1.000 17 6 7.028 17 5 2.543 17 23 1.000 17 10 2.543 17 11 4.989 17 2 2.543 17 35 5.629 17 19 1.000 17 17 3.446 17 20 6.126 17 31 3.446 17 37 1.000 17 24 1.000 17 14 4.583 17 25 6.532 17 33 1.000 17 34 2.543 17 27 2.543 17 28 5.629 17 29 5.332 17 18 1.000 18 2 1.000 18 23 1.000 18 10 2.543 18 4 2.543 18 14 4.086 18 19 1.000 18 5 1.000 18 18 1.000 18 21 4.989 18 33 1.000 18 22 1.000 18 28 5.629 19 1 7.881 19 44 7.307 19 3 5.891 19 7 1.000 19 9 2.543 19 23 1.000 19 10 2.543 19 15 4.583 19 16 2.543 19 14 4.086 19 4 2.543 19 36 2.543 19 12 6.710 19 48 5.629 19 47 2.543 19 30 2.543 19 29 5.629 19 33 1.000 19 34 2.543 19 27 3.446 19 6 6.532 19 17 3.446 19 43 1.000 19 8 1.000 19 5 1.000 19 42 2.543 19 20 5.891 19 22 1.000 19 24 5.629 19 25 5.629 19 35 6.126 19 45 7.307 19 46 7.669 19 18 1.000 19 19 1.000 19 41 5.629 19 39 2.543 19 28 5.891 19 21 7.172 19 11 4.989 20 6 2.543 20 9 1.000 20 11 5.332 20 5 4.583 20 19 5.891 20 20 4.086 20 10 4.086 20 18 7.554 21 43 1.000 21 11 2.543 21 12 3.446 21 15 3.446 21 17 4.086 21 30 5.332 21 22 2.543 21 24 5.332 21 34 3.446 22 3 4.583 22 4 1.000 22 6 7.434 22 7 2.543 22 8 1.000 22 23 1.000 22 10 1.000 22 31 2.543 22 16 1.000 22 11 4.583 22 5 2.543 22 17 1.000 22 21 5.332 22 39 1.000 22 18 1.000 22 46 3.446 22 20 4.583 23 21 5.332 23 7 4.086 23 43 5.891 23 16 5.332 23 32 5.332 23 17 6.126 23 37 5.332 23 13 4.989 23 35 5.891 24 12 4.989 24 1 5.629 24 44 6.126 24 2 2.543 24 22 1.000 24 9 1.000 24 23 1.000 24 14 4.583 24 15 5.332 24 16 2.543 24 5 2.543 24 18 1.000 24 45 5.332 24 26 4.989 24 27 1.000 24 10 2.543 24 24 5.629 24 28 5.891 24 29 4.989 24 46 5.629 25 6 4.583 25 43 1.000 25 34 2.543 25 46 4.583 25 41 4.989 25 12 4.989 25 15 5.891 25 32 4.989 25 17 5.629 25 48 5.332 25 30 3.446 25 37 4.989 25 49 4.989 25 18 5.891 25 24 5.629 25 33 1.000 25 27 3.446 25 50 4.989 26 1 4.583 26 44 3.446 26 2 4.583 26 4 5.629 26 43 4.583 26 9 4.086 26 23 4.583 26 46 3.446 26 10 6.126 26 11 4.989 26 15 4.583 26 36 5.332 26 5 4.583 26 19 4.086 26 32 2.543 26 48 4.583 26 42 4.086 26 30 4.086 26 20 5.629 26 31 1.000 26 29 5.891 26 22 2.543 26 24 1.000 26 33 5.332 26 38 5.891 26 26 4.583 26 27 1.000 26 45 3.446 26 28 5.629 26 18 4.989 26 14 4.989 27 4 1.000 27 6 7.434 27 7 1.000 27 9 1.000 27 23 1.000 27 10 1.000 27 11 4.989 27 12 5.891 27 19 1.000 27 16 1.000 27 13 1.000 27 5 1.000 27 18 1.000 27 17 1.000 27 39 1.000 27 20 6.875 27 21 6.126 27 33 1.000 27 27 4.989 27 35 6.710 27 28 5.891 27 29 6.875 28 21 1.000 28 44 1.000 28 3 1.000 28 1 1.000 28 48 1.000 28 17 1.000 28 9 1.000 28 10 1.000 28 11 4.086 28 12 1.000 28 15 1.000 28 13 1.000 28 36 1.000 28 5 1.000 28 47 1.000 28 39 1.000 28 37 2.543 28 28 1.000 28 22 1.000 28 24 2.543 28 25 7.172 28 27 3.446 28 45 1.000 28 46 1.000 28 50 2.543 29 1 4.989 29 44 4.989 29 26 2.543 29 9 4.989 29 10 3.446 29 12 4.086 29 15 4.583 29 18 4.989 29 5 4.086 29 27 1.000 29 24 4.086 29 34 1.000 29 45 4.989 29 28 2.543 29 29 5.891 29 46 4.989 30 31 4.989 30 6 6.338 30 7 1.000 30 11 4.989 30 12 2.543 30 14 1.000 30 15 6.532 30 16 1.000 30 13 2.543 30 21 4.086 30 9 1.000 30 35 5.629 30 29 5.332 31 4 5.629 31 6 2.543 31 26 1.000 31 9 1.000 31 10 5.891 31 15 6.126 31 16 5.629 31 19 4.086 31 37 1.000 31 31 5.629 31 29 5.629 31 18 7.434 31 23 1.000 31 35 2.543 31 28 6.126 32 1 4.583 32 9 1.000 32 11 4.583 32 15 5.332 32 13 5.891 32 5 2.543 32 31 3.446 32 22 1.000 32 25 4.583 32 28 4.086 32 46 4.989 32 18 3.446 32 14 1.000 32 20 4.989 33 1 1.000 33 2 5.629 33 6 7.028 33 9 5.332 33 23 4.086 33 10 6.126 33 16 4.583 33 19 2.543 33 12 4.989 33 29 4.086 33 28 3.446 33 4 1.000 33 5 4.086 33 32 4.583 33 20 4.583 33 18 5.891 33 22 2.543 33 11 4.086 34 2 5.891 34 4 3.446 34 25 4.086 34 5 4.086 34 19 4.086 34 17 3.446 34 37 1.000 34 31 6.532 34 33 2.543 34 35 7.307 34 24 7.434 35 2 1.000 35 6 6.338 35 7 1.000 35 12 4.583 35 4 4.989 35 19 4.989 35 21 5.332 35 20 5.891 35 18 5.332 35 23 4.989 35 10 4.989 35 35 4.086 36 4 6.126 36 33 1.000 36 23 6.532 36 10 6.126 36 3 4.086 36 16 4.583 36 36 5.629 36 20 6.338 36 22 2.543 36 18 7.307 36 14 5.891 36 38 5.891 36 12 1.000 36 28 5.891 37 2 3.446 37 4 4.583 37 23 5.629 37 10 5.332 37 12 4.086 37 5 4.989 37 19 4.086 37 17 4.583 37 20 5.891 37 31 4.989 37 22 1.000 37 18 5.629 37 24 5.891 37 28 4.086 38 1 4.989 38 44 4.989 38 2 1.000 38 3 1.000 38 28 1.000 38 43 1.000 38 8 1.000 38 9 1.000 38 15 1.000 38 36 1.000 38 32 5.332 38 39 1.000 38 37 2.543 38 31 7.307 38 18 1.000 38 24 6.338 38 25 7.028 38 34 1.000 38 27 2.543 38 45 4.583 38 29 4.086 39 12 4.086 39 26 1.000 39 43 1.000 39 9 4.583 39 11 4.989 39 24 4.583 39 34 2.543 39 45 3.446 39 18 5.891 40 12 3.446 40 16 4.086 40 2 4.086 40 4 3.446 40 43 1.000 40 5 3.446 40 9 4.086 40 23 4.583 40 19 5.891 40 17 1.000 40 20 5.332 40 21 4.583 40 31 6.126 40 22 1.000 40 24 4.086 40 14 2.543 40 33 5.332 40 38 3.446 40 34 2.543 40 27 2.543 40 10 4.989 40 35 5.629 40 18 7.881 41 21 5.629 41 2 3.446 41 6 2.543 41 43 1.000 41 31 5.891 41 19 2.543 41 37 4.989 41 9 1.000 41 29 5.332 41 27 2.543 41 35 6.126 41 20 1.000 42 21 1.000 42 2 3.446 42 4 1.000 42 9 1.000 42 10 1.000 42 12 1.000 42 15 1.000 42 16 1.000 42 13 1.000 42 19 1.000 42 37 1.000 42 24 1.000 42 34 1.000 42 27 2.543 42 28 4.989 43 2 4.086 43 4 2.543 43 6 6.875 43 43 5.332 43 8 3.446 43 9 1.000 43 23 1.000 43 10 2.543 43 12 4.989 43 14 5.332 43 15 4.989 43 13 2.543 43 35 6.126 43 5 3.446 43 19 1.000 43 39 2.543 43 37 5.332 43 20 6.126 43 21 3.446 43 22 1.000 43 16 1.000 43 33 1.000 43 38 3.446 43 27 2.543 43 28 5.332 43 29 4.583 43 18 1.000 43 11 5.332 44 1 2.543 44 44 2.543 44 23 1.000 44 10 1.000 44 15 2.543 44 13 1.000 44 19 1.000 44 29 2.543 44 50 3.446 44 12 1.000 44 47 2.543 44 48 3.446 44 33 3.446 44 34 1.000 44 27 1.000 44 21 1.000 44 43 2.543 44 5 1.000 44 32 1.000 44 42 1.000 44 24 2.543 44 25 3.446 44 26 2.543 44 45 2.543 44 46 2.543 44 11 4.086 44 18 1.000 44 39 1.000 45 31 1.000 45 1 6.875 45 44 7.307 45 4 1.000 45 6 2.543 45 26 1.000 45 8 2.543 45 5 1.000 45 9 4.086 45 23 1.000 45 12 6.532 45 15 4.583 45 16 3.446 45 13 1.000 45 36 4.086 45 19 4.583 45 39 1.000 45 28 6.875 45 20 7.307 45 21 6.710 45 22 4.086 45 18 1.000 45 24 7.307 45 25 6.875 45 33 7.307 45 38 6.875 45 34 1.000 45 27 5.891 45 10 1.000 45 35 6.126 45 49 2.543 45 45 7.028 45 29 6.710 45 46 6.532 45 14 6.875 46 4 4.086 46 6 4.583 46 7 1.000 46 43 5.332 46 9 2.543 46 10 2.543 46 12 2.543 46 16 1.000 46 36 1.000 46 19 2.543 46 32 2.543 46 17 1.000 46 37 1.000 46 20 4.086 46 29 5.332 46 5 1.000 46 18 3.446 46 23 1.000 46 38 2.543 46 35 4.086 47 1 4.583 47 2 4.086 47 6 6.338 47 9 2.543 47 10 2.543 47 15 5.629 47 3 4.989 47 36 3.446 47 18 1.000 47 4 2.543 47 37 2.543 47 23 1.000 47 31 4.086 47 22 1.000 47 29 2.543 47 33 5.332 47 35 4.583 47 28 4.086 47 14 4.086 47 20 4.989 48 1 4.086 48 44 4.086 48 2 3.446 48 3 2.543 48 4 3.446 48 7 3.446 48 17 1.000 48 43 5.332 48 8 2.543 48 41 1.000 48 9 2.543 48 23 1.000 48 10 1.000 48 14 5.332 48 15 2.543 48 5 4.989 48 19 4.583 48 47 2.543 48 32 2.543 48 48 2.543 48 42 2.543 48 30 2.543 48 28 5.629 48 26 2.543 48 31 3.446 48 49 1.000 48 22 1.000 48 24 2.543 48 33 4.583 48 38 2.543 48 34 2.543 48 27 2.543 48 45 4.583 48 29 2.543 48 46 4.086 48 18 1.000 49 31 5.332 49 1 5.629 49 44 5.629 49 2 4.583 49 4 1.000 49 38 5.629 49 22 1.000 49 10 3.446 49 6 6.532 49 7 1.000 49 9 6.126 49 23 1.000 49 26 5.629 49 5 2.543 49 14 5.332 49 19 4.086 49 16 4.583 49 18 6.532 49 47 5.629 49 45 5.332 49 20 6.126 49 24 4.989 49 33 5.629 49 34 5.629 49 27 4.989 49 35 5.891 49 28 5.629 49 29 6.338 50 1 5.629 50 44 5.629 50 2 5.332 50 4 4.989 50 46 6.338 50 10 3.446 50 43 2.543 50 15 5.891 50 5 2.543 50 19 4.989 50 18 1.000 50 37 4.086 50 45 5.629 50 20 5.332 50 31 4.583 50 23 1.000 50 24 6.532 51 3 5.332 51 9 4.086 51 10 1.000 51 11 5.332 51 12 4.583 51 19 3.446 51 15 1.000 51 13 2.543 51 34 5.332 51 29 5.629 52 4 6.875 52 6 7.434 52 9 4.583 52 10 4.989 52 12 1.000 52 5 6.710 52 19 7.028 52 39 6.338 52 37 3.446 52 20 7.172 52 18 4.583 52 23 4.989 52 13 3.446 52 35 7.028 52 11 2.543 53 6 5.332 53 7 1.000 53 23 3.446 53 37 3.446 53 21 3.446 53 29 1.000 53 35 7.172 53 18 2.543 54 2 3.446 54 4 5.891 54 6 1.000 54 43 2.543 54 5 6.875 54 23 6.710 54 10 5.891 54 9 1.000 54 12 6.126 54 16 4.989 54 36 1.000 54 32 7.172 54 20 6.338 54 7 4.989 54 34 5.629 54 24 6.710 54 18 7.172 55 1 4.086 55 44 4.086 55 3 4.086 55 38 1.000 55 26 5.629 55 9 4.583 55 11 4.583 55 32 2.543 55 48 4.583 55 31 1.000 55 22 1.000 55 34 4.583 55 45 4.989 55 50 5.891 56 12 4.989 56 2 4.086 56 4 4.989 56 38 4.086 56 6 6.338 56 43 3.446 56 8 1.000 56 10 5.332 56 16 4.086 56 36 4.583 56 5 1.000 56 19 4.989 56 39 4.086 56 37 2.543 56 20 5.891 56 21 4.989 56 31 6.126 56 24 4.989 56 27 1.000 56 35 5.629 56 28 4.989 56 29 5.891 56 46 4.086 56 18 6.126 57 21 4.086 57 1 3.446 57 44 3.446 57 6 6.532 57 9 5.332 57 46 3.446 57 12 3.446 57 31 4.086 57 15 6.532 57 32 4.583 57 17 3.446 57 42 4.086 57 39 3.446 57 37 3.446 57 29 3.446 57 26 4.086 57 34 1.000 57 24 3.446 57 45 3.446 58 1 5.891 58 2 4.989 58 38 4.583 58 6 6.532 58 36 5.891 58 9 4.583 58 23 5.332 58 12 4.989 58 19 5.629 58 4 5.332 58 32 6.126 58 16 4.989 58 31 5.891 58 20 5.629 58 21 4.989 58 22 5.629 58 24 5.332 58 25 4.989 58 10 5.629 58 35 4.583 58 28 4.583 58 18 4.086 58 14 5.332 59 4 5.891 59 47 5.891 59 8 6.126 59 27 5.891 59 41 5.891 59 15 6.532 59 36 7.554 59 17 5.891 59 32 5.891 59 48 7.669 59 42 5.891 59 39 5.891 59 49 5.891 59 21 5.891 59 31 6.338 59 22 6.126 59 33 5.891 59 38 5.891 59 13 5.891 59 28 6.126 59 50 5.891 60 1 4.989 60 44 4.583 60 2 1.000 60 9 2.543 60 13 1.000 60 29 1.000 60 14 2.543 60 4 1.000 60 7 4.583 60 17 1.000 60 36 5.332 60 47 1.000 60 48 4.583 60 33 1.000 60 38 2.543 60 34 3.446 60 43 2.543 60 5 1.000 60 45 4.989 60 18 1.000 60 19 2.543 60 28 2.543 60 21 4.086 60 22 2.543 61 3 1.000 61 32 1.000 61 43 3.446 61 8 1.000 61 9 2.543 61 41 1.000 61 16 1.000 61 47 1.000 61 4 3.446 61 48 1.000 61 42 1.000 61 23 1.000 61 27 1.000 61 10 2.543 61 29 1.000 61 18 2.543 62 1 4.086 62 44 4.086 62 11 4.086 62 15 3.446 62 16 4.086 62 36 3.446 62 17 4.086 62 31 5.332 62 33 5.332 62 45 3.446 62 6 1.000 62 50 4.086 62 8 1.000 63 21 4.583 63 1 4.583 63 44 3.446 63 2 3.446 63 6 6.338 63 36 3.446 63 5 1.000 63 23 1.000 63 10 1.000 63 12 1.000 63 32 2.543 63 39 1.000 63 26 4.583 63 31 4.086 63 46 4.583 63 22 1.000 63 18 1.000 63 24 3.446 63 33 4.583 63 27 4.583 63 45 3.446 63 28 4.583 63 29 1.000 63 14 4.583 64 2 1.000 64 43 5.332 64 9 1.000 64 10 1.000 64 12 5.891 64 5 5.332 64 18 1.000 64 33 5.891 64 24 4.989 64 29 5.332 65 4 3.446 65 43 3.446 65 9 3.446 65 11 3.446 65 12 1.000 65 15 3.446 65 36 3.446 65 5 1.000 65 31 4.086 65 38 1.000 65 27 1.000 65 10 1.000 65 35 1.000 65 24 2.543 65 18 2.543 66 12 2.543 66 6 2.543 66 8 1.000 66 9 4.583 66 15 4.989 66 32 4.989 66 39 1.000 66 37 1.000 66 31 4.989 66 24 4.989 66 26 4.583 66 34 3.446 66 35 4.989 67 36 4.989 67 29 1.000 67 17 1.000 67 31 1.000 67 22 1.000 67 38 1.000 67 6 1.000 67 14 1.000 68 2 2.543 68 4 1.000 68 7 1.000 68 6 1.000 68 5 1.000 68 23 1.000 68 10 1.000 68 14 4.086 68 16 1.000 68 35 6.126 68 19 5.332 68 20 6.710 68 21 5.332 68 33 1.000 68 22 1.000 68 28 5.332 68 29 5.332 68 18 1.000 69 44 5.629 69 1 5.629 69 11 4.989 69 15 5.891 69 13 5.629 69 45 5.629 69 29 5.891 69 46 5.629 70 4 5.629 70 7 1.000 70 6 4.989 70 43 3.446 70 9 1.000 70 23 1.000 70 10 1.000 70 15 5.332 70 16 1.000 70 11 1.000 70 19 1.000 70 32 1.000 70 17 1.000 70 39 1.000 70 31 4.086 70 22 1.000 70 24 4.086 70 25 1.000 70 33 5.332 70 38 2.543 70 34 1.000 70 27 1.000 70 12 1.000 70 35 4.583 70 28 2.543 70 29 5.332 70 18 4.583 70 20 4.989 71 10 5.629 71 31 6.532 71 16 5.629 71 5 7.028 71 19 5.629 71 17 1.000 71 2 3.446 71 37 6.710 71 18 1.000 71 35 7.881 71 6 4.583 71 20 5.891 72 11 1.000 72 9 4.086 72 12 5.629 72 15 5.332 72 13 1.000 72 43 1.000 72 39 2.543 72 21 5.629 72 25 6.532 72 16 5.332 72 26 5.891 72 20 4.086 73 4 3.446 73 6 4.583 73 7 2.543 73 9 1.000 73 23 3.446 73 10 2.543 73 11 1.000 73 17 2.543 73 5 4.086 73 39 3.446 73 37 2.543 73 20 5.332 73 21 5.629 73 27 2.543 73 35 7.669 74 4 6.126 74 6 2.543 74 7 1.000 74 12 1.000 74 16 7.028 74 19 4.086 74 21 6.710 74 25 4.583 74 27 2.543 74 35 7.434 75 9 2.543 75 11 4.583 75 12 5.629 75 16 5.891 75 32 5.332 75 37 1.000 75 27 5.891 75 35 6.338 76 8 1.000 76 3 3.446 76 43 1.000 76 10 4.583 76 11 4.583 76 42 2.543 76 20 1.000 76 31 4.989 76 24 4.086 76 14 1.000 76 26 4.583 76 34 4.583 76 27 2.543 76 29 4.583 77 21 1.000 77 6 6.532 77 7 2.543 77 43 2.543 77 23 1.000 77 10 4.086 77 11 1.000 77 15 3.446 77 16 4.086 77 32 2.543 77 17 1.000 77 48 4.086 77 42 5.629 77 30 5.891 77 39 2.543 77 37 2.543 77 20 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6 1.000 87 29 1.000 87 18 4.086 88 12 1.000 88 1 4.086 88 16 4.086 88 6 1.000 88 47 1.000 88 5 2.543 88 32 2.543 88 17 1.000 88 37 2.543 88 31 5.332 88 18 1.000 88 27 4.583 88 35 5.332 88 24 3.446 88 29 2.543 88 20 1.000 89 21 4.086 89 31 5.629 89 2 3.446 89 3 4.086 89 4 5.891 89 9 2.543 89 23 4.989 89 10 5.891 89 11 4.989 89 15 5.891 89 36 5.629 89 5 5.332 89 19 5.629 89 39 3.446 89 20 4.989 89 22 1.000 89 18 7.554 89 14 5.629 89 25 1.000 89 33 5.629 89 38 5.629 89 26 5.629 89 34 5.629 89 27 2.543 89 28 5.891 89 29 6.126 90 3 1.000 90 9 3.446 90 32 5.332 90 36 4.989 90 17 4.989 90 37 4.086 90 31 5.891 90 24 5.332 90 14 6.875 90 33 6.710 90 38 5.629 90 26 5.629 90 34 5.332 90 35 5.891 90 28 6.338 91 2 1.000 91 4 4.989 91 6 6.875 91 9 4.086 91 10 4.086 91 31 5.332 91 11 5.332 91 12 2.543 91 15 7.028 91 19 4.989 91 32 3.446 91 39 4.086 91 20 5.332 91 24 5.332 91 28 2.543 91 18 4.583 92 31 6.532 92 16 5.629 92 19 5.629 92 17 4.086 92 27 4.086 92 15 7.777 92 20 2.543 92 25 9.571 92 13 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97 28 7.881 97 29 5.332 98 7 5.629 98 6 6.532 98 31 5.891 98 43 1.000 98 8 3.446 98 16 1.000 98 17 5.891 98 37 5.332 98 20 4.086 98 25 3.446 99 44 7.028 99 43 3.446 99 1 4.989 99 11 1.000 99 15 8.253 99 8 2.543 99 5 7.554 99 19 6.126 99 39 1.000 99 37 3.446 99 31 4.989 99 29 7.307 99 23 1.000 99 24 4.086 99 33 7.172 99 27 4.086 99 35 4.086 99 45 4.583 99 28 7.777 99 6 3.446 100 1 4.086 100 44 4.086 100 9 3.446 100 15 7.028 100 29 4.086 100 4 4.086 100 12 5.332 100 34 5.332 100 43 1.000 100 32 1.000 100 24 4.086 100 25 6.126 100 26 1.000 100 45 4.583 101 4 5.629 101 19 1.000 101 43 4.989 101 9 2.543 101 12 1.000 101 15 4.989 101 31 5.629 101 24 4.583 101 27 4.086 101 46 2.543 101 18 1.000 102 2 2.543 102 14 4.086 102 28 4.989 102 17 4.086 102 5 4.086 102 18 4.583 102 40 2.543 102 41 4.086 102 11 4.989 102 6 6.875 102 10 4.989 102 15 5.629 102 50 3.446 102 8 3.446 102 36 2.543 102 47 3.446 102 49 2.543 102 4 4.583 102 20 6.338 102 24 4.989 102 21 3.446 102 3 1.000 102 9 2.543 102 23 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5.332 106 42 5.332 106 30 5.629 106 39 1.000 106 20 4.583 106 22 2.543 106 23 1.000 106 38 5.332 106 28 4.086 106 29 1.000 106 18 5.332 107 4 4.086 107 6 7.172 107 7 5.629 107 43 5.629 107 15 4.086 107 32 5.332 107 17 5.332 107 39 5.629 107 37 5.332 107 21 5.332 107 31 6.710 107 27 4.086 107 35 6.126 107 24 4.086 108 16 5.332 108 4 4.583 108 6 7.028 108 9 4.989 108 11 4.583 108 43 1.000 108 17 6.338 108 37 5.332 108 21 1.000 108 31 5.629 108 10 4.583 108 35 4.989 109 2 5.332 109 4 5.629 109 6 6.532 109 7 3.446 109 9 4.989 109 23 3.446 109 10 2.543 109 11 4.583 109 12 2.543 109 36 4.086 109 19 2.543 109 17 3.446 109 20 5.891 109 21 4.086 109 22 2.543 109 35 4.086 109 18 5.332 109 14 2.543 110 2 4.086 110 4 6.126 110 6 4.086 110 8 4.583 110 5 4.583 110 23 2.543 110 10 2.543 110 11 4.086 110 43 5.332 110 16 4.583 110 37 4.086 110 19 2.543 110 17 4.086 110 15 1.000 110 28 4.086 110 20 5.629 110 21 3.446 110 9 4.086 110 31 5.891 110 22 1.000 110 18 2.543 110 24 4.086 110 35 4.086 111 21 4.989 111 12 5.629 111 2 5.629 111 4 3.446 111 6 5.332 111 7 2.543 111 19 1.000 111 5 3.446 111 23 4.989 111 10 4.583 111 16 2.543 111 36 8.496 111 18 1.000 111 39 2.543 111 31 5.891 111 29 5.629 111 22 1.000 111 25 9.155 111 14 5.629 111 35 7.172 111 28 6.338 111 20 5.629 112 21 5.332 112 11 4.583 112 12 4.989 112 15 5.891 112 29 4.086 113 21 1.000 113 19 3.446 113 43 2.543 113 8 2.543 113 10 3.446 113 31 6.126 113 12 4.086 113 41 3.446 113 47 3.446 113 15 6.126 113 32 2.543 113 16 3.446 113 36 2.543 113 18 3.446 113 17 2.543 113 48 3.446 113 42 2.543 113 39 2.543 113 49 2.543 113 22 2.543 113 24 4.989 113 38 2.543 113 27 3.446 113 28 2.543 113 29 3.446 114 2 4.086 114 3 4.583 114 22 2.543 114 6 7.028 114 7 2.543 114 5 3.446 114 9 4.086 114 10 2.543 114 12 1.000 114 27 1.000 114 36 1.000 114 4 1.000 114 8 2.543 114 16 3.446 114 19 2.543 114 17 2.543 114 39 3.446 114 35 4.989 114 20 4.989 114 31 4.583 114 18 2.543 114 23 2.543 114 24 4.086 114 33 4.583 114 38 4.583 114 26 4.583 114 13 2.543 114 28 4.583 114 11 4.086 115 3 1.000 115 4 1.000 115 38 1.000 115 8 1.000 115 34 1.000 115 9 5.332 115 10 1.000 115 12 1.000 115 15 1.000 115 16 1.000 115 13 1.000 115 36 5.332 115 18 1.000 115 19 1.000 115 47 1.000 115 39 1.000 115 37 2.543 115 31 1.000 115 49 5.332 115 22 4.989 115 23 1.000 115 33 1.000 115 27 1.000 116 25 6.338 116 1 2.543 116 44 2.543 116 26 4.086 116 9 1.000 116 46 2.543 116 3 3.446 116 11 4.583 116 12 5.332 116 15 5.891 116 13 1.000 116 36 2.543 116 31 4.583 116 29 4.989 116 24 4.583 116 33 4.583 116 38 4.989 116 34 4.989 116 45 2.543 116 28 1.000 116 6 1.000 117 25 7.172 117 2 4.989 117 4 3.446 117 7 2.543 117 5 4.086 117 9 2.543 117 31 6.710 117 11 6.126 117 12 6.710 117 14 6.875 117 41 7.172 117 16 2.543 117 13 2.543 117 17 4.583 117 18 2.543 117 48 7.172 117 49 7.307 117 21 6.532 117 20 7.172 117 19 1.000 117 33 1.000 117 22 2.543 117 23 3.446 117 24 7.172 117 28 6.126 117 34 2.543 117 10 3.446 117 35 6.875 118 12 4.583 118 4 1.000 118 6 6.875 118 23 1.000 118 10 1.000 118 11 4.583 118 32 1.000 118 16 1.000 118 19 1.000 118 17 4.086 118 39 2.543 118 20 5.629 118 21 4.086 118 31 4.583 118 29 2.543 118 18 1.000 118 24 4.583 118 25 3.446 118 35 5.629 119 1 3.446 119 6 1.000 119 44 3.446 119 12 3.446 119 43 4.989 119 15 4.989 119 32 4.583 119 37 2.543 119 27 2.543 119 35 4.583 119 45 3.446 120 25 4.989 120 2 1.000 120 3 4.989 120 4 1.000 120 23 1.000 120 5 1.000 120 20 6.338 120 21 1.000 120 22 1.000 120 24 4.989 120 27 3.446 120 28 5.332 121 21 2.543 121 44 3.446 121 4 1.000 121 7 1.000 121 43 3.446 121 1 3.446 121 23 1.000 121 10 1.000 121 31 5.891 121 15 2.543 121 16 2.543 121 35 5.332 121 19 4.086 121 32 4.086 121 39 1.000 121 45 3.446 121 29 3.446 121 46 3.446 121 18 1.000 122 3 4.989 122 9 4.086 122 40 5.332 122 11 4.086 122 12 4.583 122 41 4.086 122 15 2.543 122 13 1.000 122 24 3.446 122 26 5.332 122 29 4.583 123 18 1.000 123 2 2.543 123 4 4.086 123 6 6.338 123 7 4.086 123 23 1.000 123 10 1.000 123 15 3.446 123 19 5.629 123 39 4.086 123 21 3.446 123 9 3.446 123 35 5.332 123 29 4.086 123 11 4.583 124 2 5.332 124 4 5.629 124 6 7.172 124 10 4.583 124 11 1.000 124 19 5.629 124 16 1.000 124 36 2.543 124 5 5.629 124 37 1.000 124 20 6.338 124 29 2.543 124 22 1.000 124 23 4.989 124 24 3.446 124 33 1.000 124 38 4.583 124 35 6.126 124 28 5.629 124 18 5.891 124 14 4.583 125 31 1.000 125 2 4.989 125 3 1.000 125 4 2.543 125 43 2.543 125 8 1.000 125 10 1.000 125 16 1.000 125 36 2.543 125 18 2.543 125 19 2.543 125 17 1.000 125 20 4.086 125 21 1.000 125 22 2.543 125 23 2.543 125 33 4.989 125 38 1.000 125 27 1.000 125 35 4.583 125 28 3.446 125 29 4.583 126 44 5.629 126 2 2.543 126 4 5.891 126 1 5.332 126 26 1.000 126 12 5.629 126 15 5.629 126 11 4.583 126 43 3.446 126 48 5.332 126 30 5.629 126 24 5.629 126 34 5.629 126 28 5.332 126 18 6.532 126 50 5.629 127 6 2.543 127 9 2.543 127 10 4.989 127 11 4.989 127 32 5.332 127 37 4.086 127 29 4.086 127 24 5.332 127 35 4.989 128 2 4.086 128 10 2.543 128 36 5.891 128 5 4.086 128 19 6.338 128 37 5.629 128 20 4.086 128 21 2.543 128 31 6.126 128 24 4.086 129 12 5.629 129 23 4.989 129 46 4.086 129 10 8.715 129 16 6.532 129 5 9.038 129 19 7.028 129 4 7.980 129 39 5.332 129 37 6.875 129 21 4.086 129 33 5.332 129 38 4.086 129 18 3.446 129 20 6.875 130 1 6.126 130 44 5.332 130 2 7.028 130 3 7.172 130 9 3.446 130 15 4.583 130 16 2.543 130 13 1.000 130 14 4.989 130 6 4.086 130 29 5.891 130 50 7.434 130 25 2.543 130 12 5.629 130 17 1.000 130 47 1.000 130 30 1.000 130 33 1.000 130 27 3.446 130 49 6.338 130 28 6.710 130 42 1.000 130 20 4.583 130 22 2.543 130 26 6.532 130 35 3.446 130 45 5.891 130 46 6.338 130 11 6.532 130 40 6.532 130 41 6.532 130 21 5.332 131 21 2.543 131 1 1.000 131 44 2.543 131 3 2.543 131 7 3.446 131 11 4.989 131 12 4.086 131 16 1.000 131 36 1.000 131 43 1.000 131 19 2.543 131 32 2.543 131 46 1.000 131 37 1.000 131 26 3.446 131 6 5.629 131 35 4.086 131 45 1.000 131 29 3.446 132 44 3.446 132 6 6.532 132 7 2.543 132 43 2.543 132 8 2.543 132 10 3.446 132 11 4.583 132 19 3.446 132 4 3.446 132 16 2.543 132 36 3.446 132 5 3.446 132 18 3.446 132 32 3.446 132 17 2.543 132 39 3.446 132 21 2.543 132 31 2.543 132 46 3.446 132 24 3.446 132 27 3.446 132 45 3.446 133 2 1.000 133 4 5.629 133 7 1.000 133 9 5.332 133 23 5.629 133 10 5.629 133 12 2.543 133 15 5.629 133 5 3.446 133 18 1.000 133 19 5.629 133 17 3.446 133 20 6.126 133 21 4.583 133 22 3.446 133 35 5.332 133 14 1.000 133 11 4.583 134 31 4.086 134 1 5.629 134 44 5.629 134 6 6.875 134 9 4.583 134 10 5.891 134 11 5.332 134 12 5.629 134 43 5.891 134 15 1.000 134 13 3.446 134 5 4.583 134 19 5.629 134 47 3.446 134 29 5.332 134 18 4.989 134 26 5.891 134 24 5.891 134 45 5.629 134 46 5.629 135 2 8.418 135 14 8.418 135 36 4.989 135 5 6.532 135 29 4.583 135 37 2.543 135 21 6.875 135 18 10.000 135 33 2.543 135 35 7.172 135 28 8.496 136 3 4.086 136 6 6.875 136 7 2.543 136 9 1.000 136 12 4.583 136 43 1.000 136 11 4.086 136 17 1.000 136 37 1.000 136 20 4.086 136 24 2.543 136 26 4.583 136 35 5.629 137 1 4.086 137 44 4.086 137 43 4.989 137 11 4.583 137 15 5.891 137 13 2.543 137 19 1.000 137 45 5.332 137 46 4.086 137 18 2.543 138 1 5.629 138 44 5.332 138 3 5.629 138 7 2.543 138 9 1.000 138 40 5.332 138 11 4.583 138 41 5.332 138 15 5.891 138 25 5.629 138 34 5.332 138 27 2.543 138 24 5.332 138 49 5.332 138 45 5.629 138 46 5.629 139 6 2.543 139 7 5.332 139 43 1.000 139 12 4.989 139 17 6.338 139 20 6.126 139 21 2.543 139 31 5.332 139 35 4.086 140 3 5.891 140 4 5.629 140 23 1.000 140 10 1.000 140 5 5.629 140 19 5.891 140 20 6.532 140 22 1.000 140 18 5.332 141 25 6.338 141 18 2.543 141 1 2.543 141 44 2.543 141 38 2.543 141 11 3.446 141 23 2.543 141 10 2.543 141 15 4.583 141 2 4.583 141 35 4.583 141 36 4.086 141 19 2.543 141 20 5.332 141 46 2.543 141 33 1.000 141 45 2.543 141 28 1.000 141 29 4.583 141 14 4.086 142 2 5.332 142 38 4.583 142 6 1.000 142 26 5.332 142 23 1.000 142 10 1.000 142 19 4.583 142 5 3.446 142 18 1.000 142 37 4.989 142 22 1.000 142 24 4.989 142 33 6.126 142 28 6.126 142 14 5.332 143 33 5.332 143 47 2.543 143 2 4.583 143 4 1.000 143 38 1.000 143 19 1.000 143 23 4.583 143 10 4.583 143 12 3.446 143 15 8.644 143 36 4.989 143 5 5.629 143 20 3.446 143 31 6.126 143 22 7.669 143 18 6.875 143 37 1.000 143 24 5.332 143 28 4.086 143 29 1.000 144 21 2.543 144 8 2.543 144 43 1.000 144 16 6.126 144 5 5.891 144 32 4.086 144 20 6.338 144 39 5.332 144 23 4.583 144 35 7.669 144 29 6.710 144 18 5.629 145 21 7.307 145 2 7.172 145 4 8.644 145 23 7.307 145 10 8.253 145 11 5.891 145 46 4.086 145 36 7.172 145 5 6.710 145 19 7.172 145 17 1.000 145 48 5.629 145 39 4.086 145 20 7.434 145 31 5.629 145 22 4.583 145 18 8.337 145 33 6.126 145 38 7.980 145 28 7.172 145 14 7.172 146 4 5.891 146 43 2.543 146 9 5.332 146 23 6.126 146 10 6.710 146 19 4.583 146 37 4.583 146 20 5.332 146 35 4.989 146 18 7.881 147 25 5.332 147 12 1.000 147 31 1.000 147 2 2.543 147 3 1.000 147 4 1.000 147 6 6.338 147 7 1.000 147 23 1.000 147 11 4.583 147 15 1.000 147 32 2.543 147 16 1.000 147 13 1.000 147 36 1.000 147 5 2.543 147 18 1.000 147 17 1.000 147 10 1.000 147 39 1.000 147 20 4.583 147 21 1.000 147 22 1.000 147 19 1.000 147 14 2.543 147 33 2.543 147 38 2.543 147 26 2.543 147 34 1.000 147 27 1.000 147 35 4.086 147 24 2.543 147 28 2.543 147 29 1.000 148 4 4.583 148 6 6.532 148 8 3.446 148 5 1.000 148 31 7.554 148 32 4.086 148 17 4.583 148 39 4.086 148 37 2.543 148 9 1.000 148 27 4.086 148 10 2.543 148 35 3.446 148 28 3.446 148 18 1.000 148 50 4.086 149 6 6.338 149 7 1.000 149 1 1.000 149 44 1.000 149 9 2.543 149 11 4.086 149 12 1.000 149 15 1.000 149 32 1.000 149 31 1.000 149 39 1.000 149 21 1.000 149 46 1.000 149 29 1.000 149 25 1.000 149 26 1.000 149 34 1.000 149 27 1.000 149 35 4.583 149 24 1.000 149 45 1.000 150 2 1.000 150 6 3.446 150 10 5.332 150 11 4.086 150 12 2.543 150 40 1.000 150 41 1.000 150 36 4.086 150 5 1.000 150 19 2.543 150 20 5.332 150 31 1.000 150 22 1.000 150 24 1.000 150 14 3.446 150 33 3.446 150 38 2.543 150 26 1.000 150 34 1.000 150 27 1.000 150 49 1.000 150 28 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29 28 2.543 29 29 5.891 29 46 4.989 30 31 4.989 30 6 6.338 30 7 1.000 30 11 4.989 30 12 2.543 30 14 1.000 30 15 6.532 30 16 1.000 30 13 2.543 30 21 4.086 30 9 1.000 30 35 5.629 30 29 5.332 31 4 5.629 31 6 2.543 31 26 1.000 31 9 1.000 31 10 5.891 31 15 6.126 31 16 5.629 31 19 4.086 31 37 1.000 31 31 5.629 31 29 5.629 31 18 7.434 31 23 1.000 31 35 2.543 31 28 6.126 32 1 4.583 32 9 1.000 32 11 4.583 32 15 5.332 32 13 5.891 32 5 2.543 32 31 3.446 32 22 1.000 32 25 4.583 32 28 4.086 32 46 4.989 32 18 3.446 32 14 1.000 32 20 4.989 33 1 1.000 33 2 5.629 33 6 7.028 33 9 5.332 33 23 4.086 33 10 6.126 33 16 4.583 33 19 2.543 33 12 4.989 33 29 4.086 33 28 3.446 33 4 1.000 33 5 4.086 33 32 4.583 33 20 4.583 33 18 5.891 33 22 2.543 33 11 4.086 34 2 5.891 34 4 3.446 34 25 4.086 34 5 4.086 34 19 4.086 34 17 3.446 34 37 1.000 34 31 6.532 34 33 2.543 34 35 7.307 34 24 7.434 35 2 1.000 35 6 6.338 35 7 1.000 35 12 4.583 35 4 4.989 35 19 4.989 35 21 5.332 35 20 5.891 35 18 5.332 35 23 4.989 35 10 4.989 35 35 4.086 36 4 6.126 36 33 1.000 36 23 6.532 36 10 6.126 36 3 4.086 36 16 4.583 36 36 5.629 36 20 6.338 36 22 2.543 36 18 7.307 36 14 5.891 36 38 5.891 36 12 1.000 36 28 5.891 37 2 3.446 37 4 4.583 37 23 5.629 37 10 5.332 37 12 4.086 37 5 4.989 37 19 4.086 37 17 4.583 37 20 5.891 37 31 4.989 37 22 1.000 37 18 5.629 37 24 5.891 37 28 4.086 38 1 4.989 38 44 4.989 38 2 1.000 38 3 1.000 38 28 1.000 38 43 1.000 38 8 1.000 38 9 1.000 38 15 1.000 38 36 1.000 38 32 5.332 38 39 1.000 38 37 2.543 38 31 7.307 38 18 1.000 38 24 6.338 38 25 7.028 38 34 1.000 38 27 2.543 38 45 4.583 38 29 4.086 39 12 4.086 39 26 1.000 39 43 1.000 39 9 4.583 39 11 4.989 39 24 4.583 39 34 2.543 39 45 3.446 39 18 5.891 40 12 3.446 40 16 4.086 40 2 4.086 40 4 3.446 40 43 1.000 40 5 3.446 40 9 4.086 40 23 4.583 40 19 5.891 40 17 1.000 40 20 5.332 40 21 4.583 40 31 6.126 40 22 1.000 40 24 4.086 40 14 2.543 40 33 5.332 40 38 3.446 40 34 2.543 40 27 2.543 40 10 4.989 40 35 5.629 40 18 7.881 41 21 5.629 41 2 3.446 41 6 2.543 41 43 1.000 41 31 5.891 41 19 2.543 41 37 4.989 41 9 1.000 41 29 5.332 41 27 2.543 41 35 6.126 41 20 1.000 42 21 1.000 42 2 3.446 42 4 1.000 42 9 1.000 42 10 1.000 42 12 1.000 42 15 1.000 42 16 1.000 42 13 1.000 42 19 1.000 42 37 1.000 42 24 1.000 42 34 1.000 42 27 2.543 42 28 4.989 43 2 4.086 43 4 2.543 43 6 6.875 43 43 5.332 43 8 3.446 43 9 1.000 43 23 1.000 43 10 2.543 43 12 4.989 43 14 5.332 43 15 4.989 43 13 2.543 43 35 6.126 43 5 3.446 43 19 1.000 43 39 2.543 43 37 5.332 43 20 6.126 43 21 3.446 43 22 1.000 43 16 1.000 43 33 1.000 43 38 3.446 43 27 2.543 43 28 5.332 43 29 4.583 43 18 1.000 43 11 5.332 44 1 2.543 44 44 2.543 44 23 1.000 44 10 1.000 44 15 2.543 44 13 1.000 44 19 1.000 44 29 2.543 44 50 3.446 44 12 1.000 44 47 2.543 44 48 3.446 44 33 3.446 44 34 1.000 44 27 1.000 44 21 1.000 44 43 2.543 44 5 1.000 44 32 1.000 44 42 1.000 44 24 2.543 44 25 3.446 44 26 2.543 44 45 2.543 44 46 2.543 44 11 4.086 44 18 1.000 44 39 1.000 45 31 1.000 45 1 6.875 45 44 7.307 45 4 1.000 45 6 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2.543 48 5 4.989 48 19 4.583 48 47 2.543 48 32 2.543 48 48 2.543 48 42 2.543 48 30 2.543 48 28 5.629 48 26 2.543 48 31 3.446 48 49 1.000 48 22 1.000 48 24 2.543 48 33 4.583 48 38 2.543 48 34 2.543 48 27 2.543 48 45 4.583 48 29 2.543 48 46 4.086 48 18 1.000 49 31 5.332 49 1 5.629 49 44 5.629 49 2 4.583 49 4 1.000 49 38 5.629 49 22 1.000 49 10 3.446 49 6 6.532 49 7 1.000 49 9 6.126 49 23 1.000 49 26 5.629 49 5 2.543 49 14 5.332 49 19 4.086 49 16 4.583 49 18 6.532 49 47 5.629 49 45 5.332 49 20 6.126 49 24 4.989 49 33 5.629 49 34 5.629 49 27 4.989 49 35 5.891 49 28 5.629 49 29 6.338 50 1 5.629 50 44 5.629 50 2 5.332 50 4 4.989 50 46 6.338 50 10 3.446 50 43 2.543 50 15 5.891 50 5 2.543 50 19 4.989 50 18 1.000 50 37 4.086 50 45 5.629 50 20 5.332 50 31 4.583 50 23 1.000 50 24 6.532 51 3 5.332 51 9 4.086 51 10 1.000 51 11 5.332 51 12 4.583 51 19 3.446 51 15 1.000 51 13 2.543 51 34 5.332 51 29 5.629 52 4 6.875 52 6 7.434 52 9 4.583 52 10 4.989 52 12 1.000 52 5 6.710 52 19 7.028 52 39 6.338 52 37 3.446 52 20 7.172 52 18 4.583 52 23 4.989 52 13 3.446 52 35 7.028 52 11 2.543 53 6 5.332 53 7 1.000 53 23 3.446 53 37 3.446 53 21 3.446 53 29 1.000 53 35 7.172 53 18 2.543 54 2 3.446 54 4 5.891 54 6 1.000 54 43 2.543 54 5 6.875 54 23 6.710 54 10 5.891 54 9 1.000 54 12 6.126 54 16 4.989 54 36 1.000 54 32 7.172 54 20 6.338 54 7 4.989 54 34 5.629 54 24 6.710 54 18 7.172 55 1 4.086 55 44 4.086 55 3 4.086 55 38 1.000 55 26 5.629 55 9 4.583 55 11 4.583 55 32 2.543 55 48 4.583 55 31 1.000 55 22 1.000 55 34 4.583 55 45 4.989 55 50 5.891 56 12 4.989 56 2 4.086 56 4 4.989 56 38 4.086 56 6 6.338 56 43 3.446 56 8 1.000 56 10 5.332 56 16 4.086 56 36 4.583 56 5 1.000 56 19 4.989 56 39 4.086 56 37 2.543 56 20 5.891 56 21 4.989 56 31 6.126 56 24 4.989 56 27 1.000 56 35 5.629 56 28 4.989 56 29 5.891 56 46 4.086 56 18 6.126 57 21 4.086 57 1 3.446 57 44 3.446 57 6 6.532 57 9 5.332 57 46 3.446 57 12 3.446 57 31 4.086 57 15 6.532 57 32 4.583 57 17 3.446 57 42 4.086 57 39 3.446 57 37 3.446 57 29 3.446 57 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1.000 67 14 1.000 68 2 2.543 68 4 1.000 68 7 1.000 68 6 1.000 68 5 1.000 68 23 1.000 68 10 1.000 68 14 4.086 68 16 1.000 68 35 6.126 68 19 5.332 68 20 6.710 68 21 5.332 68 33 1.000 68 22 1.000 68 28 5.332 68 29 5.332 68 18 1.000 69 44 5.629 69 1 5.629 69 11 4.989 69 15 5.891 69 13 5.629 69 45 5.629 69 29 5.891 69 46 5.629 70 4 5.629 70 7 1.000 70 6 4.989 70 43 3.446 70 9 1.000 70 23 1.000 70 10 1.000 70 15 5.332 70 16 1.000 70 11 1.000 70 19 1.000 70 32 1.000 70 17 1.000 70 39 1.000 70 31 4.086 70 22 1.000 70 24 4.086 70 25 1.000 70 33 5.332 70 38 2.543 70 34 1.000 70 27 1.000 70 12 1.000 70 35 4.583 70 28 2.543 70 29 5.332 70 18 4.583 70 20 4.989 71 10 5.629 71 31 6.532 71 16 5.629 71 5 7.028 71 19 5.629 71 17 1.000 71 2 3.446 71 37 6.710 71 18 1.000 71 35 7.881 71 6 4.583 71 20 5.891 72 11 1.000 72 9 4.086 72 12 5.629 72 15 5.332 72 13 1.000 72 43 1.000 72 39 2.543 72 21 5.629 72 25 6.532 72 16 5.332 72 26 5.891 72 20 4.086 73 4 3.446 73 6 4.583 73 7 2.543 73 9 1.000 73 23 3.446 73 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4.086 79 36 1.000 79 5 4.989 79 32 1.000 79 30 5.332 79 39 4.086 79 20 5.629 79 22 4.989 79 14 4.583 79 33 5.332 79 10 5.629 79 46 4.086 79 18 4.583 80 25 1.000 80 1 1.000 80 44 1.000 80 2 1.000 80 6 1.000 80 43 1.000 80 8 1.000 80 40 1.000 80 41 2.543 80 15 1.000 80 32 1.000 80 17 2.543 80 48 2.543 80 39 1.000 80 45 1.000 80 31 1.000 80 24 1.000 80 26 1.000 80 27 1.000 80 49 1.000 80 29 1.000 80 46 1.000 80 50 1.000 81 12 1.000 81 2 3.446 81 4 1.000 81 11 4.583 81 17 1.000 81 36 1.000 81 5 3.446 81 19 1.000 81 29 3.446 81 18 1.000 81 24 2.543 81 14 1.000 81 33 3.446 81 26 1.000 81 38 3.446 81 6 6.338 82 9 1.000 82 23 1.000 82 10 1.000 82 15 1.000 82 14 1.000 82 17 1.000 82 36 1.000 82 29 1.000 82 33 1.000 82 34 1.000 82 27 1.000 82 28 1.000 82 43 4.086 82 8 1.000 82 11 4.086 82 5 1.000 82 32 1.000 82 24 1.000 82 26 1.000 82 18 1.000 82 39 1.000 82 22 1.000 83 4 5.891 83 23 5.629 83 10 5.891 83 2 5.891 83 36 6.532 83 5 6.126 83 19 5.629 83 20 6.126 83 33 4.989 83 7 4.989 83 22 5.332 83 18 6.875 83 38 4.989 83 28 6.532 84 12 4.583 84 4 5.629 84 6 7.172 84 43 4.086 84 8 5.629 84 9 1.000 84 26 4.086 84 31 6.126 84 18 7.172 84 16 5.332 84 3 5.332 84 5 4.583 84 17 5.332 84 24 5.332 84 25 5.332 84 27 3.446 84 35 4.086 84 29 5.629 85 25 7.172 85 1 4.086 85 44 4.989 85 2 1.000 85 7 2.543 85 9 4.989 85 15 4.086 85 36 3.446 85 39 2.543 85 22 5.332 85 29 1.000 85 24 4.086 85 35 4.989 85 45 4.989 85 28 4.086 86 4 6.126 86 6 3.446 86 11 2.543 86 5 1.000 86 20 5.891 86 21 2.543 86 35 3.446 86 28 5.891 87 2 1.000 87 10 2.543 87 31 3.446 87 27 2.543 87 5 2.543 87 19 1.000 87 17 4.086 87 8 1.000 87 20 4.583 87 21 1.000 87 24 4.086 87 33 1.000 87 38 2.543 87 35 4.989 87 28 1.000 87 6 1.000 87 29 1.000 87 18 4.086 88 12 1.000 88 1 4.086 88 16 4.086 88 6 1.000 88 47 1.000 88 5 2.543 88 32 2.543 88 17 1.000 88 37 2.543 88 31 5.332 88 18 1.000 88 27 4.583 88 35 5.332 88 24 3.446 88 29 2.543 88 20 1.000 89 21 4.086 89 31 5.629 89 2 3.446 89 3 4.086 89 4 5.891 89 9 2.543 89 23 4.989 89 10 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94 43 5.332 94 9 4.086 94 10 5.332 94 12 4.989 94 15 6.126 94 32 5.332 94 13 5.332 94 36 5.332 94 19 6.126 94 47 5.332 94 37 4.583 94 31 5.629 94 7 3.446 94 22 2.543 94 18 6.126 94 24 5.332 94 25 6.338 94 33 5.629 94 29 5.629 94 38 4.583 94 45 4.086 94 28 5.332 94 46 4.086 95 23 4.583 95 11 4.583 95 19 4.086 95 20 1.000 95 21 4.583 95 31 4.583 95 39 4.989 95 18 5.332 95 25 6.710 95 27 4.086 95 29 5.891 96 25 6.710 96 26 1.000 96 9 2.543 96 11 4.989 96 15 3.446 96 13 1.000 96 19 2.543 96 31 4.086 96 27 4.583 97 2 3.446 97 4 1.000 97 8 1.000 97 10 2.543 97 19 1.000 97 16 1.000 97 5 2.543 97 17 2.543 97 42 4.989 97 39 1.000 97 20 6.126 97 21 4.989 97 22 1.000 97 18 1.000 97 35 5.332 97 28 7.881 97 29 5.332 98 7 5.629 98 6 6.532 98 31 5.891 98 43 1.000 98 8 3.446 98 16 1.000 98 17 5.891 98 37 5.332 98 20 4.086 98 25 3.446 99 44 7.028 99 43 3.446 99 1 4.989 99 11 1.000 99 15 8.253 99 8 2.543 99 5 7.554 99 19 6.126 99 39 1.000 99 37 3.446 99 31 4.989 99 29 7.307 99 23 1.000 99 24 4.086 99 33 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103 15 6.126 103 36 3.446 103 32 2.543 103 39 2.543 103 21 2.543 103 22 1.000 103 37 2.543 103 27 3.446 103 24 5.891 103 45 2.543 103 28 4.583 103 11 4.989 104 1 4.086 104 44 4.086 104 6 1.000 104 43 4.989 104 23 2.543 104 10 5.891 104 11 4.583 104 15 2.543 104 32 4.583 104 19 5.332 104 45 4.583 104 25 3.446 104 26 4.086 104 12 1.000 104 29 4.583 104 18 6.710 104 20 4.989 105 2 1.000 105 4 6.710 105 9 3.446 105 23 3.446 105 14 7.554 105 6 1.000 105 19 6.532 105 30 7.980 105 20 8.074 105 21 8.644 105 22 4.086 105 18 6.532 105 33 6.875 105 38 7.554 105 10 4.989 105 35 7.669 105 28 8.496 105 29 8.165 106 2 2.543 106 4 5.332 106 7 4.583 106 10 4.583 106 35 4.583 106 5 5.332 106 19 5.332 106 42 5.332 106 30 5.629 106 39 1.000 106 20 4.583 106 22 2.543 106 23 1.000 106 38 5.332 106 28 4.086 106 29 1.000 106 18 5.332 107 4 4.086 107 6 7.172 107 7 5.629 107 43 5.629 107 15 4.086 107 32 5.332 107 17 5.332 107 39 5.629 107 37 5.332 107 21 5.332 107 31 6.710 107 27 4.086 107 35 6.126 107 24 4.086 108 16 5.332 108 4 4.583 108 6 7.028 108 9 4.989 108 11 4.583 108 43 1.000 108 17 6.338 108 37 5.332 108 21 1.000 108 31 5.629 108 10 4.583 108 35 4.989 109 2 5.332 109 4 5.629 109 6 6.532 109 7 3.446 109 9 4.989 109 23 3.446 109 10 2.543 109 11 4.583 109 12 2.543 109 36 4.086 109 19 2.543 109 17 3.446 109 20 5.891 109 21 4.086 109 22 2.543 109 35 4.086 109 18 5.332 109 14 2.543 110 2 4.086 110 4 6.126 110 6 4.086 110 8 4.583 110 5 4.583 110 23 2.543 110 10 2.543 110 11 4.086 110 43 5.332 110 16 4.583 110 37 4.086 110 19 2.543 110 17 4.086 110 15 1.000 110 28 4.086 110 20 5.629 110 21 3.446 110 9 4.086 110 31 5.891 110 22 1.000 110 18 2.543 110 24 4.086 110 35 4.086 111 21 4.989 111 12 5.629 111 2 5.629 111 4 3.446 111 6 5.332 111 7 2.543 111 19 1.000 111 5 3.446 111 23 4.989 111 10 4.583 111 16 2.543 111 36 8.496 111 18 1.000 111 39 2.543 111 31 5.891 111 29 5.629 111 22 1.000 111 25 9.155 111 14 5.629 111 35 7.172 111 28 6.338 111 20 5.629 112 21 5.332 112 11 4.583 112 12 4.989 112 15 5.891 112 29 4.086 113 21 1.000 113 19 3.446 113 43 2.543 113 8 2.543 113 10 3.446 113 31 6.126 113 12 4.086 113 41 3.446 113 47 3.446 113 15 6.126 113 32 2.543 113 16 3.446 113 36 2.543 113 18 3.446 113 17 2.543 113 48 3.446 113 42 2.543 113 39 2.543 113 49 2.543 113 22 2.543 113 24 4.989 113 38 2.543 113 27 3.446 113 28 2.543 113 29 3.446 114 2 4.086 114 3 4.583 114 22 2.543 114 6 7.028 114 7 2.543 114 5 3.446 114 9 4.086 114 10 2.543 114 12 1.000 114 27 1.000 114 36 1.000 114 4 1.000 114 8 2.543 114 16 3.446 114 19 2.543 114 17 2.543 114 39 3.446 114 35 4.989 114 20 4.989 114 31 4.583 114 18 2.543 114 23 2.543 114 24 4.086 114 33 4.583 114 38 4.583 114 26 4.583 114 13 2.543 114 28 4.583 114 11 4.086 115 3 1.000 115 4 1.000 115 38 1.000 115 8 1.000 115 34 1.000 115 9 5.332 115 10 1.000 115 12 1.000 115 15 1.000 115 16 1.000 115 13 1.000 115 36 5.332 115 18 1.000 115 19 1.000 115 47 1.000 115 39 1.000 115 37 2.543 115 31 1.000 115 49 5.332 115 22 4.989 115 23 1.000 115 33 1.000 115 27 1.000 116 25 6.338 116 1 2.543 116 44 2.543 116 26 4.086 116 9 1.000 116 46 2.543 116 3 3.446 116 11 4.583 116 12 5.332 116 15 5.891 116 13 1.000 116 36 2.543 116 31 4.583 116 29 4.989 116 24 4.583 116 33 4.583 116 38 4.989 116 34 4.989 116 45 2.543 116 28 1.000 116 6 1.000 117 25 7.172 117 2 4.989 117 4 3.446 117 7 2.543 117 5 4.086 117 9 2.543 117 31 6.710 117 11 6.126 117 12 6.710 117 14 6.875 117 41 7.172 117 16 2.543 117 13 2.543 117 17 4.583 117 18 2.543 117 48 7.172 117 49 7.307 117 21 6.532 117 20 7.172 117 19 1.000 117 33 1.000 117 22 2.543 117 23 3.446 117 24 7.172 117 28 6.126 117 34 2.543 117 10 3.446 117 35 6.875 118 12 4.583 118 4 1.000 118 6 6.875 118 23 1.000 118 10 1.000 118 11 4.583 118 32 1.000 118 16 1.000 118 19 1.000 118 17 4.086 118 39 2.543 118 20 5.629 118 21 4.086 118 31 4.583 118 29 2.543 118 18 1.000 118 24 4.583 118 25 3.446 118 35 5.629 119 1 3.446 119 6 1.000 119 44 3.446 119 12 3.446 119 43 4.989 119 15 4.989 119 32 4.583 119 37 2.543 119 27 2.543 119 35 4.583 119 45 3.446 120 25 4.989 120 2 1.000 120 3 4.989 120 4 1.000 120 23 1.000 120 5 1.000 120 20 6.338 120 21 1.000 120 22 1.000 120 24 4.989 120 27 3.446 120 28 5.332 121 21 2.543 121 44 3.446 121 4 1.000 121 7 1.000 121 43 3.446 121 1 3.446 121 23 1.000 121 10 1.000 121 31 5.891 121 15 2.543 121 16 2.543 121 35 5.332 121 19 4.086 121 32 4.086 121 39 1.000 121 45 3.446 121 29 3.446 121 46 3.446 121 18 1.000 122 3 4.989 122 9 4.086 122 40 5.332 122 11 4.086 122 12 4.583 122 41 4.086 122 15 2.543 122 13 1.000 122 24 3.446 122 26 5.332 122 29 4.583 123 18 1.000 123 2 2.543 123 4 4.086 123 6 6.338 123 7 4.086 123 23 1.000 123 10 1.000 123 15 3.446 123 19 5.629 123 39 4.086 123 21 3.446 123 9 3.446 123 35 5.332 123 29 4.086 123 11 4.583 124 2 5.332 124 4 5.629 124 6 7.172 124 10 4.583 124 11 1.000 124 19 5.629 124 16 1.000 124 36 2.543 124 5 5.629 124 37 1.000 124 20 6.338 124 29 2.543 124 22 1.000 124 23 4.989 124 24 3.446 124 33 1.000 124 38 4.583 124 35 6.126 124 28 5.629 124 18 5.891 124 14 4.583 125 31 1.000 125 2 4.989 125 3 1.000 125 4 2.543 125 43 2.543 125 8 1.000 125 10 1.000 125 16 1.000 125 36 2.543 125 18 2.543 125 19 2.543 125 17 1.000 125 20 4.086 125 21 1.000 125 22 2.543 125 23 2.543 125 33 4.989 125 38 1.000 125 27 1.000 125 35 4.583 125 28 3.446 125 29 4.583 126 44 5.629 126 2 2.543 126 4 5.891 126 1 5.332 126 26 1.000 126 12 5.629 126 15 5.629 126 11 4.583 126 43 3.446 126 48 5.332 126 30 5.629 126 24 5.629 126 34 5.629 126 28 5.332 126 18 6.532 126 50 5.629 127 6 2.543 127 9 2.543 127 10 4.989 127 11 4.989 127 32 5.332 127 37 4.086 127 29 4.086 127 24 5.332 127 35 4.989 128 2 4.086 128 10 2.543 128 36 5.891 128 5 4.086 128 19 6.338 128 37 5.629 128 20 4.086 128 21 2.543 128 31 6.126 128 24 4.086 129 12 5.629 129 23 4.989 129 46 4.086 129 10 8.715 129 16 6.532 129 5 9.038 129 19 7.028 129 4 7.980 129 39 5.332 129 37 6.875 129 21 4.086 129 33 5.332 129 38 4.086 129 18 3.446 129 20 6.875 130 1 6.126 130 44 5.332 130 2 7.028 130 3 7.172 130 9 3.446 130 15 4.583 130 16 2.543 130 13 1.000 130 14 4.989 130 6 4.086 130 29 5.891 130 50 7.434 130 25 2.543 130 12 5.629 130 17 1.000 130 47 1.000 130 30 1.000 130 33 1.000 130 27 3.446 130 49 6.338 130 28 6.710 130 42 1.000 130 20 4.583 130 22 2.543 130 26 6.532 130 35 3.446 130 45 5.891 130 46 6.338 130 11 6.532 130 40 6.532 130 41 6.532 130 21 5.332 131 21 2.543 131 1 1.000 131 44 2.543 131 3 2.543 131 7 3.446 131 11 4.989 131 12 4.086 131 16 1.000 131 36 1.000 131 43 1.000 131 19 2.543 131 32 2.543 131 46 1.000 131 37 1.000 131 26 3.446 131 6 5.629 131 35 4.086 131 45 1.000 131 29 3.446 132 44 3.446 132 6 6.532 132 7 2.543 132 43 2.543 132 8 2.543 132 10 3.446 132 11 4.583 132 19 3.446 132 4 3.446 132 16 2.543 132 36 3.446 132 5 3.446 132 18 3.446 132 32 3.446 132 17 2.543 132 39 3.446 132 21 2.543 132 31 2.543 132 46 3.446 132 24 3.446 132 27 3.446 132 45 3.446 133 2 1.000 133 4 5.629 133 7 1.000 133 9 5.332 133 23 5.629 133 10 5.629 133 12 2.543 133 15 5.629 133 5 3.446 133 18 1.000 133 19 5.629 133 17 3.446 133 20 6.126 133 21 4.583 133 22 3.446 133 35 5.332 133 14 1.000 133 11 4.583 134 31 4.086 134 1 5.629 134 44 5.629 134 6 6.875 134 9 4.583 134 10 5.891 134 11 5.332 134 12 5.629 134 43 5.891 134 15 1.000 134 13 3.446 134 5 4.583 134 19 5.629 134 47 3.446 134 29 5.332 134 18 4.989 134 26 5.891 134 24 5.891 134 45 5.629 134 46 5.629 135 2 8.418 135 14 8.418 135 36 4.989 135 5 6.532 135 29 4.583 135 37 2.543 135 21 6.875 135 18 10.000 135 33 2.543 135 35 7.172 135 28 8.496 136 3 4.086 136 6 6.875 136 7 2.543 136 9 1.000 136 12 4.583 136 43 1.000 136 11 4.086 136 17 1.000 136 37 1.000 136 20 4.086 136 24 2.543 136 26 4.583 136 35 5.629 137 1 4.086 137 44 4.086 137 43 4.989 137 11 4.583 137 15 5.891 137 13 2.543 137 19 1.000 137 45 5.332 137 46 4.086 137 18 2.543 138 1 5.629 138 44 5.332 138 3 5.629 138 7 2.543 138 9 1.000 138 40 5.332 138 11 4.583 138 41 5.332 138 15 5.891 138 25 5.629 138 34 5.332 138 27 2.543 138 24 5.332 138 49 5.332 138 45 5.629 138 46 5.629 139 6 2.543 139 7 5.332 139 43 1.000 139 12 4.989 139 17 6.338 139 20 6.126 139 21 2.543 139 31 5.332 139 35 4.086 140 3 5.891 140 4 5.629 140 23 1.000 140 10 1.000 140 5 5.629 140 19 5.891 140 20 6.532 140 22 1.000 140 18 5.332 141 25 6.338 141 18 2.543 141 1 2.543 141 44 2.543 141 38 2.543 141 11 3.446 141 23 2.543 141 10 2.543 141 15 4.583 141 2 4.583 141 35 4.583 141 36 4.086 141 19 2.543 141 20 5.332 141 46 2.543 141 33 1.000 141 45 2.543 141 28 1.000 141 29 4.583 141 14 4.086 142 2 5.332 142 38 4.583 142 6 1.000 142 26 5.332 142 23 1.000 142 10 1.000 142 19 4.583 142 5 3.446 142 18 1.000 142 37 4.989 142 22 1.000 142 24 4.989 142 33 6.126 142 28 6.126 142 14 5.332 143 33 5.332 143 47 2.543 143 2 4.583 143 4 1.000 143 38 1.000 143 19 1.000 143 23 4.583 143 10 4.583 143 12 3.446 143 15 8.644 143 36 4.989 143 5 5.629 143 20 3.446 143 31 6.126 143 22 7.669 143 18 6.875 143 37 1.000 143 24 5.332 143 28 4.086 143 29 1.000 144 21 2.543 144 8 2.543 144 43 1.000 144 16 6.126 144 5 5.891 144 32 4.086 144 20 6.338 144 39 5.332 144 23 4.583 144 35 7.669 144 29 6.710 144 18 5.629 145 21 7.307 145 2 7.172 145 4 8.644 145 23 7.307 145 10 8.253 145 11 5.891 145 46 4.086 145 36 7.172 145 5 6.710 145 19 7.172 145 17 1.000 145 48 5.629 145 39 4.086 145 20 7.434 145 31 5.629 145 22 4.583 145 18 8.337 145 33 6.126 145 38 7.980 145 28 7.172 145 14 7.172 146 4 5.891 146 43 2.543 146 9 5.332 146 23 6.126 146 10 6.710 146 19 4.583 146 37 4.583 146 20 5.332 146 35 4.989 146 18 7.881 147 25 5.332 147 12 1.000 147 31 1.000 147 2 2.543 147 3 1.000 147 4 1.000 147 6 6.338 147 7 1.000 147 23 1.000 147 11 4.583 147 15 1.000 147 32 2.543 147 16 1.000 147 13 1.000 147 36 1.000 147 5 2.543 147 18 1.000 147 17 1.000 147 10 1.000 147 39 1.000 147 20 4.583 147 21 1.000 147 22 1.000 147 19 1.000 147 14 2.543 147 33 2.543 147 38 2.543 147 26 2.543 147 34 1.000 147 27 1.000 147 35 4.086 147 24 2.543 147 28 2.543 147 29 1.000 148 4 4.583 148 6 6.532 148 8 3.446 148 5 1.000 148 31 7.554 148 32 4.086 148 17 4.583 148 39 4.086 148 37 2.543 148 9 1.000 148 27 4.086 148 10 2.543 148 35 3.446 148 28 3.446 148 18 1.000 148 50 4.086 149 6 6.338 149 7 1.000 149 1 1.000 149 44 1.000 149 9 2.543 149 11 4.086 149 12 1.000 149 15 1.000 149 32 1.000 149 31 1.000 149 39 1.000 149 21 1.000 149 46 1.000 149 29 1.000 149 25 1.000 149 26 1.000 149 34 1.000 149 27 1.000 149 35 4.583 149 24 1.000 149 45 1.000 150 2 1.000 150 6 3.446 150 10 5.332 150 11 4.086 150 12 2.543 150 40 1.000 150 41 1.000 150 36 4.086 150 5 1.000 150 19 2.543 150 20 5.332 150 31 1.000 150 22 1.000 150 24 1.000 150 14 3.446 150 33 3.446 150 38 2.543 150 26 1.000 150 34 1.000 150 27 1.000 150 49 1.000 150 28 4.989 150 18 1.000 151 1 1.000 151 44 1.000 151 3 1.000 151 9 1.000 151 15 1.000 151 13 1.000 151 19 1.000 151 12 1.000 151 48 1.000 151 29 1.000 151 34 1.000 151 43 4.989 151 8 1.000 151 32 1.000 151 26 1.000 151 45 1.000 151 41 1.000 152 25 7.028 152 1 4.086 152 44 4.583 152 2 4.989 152 36 2.543 152 9 4.583 152 43 2.543 152 40 2.543 152 41 3.446 152 15 4.989 152 28 4.086 152 31 5.332 152 22 1.000 152 14 4.583 152 38 4.583 152 49 4.086 152 45 4.086 152 46 4.086 153 12 2.543 153 4 6.126 153 6 1.000 153 5 5.629 153 9 5.332 153 10 6.875 153 15 6.338 153 36 1.000 153 19 5.332 153 32 1.000 153 20 6.338 153 21 1.000 153 24 5.629 153 35 1.000 154 6 6.875 154 2 4.989 154 5 4.989 154 11 4.989 154 16 4.989 154 18 4.583 154 19 4.989 154 20 3.446 154 21 4.989 154 35 5.332 155 2 5.332 155 6 7.881 155 9 5.332 155 10 5.891 155 16 6.126 155 31 3.446 155 14 6.126 155 29 6.126 155 7 5.629 155 12 6.126 155 33 1.000 155 38 3.446 155 27 5.629 155 8 4.086 155 5 6.710 155 20 7.307 155 13 5.332 155 35 7.434 155 39 6.338 155 28 6.338 155 21 6.532 155 22 5.629 156 33 5.629 156 2 4.086 156 6 1.000 156 43 1.000 156 8 4.583 156 47 1.000 156 42 2.543 156 30 3.446 156 22 1.000 156 14 4.989 156 38 4.989 156 28 5.629 157 1 2.543 157 44 2.543 157 2 2.543 157 7 1.000 157 23 1.000 157 10 1.000 157 31 4.583 157 16 2.543 157 14 3.446 157 50 3.446 157 4 1.000 157 36 3.446 157 12 4.086 157 48 4.583 157 9 4.583 157 18 5.891 157 33 3.446 157 38 2.543 157 28 3.446 157 17 1.000 157 8 1.000 157 5 2.543 157 29 2.543 157 20 1.000 157 13 1.000 157 35 4.989 157 45 2.543 157 46 1.000 157 11 4.583 157 19 3.446 157 22 1.000 158 4 5.629 158 43 1.000 158 8 1.000 158 9 1.000 158 23 1.000 158 10 1.000 158 31 5.891 158 11 5.332 158 41 1.000 158 16 1.000 158 13 1.000 158 19 1.000 158 32 3.446 158 17 1.000 158 48 1.000 158 42 1.000 158 39 2.543 158 37 1.000 158 21 1.000 158 22 1.000 158 18 1.000 158 24 5.332 158 38 1.000 158 28 1.000 159 3 5.891 159 4 1.000 159 41 1.000 159 40 1.000 159 10 6.875 159 11 5.891 159 12 5.629 159 15 6.126 159 16 7.307 159 1 4.583 159 9 1.000 159 29 1.000 159 25 6.532 159 27 2.543 159 45 4.583 159 28 5.629 159 46 4.583 160 12 3.446 160 1 4.583 160 44 4.583 160 6 1.000 160 9 2.543 160 26 1.000 160 11 4.583 160 15 4.583 160 36 4.086 160 17 1.000 160 14 2.543 160 25 5.891 160 38 3.446 160 45 4.583 160 28 4.583 160 29 4.989 160 46 4.583 161 12 2.543 161 1 4.583 161 44 4.583 161 11 4.086 161 9 1.000 161 23 1.000 161 10 2.543 161 8 1.000 161 16 1.000 161 35 5.332 161 5 4.583 161 19 1.000 161 20 6.126 161 21 1.000 161 18 1.000 161 27 3.446 161 24 4.583 161 45 4.583 161 29 1.000 161 46 4.583 162 21 4.086 162 1 4.989 162 44 5.629 162 6 1.000 162 10 1.000 162 43 4.086 162 9 2.543 162 11 4.583 162 19 1.000 162 15 4.086 162 18 5.332 162 16 4.583 162 13 4.583 162 5 2.543 162 31 4.989 162 24 5.332 162 27 4.086 162 45 5.332 162 29 4.583 162 20 4.086 163 18 1.000 163 2 2.543 163 3 4.989 163 4 2.543 163 6 1.000 163 43 1.000 163 11 2.543 163 15 1.000 163 5 1.000 163 31 5.332 163 22 1.000 163 24 4.086 163 38 3.446 163 10 3.446 163 28 5.891 163 29 2.543 163 20 2.543 164 4 4.989 164 6 3.446 164 7 4.086 164 23 1.000 164 10 2.543 164 11 4.989 164 5 5.332 164 19 4.989 164 20 4.989 164 21 1.000 164 29 4.989 164 18 1.000 164 14 4.989 165 21 2.543 165 2 5.332 165 23 4.583 165 12 4.989 165 15 5.891 165 4 5.629 165 13 1.000 165 5 4.583 165 18 3.446 165 19 4.086 165 20 2.543 165 33 1.000 165 10 3.446 165 28 5.629 165 14 1.000 166 25 2.543 166 11 1.000 166 37 1.000 166 20 1.000 166 31 4.086 166 29 1.000 166 27 1.000 166 35 4.583 167 47 2.543 167 8 1.000 167 31 4.989 167 15 5.891 167 16 5.332 167 3 2.543 167 39 1.000 167 37 4.583 167 27 5.891 167 35 5.332 167 29 5.332 168 4 5.629 168 23 6.126 168 10 5.891 168 19 4.989 168 5 5.332 168 37 4.086 168 20 6.126 168 22 2.543 168 38 4.086 168 14 3.446 168 28 5.629 168 18 7.028 169 14 3.446 169 4 3.446 169 38 4.989 169 6 6.532 169 7 5.332 169 9 4.086 169 21 5.332 169 23 4.583 169 10 5.332 169 15 5.332 169 16 5.332 169 36 4.989 169 5 4.086 169 19 4.989 169 17 4.086 169 37 4.583 169 33 4.583 169 22 2.543 169 18 3.446 169 28 4.989 169 29 5.891 170 1 1.000 170 43 1.000 170 44 1.000 170 34 3.446 170 23 1.000 170 12 1.000 170 27 1.000 170 8 4.086 170 47 1.000 170 31 4.086 170 24 3.446 170 35 4.086 170 45 1.000 170 29 3.446 170 20 1.000 171 12 5.332 171 1 4.989 171 44 4.989 171 43 2.543 171 9 4.583 171 15 6.126 171 36 4.583 171 24 4.989 171 25 4.583 171 38 3.446 171 34 5.332 171 27 1.000 171 45 4.989 171 46 4.583 172 2 5.629 172 4 5.332 172 39 1.000 172 8 4.989 172 17 5.332 172 36 5.891 172 5 4.989 172 19 6.875 172 46 4.086 172 30 5.332 172 9 5.332 172 22 5.629 172 24 4.989 172 33 6.338 172 38 4.989 172 27 1.000 172 10 5.891 172 18 5.891 172 14 1.000 173 4 7.172 173 6 1.000 173 21 2.543 173 23 5.629 173 10 5.629 173 19 6.338 173 5 4.583 173 17 2.543 173 37 1.000 173 20 5.629 173 31 1.000 173 22 3.446 173 28 2.543 173 18 6.126 174 1 5.629 174 44 5.629 174 6 2.543 174 43 1.000 174 25 5.332 174 9 1.000 174 12 4.583 174 15 5.332 174 8 1.000 174 16 1.000 174 13 1.000 174 48 1.000 174 31 3.446 174 24 5.629 174 45 5.891 174 29 4.989 174 46 5.629 174 50 1.000 175 48 1.000 175 4 3.446 175 8 3.446 175 34 1.000 175 23 1.000 175 10 1.000 175 12 4.583 175 19 1.000 175 15 8.644 175 16 2.543 175 13 2.543 175 36 4.583 175 5 2.543 175 47 1.000 175 32 4.583 175 39 2.543 175 28 3.446 175 20 5.332 175 21 4.583 175 31 4.583 175 22 2.543 175 18 3.446 175 33 4.583 175 38 4.583 175 27 2.543 175 35 5.629 175 45 4.989 175 29 4.583 175 46 4.583 176 44 4.989 176 2 4.989 176 31 5.891 176 11 4.583 176 41 5.629 176 15 6.126 176 48 5.332 176 33 5.332 176 38 4.583 176 34 1.000 176 24 2.543 176 49 5.629 176 45 4.086 176 29 5.332 176 46 5.629 177 1 1.000 177 44 1.000 177 10 1.000 177 15 1.000 177 13 1.000 177 19 1.000 177 31 1.000 177 29 1.000 177 4 1.000 177 12 1.000 177 36 1.000 177 33 1.000 177 38 1.000 177 34 1.000 177 27 1.000 177 43 1.000 177 5 1.000 177 32 1.000 177 24 1.000 177 25 1.000 177 26 1.000 177 45 1.000 177 46 1.000 177 37 1.000 177 21 1.000 177 22 1.000 178 3 4.989 178 6 6.875 178 7 1.000 178 8 4.583 178 10 2.543 178 31 1.000 178 11 4.086 178 12 1.000 178 15 3.446 178 16 1.000 178 13 1.000 178 18 4.086 178 19 2.543 178 32 2.543 178 17 1.000 178 39 1.000 178 21 5.332 178 9 1.000 178 22 2.543 178 33 1.000 178 38 1.000 178 35 4.989 178 29 3.446 178 20 4.086 179 4 5.629 179 6 2.543 179 47 2.543 179 7 1.000 179 8 1.000 179 5 1.000 179 23 5.629 179 10 3.446 179 12 1.000 179 15 2.543 179 16 1.000 179 13 1.000 179 19 5.891 179 17 2.543 179 39 1.000 179 37 1.000 179 20 5.332 179 21 5.629 179 29 5.629 179 46 4.086 179 22 1.000 179 38 4.583 179 26 5.332 179 34 1.000 179 27 4.583 179 35 5.332 179 28 5.629 179 18 6.126 179 14 4.989 180 3 4.086 180 4 1.000 180 38 3.446 180 9 3.446 180 26 3.446 180 10 1.000 180 11 4.583 180 12 5.332 180 36 3.446 180 19 3.446 180 31 1.000 180 29 4.989 180 33 2.543 180 24 4.989 180 25 5.891 180 27 4.086 180 28 3.446 181 3 4.086 181 4 4.989 181 1 1.000 181 5 1.000 181 9 5.629 181 23 4.583 181 46 1.000 181 10 5.629 181 15 5.332 181 44 1.000 181 2 1.000 181 36 4.989 181 19 4.989 181 20 5.629 181 29 1.000 181 22 1.000 181 24 1.000 181 14 4.583 181 33 4.086 181 34 1.000 181 27 1.000 181 45 1.000 181 28 4.583 181 18 4.989 181 38 1.000 182 7 2.543 182 16 3.446 182 13 3.446 182 37 1.000 182 21 6.338 182 27 4.583 183 4 5.891 183 7 1.000 183 23 1.000 183 10 1.000 183 16 1.000 183 36 4.583 183 19 5.332 183 35 5.629 183 20 5.891 183 21 5.332 183 31 3.446 183 22 1.000 183 33 2.543 183 28 5.332 183 18 1.000 184 3 4.583 184 7 3.446 184 12 4.086 184 15 5.332 184 36 5.332 184 17 4.583 184 31 4.989 184 18 4.086 184 24 4.086 184 25 4.086 184 34 4.086 184 11 4.086 185 4 7.777 185 6 5.332 185 7 4.989 185 23 2.543 185 10 5.332 185 12 5.629 185 16 8.337 185 19 7.777 185 17 4.989 185 20 5.629 185 21 8.253 185 22 2.543 185 18 2.543 185 35 8.337 185 28 7.554 186 2 4.086 186 4 6.126 186 5 5.891 186 23 5.629 186 19 5.891 186 20 6.126 186 31 1.000 186 24 1.000 186 28 4.583 186 18 5.629 187 6 6.338 187 23 5.332 187 10 5.332 187 5 2.543 187 4 5.332 187 20 6.532 187 21 4.989 187 22 1.000 187 24 5.332 187 28 5.332 187 18 5.629 188 33 2.543 188 26 1.000 188 12 4.086 188 15 3.446 188 18 2.543 188 36 2.543 188 14 1.000 188 22 3.446 188 24 4.086 188 38 1.000 188 28 2.543 188 29 2.543 189 21 3.446 189 4 4.583 189 6 6.532 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70 43 3.446 70 9 1.000 70 23 1.000 70 10 1.000 70 15 5.332 70 16 1.000 70 11 1.000 70 19 1.000 70 32 1.000 70 17 1.000 70 39 1.000 70 31 4.086 70 22 1.000 70 24 4.086 70 25 1.000 70 33 5.332 70 38 2.543 70 34 1.000 70 27 1.000 70 12 1.000 70 35 4.583 70 28 2.543 70 29 5.332 70 18 4.583 70 20 4.989 71 10 5.629 71 31 6.532 71 16 5.629 71 5 7.028 71 19 5.629 71 17 1.000 71 2 3.446 71 37 6.710 71 18 1.000 71 35 7.881 71 6 4.583 71 20 5.891 72 11 1.000 72 9 4.086 72 12 5.629 72 15 5.332 72 13 1.000 72 43 1.000 72 39 2.543 72 21 5.629 72 25 6.532 72 16 5.332 72 26 5.891 72 20 4.086 73 4 3.446 73 6 4.583 73 7 2.543 73 9 1.000 73 23 3.446 73 10 2.543 73 11 1.000 73 17 2.543 73 5 4.086 73 39 3.446 73 37 2.543 73 20 5.332 73 21 5.629 73 27 2.543 73 35 7.669 74 4 6.126 74 6 2.543 74 7 1.000 74 12 1.000 74 16 7.028 74 19 4.086 74 21 6.710 74 25 4.583 74 27 2.543 74 35 7.434 75 9 2.543 75 11 4.583 75 12 5.629 75 16 5.891 75 32 5.332 75 37 1.000 75 27 5.891 75 35 6.338 76 8 1.000 76 3 3.446 76 43 1.000 76 10 4.583 76 11 4.583 76 42 2.543 76 20 1.000 76 31 4.989 76 24 4.086 76 14 1.000 76 26 4.583 76 34 4.583 76 27 2.543 76 29 4.583 77 21 1.000 77 6 6.532 77 7 2.543 77 43 2.543 77 23 1.000 77 10 4.086 77 11 1.000 77 15 3.446 77 16 4.086 77 32 2.543 77 17 1.000 77 48 4.086 77 42 5.629 77 30 5.891 77 39 2.543 77 37 2.543 77 20 4.989 77 31 4.989 77 18 4.086 77 35 4.583 77 29 4.086 78 31 1.000 78 44 4.583 78 43 5.629 78 1 4.583 78 9 4.086 78 11 4.583 78 12 4.989 78 15 4.086 78 32 4.989 78 39 2.543 78 29 4.583 78 33 4.583 78 46 4.989 78 18 4.086 78 19 1.000 78 10 4.086 78 45 4.583 79 4 5.629 79 38 4.583 79 9 1.000 79 23 4.583 79 43 4.086 79 36 1.000 79 5 4.989 79 32 1.000 79 30 5.332 79 39 4.086 79 20 5.629 79 22 4.989 79 14 4.583 79 33 5.332 79 10 5.629 79 46 4.086 79 18 4.583 80 25 1.000 80 1 1.000 80 44 1.000 80 2 1.000 80 6 1.000 80 43 1.000 80 8 1.000 80 40 1.000 80 41 2.543 80 15 1.000 80 32 1.000 80 17 2.543 80 48 2.543 80 39 1.000 80 45 1.000 80 31 1.000 80 24 1.000 80 26 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5.332 85 29 1.000 85 24 4.086 85 35 4.989 85 45 4.989 85 28 4.086 86 4 6.126 86 6 3.446 86 11 2.543 86 5 1.000 86 20 5.891 86 21 2.543 86 35 3.446 86 28 5.891 87 2 1.000 87 10 2.543 87 31 3.446 87 27 2.543 87 5 2.543 87 19 1.000 87 17 4.086 87 8 1.000 87 20 4.583 87 21 1.000 87 24 4.086 87 33 1.000 87 38 2.543 87 35 4.989 87 28 1.000 87 6 1.000 87 29 1.000 87 18 4.086 88 12 1.000 88 1 4.086 88 16 4.086 88 6 1.000 88 47 1.000 88 5 2.543 88 32 2.543 88 17 1.000 88 37 2.543 88 31 5.332 88 18 1.000 88 27 4.583 88 35 5.332 88 24 3.446 88 29 2.543 88 20 1.000 89 21 4.086 89 31 5.629 89 2 3.446 89 3 4.086 89 4 5.891 89 9 2.543 89 23 4.989 89 10 5.891 89 11 4.989 89 15 5.891 89 36 5.629 89 5 5.332 89 19 5.629 89 39 3.446 89 20 4.989 89 22 1.000 89 18 7.554 89 14 5.629 89 25 1.000 89 33 5.629 89 38 5.629 89 26 5.629 89 34 5.629 89 27 2.543 89 28 5.891 89 29 6.126 90 3 1.000 90 9 3.446 90 32 5.332 90 36 4.989 90 17 4.989 90 37 4.086 90 31 5.891 90 24 5.332 90 14 6.875 90 33 6.710 90 38 5.629 90 26 5.629 90 34 5.332 90 35 5.891 90 28 6.338 91 2 1.000 91 4 4.989 91 6 6.875 91 9 4.086 91 10 4.086 91 31 5.332 91 11 5.332 91 12 2.543 91 15 7.028 91 19 4.989 91 32 3.446 91 39 4.086 91 20 5.332 91 24 5.332 91 28 2.543 91 18 4.583 92 31 6.532 92 16 5.629 92 19 5.629 92 17 4.086 92 27 4.086 92 15 7.777 92 20 2.543 92 25 9.571 92 13 3.446 92 11 4.989 92 37 3.446 93 6 6.875 93 7 4.989 93 43 5.332 93 11 4.989 93 12 4.989 93 32 1.000 93 16 4.989 93 13 5.332 93 5 4.989 93 39 4.989 93 37 2.543 93 20 4.989 93 21 5.629 93 31 5.332 93 18 5.629 93 25 7.028 93 27 5.332 93 29 4.989 94 1 4.086 94 44 4.086 94 2 4.086 94 3 5.629 94 4 5.629 94 6 6.710 94 43 5.332 94 9 4.086 94 10 5.332 94 12 4.989 94 15 6.126 94 32 5.332 94 13 5.332 94 36 5.332 94 19 6.126 94 47 5.332 94 37 4.583 94 31 5.629 94 7 3.446 94 22 2.543 94 18 6.126 94 24 5.332 94 25 6.338 94 33 5.629 94 29 5.629 94 38 4.583 94 45 4.086 94 28 5.332 94 46 4.086 95 23 4.583 95 11 4.583 95 19 4.086 95 20 1.000 95 21 4.583 95 31 4.583 95 39 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27 4.086 101 46 2.543 101 18 1.000 102 2 2.543 102 14 4.086 102 28 4.989 102 17 4.086 102 5 4.086 102 18 4.583 102 40 2.543 102 41 4.086 102 11 4.989 102 6 6.875 102 10 4.989 102 15 5.629 102 50 3.446 102 8 3.446 102 36 2.543 102 47 3.446 102 49 2.543 102 4 4.583 102 20 6.338 102 24 4.989 102 21 3.446 102 3 1.000 102 9 2.543 102 23 2.543 102 19 4.583 102 7 2.543 102 12 3.446 102 48 1.000 102 30 4.583 102 34 4.086 102 42 3.446 102 26 3.446 102 13 1.000 102 39 3.446 102 16 2.543 102 31 4.989 102 33 4.086 102 38 4.583 102 27 1.000 102 32 1.000 102 35 5.891 102 37 4.086 102 22 2.543 103 1 2.543 103 44 2.543 103 7 2.543 103 10 4.989 103 31 4.583 103 15 6.126 103 36 3.446 103 32 2.543 103 39 2.543 103 21 2.543 103 22 1.000 103 37 2.543 103 27 3.446 103 24 5.891 103 45 2.543 103 28 4.583 103 11 4.989 104 1 4.086 104 44 4.086 104 6 1.000 104 43 4.989 104 23 2.543 104 10 5.891 104 11 4.583 104 15 2.543 104 32 4.583 104 19 5.332 104 45 4.583 104 25 3.446 104 26 4.086 104 12 1.000 104 29 4.583 104 18 6.710 104 20 4.989 105 2 1.000 105 4 6.710 105 9 3.446 105 23 3.446 105 14 7.554 105 6 1.000 105 19 6.532 105 30 7.980 105 20 8.074 105 21 8.644 105 22 4.086 105 18 6.532 105 33 6.875 105 38 7.554 105 10 4.989 105 35 7.669 105 28 8.496 105 29 8.165 106 2 2.543 106 4 5.332 106 7 4.583 106 10 4.583 106 35 4.583 106 5 5.332 106 19 5.332 106 42 5.332 106 30 5.629 106 39 1.000 106 20 4.583 106 22 2.543 106 23 1.000 106 38 5.332 106 28 4.086 106 29 1.000 106 18 5.332 107 4 4.086 107 6 7.172 107 7 5.629 107 43 5.629 107 15 4.086 107 32 5.332 107 17 5.332 107 39 5.629 107 37 5.332 107 21 5.332 107 31 6.710 107 27 4.086 107 35 6.126 107 24 4.086 108 16 5.332 108 4 4.583 108 6 7.028 108 9 4.989 108 11 4.583 108 43 1.000 108 17 6.338 108 37 5.332 108 21 1.000 108 31 5.629 108 10 4.583 108 35 4.989 109 2 5.332 109 4 5.629 109 6 6.532 109 7 3.446 109 9 4.989 109 23 3.446 109 10 2.543 109 11 4.583 109 12 2.543 109 36 4.086 109 19 2.543 109 17 3.446 109 20 5.891 109 21 4.086 109 22 2.543 109 35 4.086 109 18 5.332 109 14 2.543 110 2 4.086 110 4 6.126 110 6 4.086 110 8 4.583 110 5 4.583 110 23 2.543 110 10 2.543 110 11 4.086 110 43 5.332 110 16 4.583 110 37 4.086 110 19 2.543 110 17 4.086 110 15 1.000 110 28 4.086 110 20 5.629 110 21 3.446 110 9 4.086 110 31 5.891 110 22 1.000 110 18 2.543 110 24 4.086 110 35 4.086 111 21 4.989 111 12 5.629 111 2 5.629 111 4 3.446 111 6 5.332 111 7 2.543 111 19 1.000 111 5 3.446 111 23 4.989 111 10 4.583 111 16 2.543 111 36 8.496 111 18 1.000 111 39 2.543 111 31 5.891 111 29 5.629 111 22 1.000 111 25 9.155 111 14 5.629 111 35 7.172 111 28 6.338 111 20 5.629 112 21 5.332 112 11 4.583 112 12 4.989 112 15 5.891 112 29 4.086 113 21 1.000 113 19 3.446 113 43 2.543 113 8 2.543 113 10 3.446 113 31 6.126 113 12 4.086 113 41 3.446 113 47 3.446 113 15 6.126 113 32 2.543 113 16 3.446 113 36 2.543 113 18 3.446 113 17 2.543 113 48 3.446 113 42 2.543 113 39 2.543 113 49 2.543 113 22 2.543 113 24 4.989 113 38 2.543 113 27 3.446 113 28 2.543 113 29 3.446 114 2 4.086 114 3 4.583 114 22 2.543 114 6 7.028 114 7 2.543 114 5 3.446 114 9 4.086 114 10 2.543 114 12 1.000 114 27 1.000 114 36 1.000 114 4 1.000 114 8 2.543 114 16 3.446 114 19 2.543 114 17 2.543 114 39 3.446 114 35 4.989 114 20 4.989 114 31 4.583 114 18 2.543 114 23 2.543 114 24 4.086 114 33 4.583 114 38 4.583 114 26 4.583 114 13 2.543 114 28 4.583 114 11 4.086 115 3 1.000 115 4 1.000 115 38 1.000 115 8 1.000 115 34 1.000 115 9 5.332 115 10 1.000 115 12 1.000 115 15 1.000 115 16 1.000 115 13 1.000 115 36 5.332 115 18 1.000 115 19 1.000 115 47 1.000 115 39 1.000 115 37 2.543 115 31 1.000 115 49 5.332 115 22 4.989 115 23 1.000 115 33 1.000 115 27 1.000 116 25 6.338 116 1 2.543 116 44 2.543 116 26 4.086 116 9 1.000 116 46 2.543 116 3 3.446 116 11 4.583 116 12 5.332 116 15 5.891 116 13 1.000 116 36 2.543 116 31 4.583 116 29 4.989 116 24 4.583 116 33 4.583 116 38 4.989 116 34 4.989 116 45 2.543 116 28 1.000 116 6 1.000 117 25 7.172 117 2 4.989 117 4 3.446 117 7 2.543 117 5 4.086 117 9 2.543 117 31 6.710 117 11 6.126 117 12 6.710 117 14 6.875 117 41 7.172 117 16 2.543 117 13 2.543 117 17 4.583 117 18 2.543 117 48 7.172 117 49 7.307 117 21 6.532 117 20 7.172 117 19 1.000 117 33 1.000 117 22 2.543 117 23 3.446 117 24 7.172 117 28 6.126 117 34 2.543 117 10 3.446 117 35 6.875 118 12 4.583 118 4 1.000 118 6 6.875 118 23 1.000 118 10 1.000 118 11 4.583 118 32 1.000 118 16 1.000 118 19 1.000 118 17 4.086 118 39 2.543 118 20 5.629 118 21 4.086 118 31 4.583 118 29 2.543 118 18 1.000 118 24 4.583 118 25 3.446 118 35 5.629 119 1 3.446 119 6 1.000 119 44 3.446 119 12 3.446 119 43 4.989 119 15 4.989 119 32 4.583 119 37 2.543 119 27 2.543 119 35 4.583 119 45 3.446 120 25 4.989 120 2 1.000 120 3 4.989 120 4 1.000 120 23 1.000 120 5 1.000 120 20 6.338 120 21 1.000 120 22 1.000 120 24 4.989 120 27 3.446 120 28 5.332 121 21 2.543 121 44 3.446 121 4 1.000 121 7 1.000 121 43 3.446 121 1 3.446 121 23 1.000 121 10 1.000 121 31 5.891 121 15 2.543 121 16 2.543 121 35 5.332 121 19 4.086 121 32 4.086 121 39 1.000 121 45 3.446 121 29 3.446 121 46 3.446 121 18 1.000 122 3 4.989 122 9 4.086 122 40 5.332 122 11 4.086 122 12 4.583 122 41 4.086 122 15 2.543 122 13 1.000 122 24 3.446 122 26 5.332 122 29 4.583 123 18 1.000 123 2 2.543 123 4 4.086 123 6 6.338 123 7 4.086 123 23 1.000 123 10 1.000 123 15 3.446 123 19 5.629 123 39 4.086 123 21 3.446 123 9 3.446 123 35 5.332 123 29 4.086 123 11 4.583 124 2 5.332 124 4 5.629 124 6 7.172 124 10 4.583 124 11 1.000 124 19 5.629 124 16 1.000 124 36 2.543 124 5 5.629 124 37 1.000 124 20 6.338 124 29 2.543 124 22 1.000 124 23 4.989 124 24 3.446 124 33 1.000 124 38 4.583 124 35 6.126 124 28 5.629 124 18 5.891 124 14 4.583 125 31 1.000 125 2 4.989 125 3 1.000 125 4 2.543 125 43 2.543 125 8 1.000 125 10 1.000 125 16 1.000 125 36 2.543 125 18 2.543 125 19 2.543 125 17 1.000 125 20 4.086 125 21 1.000 125 22 2.543 125 23 2.543 125 33 4.989 125 38 1.000 125 27 1.000 125 35 4.583 125 28 3.446 125 29 4.583 126 44 5.629 126 2 2.543 126 4 5.891 126 1 5.332 126 26 1.000 126 12 5.629 126 15 5.629 126 11 4.583 126 43 3.446 126 48 5.332 126 30 5.629 126 24 5.629 126 34 5.629 126 28 5.332 126 18 6.532 126 50 5.629 127 6 2.543 127 9 2.543 127 10 4.989 127 11 4.989 127 32 5.332 127 37 4.086 127 29 4.086 127 24 5.332 127 35 4.989 128 2 4.086 128 10 2.543 128 36 5.891 128 5 4.086 128 19 6.338 128 37 5.629 128 20 4.086 128 21 2.543 128 31 6.126 128 24 4.086 129 12 5.629 129 23 4.989 129 46 4.086 129 10 8.715 129 16 6.532 129 5 9.038 129 19 7.028 129 4 7.980 129 39 5.332 129 37 6.875 129 21 4.086 129 33 5.332 129 38 4.086 129 18 3.446 129 20 6.875 130 1 6.126 130 44 5.332 130 2 7.028 130 3 7.172 130 9 3.446 130 15 4.583 130 16 2.543 130 13 1.000 130 14 4.989 130 6 4.086 130 29 5.891 130 50 7.434 130 25 2.543 130 12 5.629 130 17 1.000 130 47 1.000 130 30 1.000 130 33 1.000 130 27 3.446 130 49 6.338 130 28 6.710 130 42 1.000 130 20 4.583 130 22 2.543 130 26 6.532 130 35 3.446 130 45 5.891 130 46 6.338 130 11 6.532 130 40 6.532 130 41 6.532 130 21 5.332 131 21 2.543 131 1 1.000 131 44 2.543 131 3 2.543 131 7 3.446 131 11 4.989 131 12 4.086 131 16 1.000 131 36 1.000 131 43 1.000 131 19 2.543 131 32 2.543 131 46 1.000 131 37 1.000 131 26 3.446 131 6 5.629 131 35 4.086 131 45 1.000 131 29 3.446 132 44 3.446 132 6 6.532 132 7 2.543 132 43 2.543 132 8 2.543 132 10 3.446 132 11 4.583 132 19 3.446 132 4 3.446 132 16 2.543 132 36 3.446 132 5 3.446 132 18 3.446 132 32 3.446 132 17 2.543 132 39 3.446 132 21 2.543 132 31 2.543 132 46 3.446 132 24 3.446 132 27 3.446 132 45 3.446 133 2 1.000 133 4 5.629 133 7 1.000 133 9 5.332 133 23 5.629 133 10 5.629 133 12 2.543 133 15 5.629 133 5 3.446 133 18 1.000 133 19 5.629 133 17 3.446 133 20 6.126 133 21 4.583 133 22 3.446 133 35 5.332 133 14 1.000 133 11 4.583 134 31 4.086 134 1 5.629 134 44 5.629 134 6 6.875 134 9 4.583 134 10 5.891 134 11 5.332 134 12 5.629 134 43 5.891 134 15 1.000 134 13 3.446 134 5 4.583 134 19 5.629 134 47 3.446 134 29 5.332 134 18 4.989 134 26 5.891 134 24 5.891 134 45 5.629 134 46 5.629 135 2 8.418 135 14 8.418 135 36 4.989 135 5 6.532 135 29 4.583 135 37 2.543 135 21 6.875 135 18 10.000 135 33 2.543 135 35 7.172 135 28 8.496 136 3 4.086 136 6 6.875 136 7 2.543 136 9 1.000 136 12 4.583 136 43 1.000 136 11 4.086 136 17 1.000 136 37 1.000 136 20 4.086 136 24 2.543 136 26 4.583 136 35 5.629 137 1 4.086 137 44 4.086 137 43 4.989 137 11 4.583 137 15 5.891 137 13 2.543 137 19 1.000 137 45 5.332 137 46 4.086 137 18 2.543 138 1 5.629 138 44 5.332 138 3 5.629 138 7 2.543 138 9 1.000 138 40 5.332 138 11 4.583 138 41 5.332 138 15 5.891 138 25 5.629 138 34 5.332 138 27 2.543 138 24 5.332 138 49 5.332 138 45 5.629 138 46 5.629 139 6 2.543 139 7 5.332 139 43 1.000 139 12 4.989 139 17 6.338 139 20 6.126 139 21 2.543 139 31 5.332 139 35 4.086 140 3 5.891 140 4 5.629 140 23 1.000 140 10 1.000 140 5 5.629 140 19 5.891 140 20 6.532 140 22 1.000 140 18 5.332 141 25 6.338 141 18 2.543 141 1 2.543 141 44 2.543 141 38 2.543 141 11 3.446 141 23 2.543 141 10 2.543 141 15 4.583 141 2 4.583 141 35 4.583 141 36 4.086 141 19 2.543 141 20 5.332 141 46 2.543 141 33 1.000 141 45 2.543 141 28 1.000 141 29 4.583 141 14 4.086 142 2 5.332 142 38 4.583 142 6 1.000 142 26 5.332 142 23 1.000 142 10 1.000 142 19 4.583 142 5 3.446 142 18 1.000 142 37 4.989 142 22 1.000 142 24 4.989 142 33 6.126 142 28 6.126 142 14 5.332 143 33 5.332 143 47 2.543 143 2 4.583 143 4 1.000 143 38 1.000 143 19 1.000 143 23 4.583 143 10 4.583 143 12 3.446 143 15 8.644 143 36 4.989 143 5 5.629 143 20 3.446 143 31 6.126 143 22 7.669 143 18 6.875 143 37 1.000 143 24 5.332 143 28 4.086 143 29 1.000 144 21 2.543 144 8 2.543 144 43 1.000 144 16 6.126 144 5 5.891 144 32 4.086 144 20 6.338 144 39 5.332 144 23 4.583 144 35 7.669 144 29 6.710 144 18 5.629 145 21 7.307 145 2 7.172 145 4 8.644 145 23 7.307 145 10 8.253 145 11 5.891 145 46 4.086 145 36 7.172 145 5 6.710 145 19 7.172 145 17 1.000 145 48 5.629 145 39 4.086 145 20 7.434 145 31 5.629 145 22 4.583 145 18 8.337 145 33 6.126 145 38 7.980 145 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24 61 5.122 24 1 3.327 24 49 6.080 24 35 3.327 24 16 4.409 24 37 1.000 24 6 2.468 24 23 3.937 24 44 1.000 24 26 5.122 24 38 3.327 24 39 5.122 24 36 6.591 24 52 6.264 24 53 4.796 24 41 5.122 24 45 3.327 24 22 1.000 24 64 5.122 24 42 5.122 25 32 2.468 25 38 1.000 25 33 6.737 25 27 5.655 25 7 2.468 25 2 1.000 25 22 2.468 25 17 4.796 25 1 2.468 25 24 5.405 25 8 1.000 25 23 3.327 25 43 1.000 25 12 5.878 25 26 3.327 25 44 1.000 25 11 1.000 25 39 1.000 25 36 4.409 25 40 6.264 25 52 1.000 25 28 5.122 25 45 2.468 25 16 2.468 25 42 5.405 25 29 5.122 25 60 5.405 25 18 1.000 26 1 1.000 26 15 2.468 26 2 1.000 26 22 2.468 26 32 2.468 26 36 3.937 26 8 1.000 26 5 1.000 26 7 1.000 26 18 1.000 26 25 4.796 26 52 1.000 26 38 1.000 26 28 3.937 26 42 5.405 26 47 1.000 27 30 7.548 27 63 7.002 27 61 7.002 27 31 5.655 27 19 1.000 27 34 2.468 27 2 1.000 27 22 2.468 27 37 4.409 27 4 2.468 27 36 3.937 27 10 2.468 27 32 2.468 27 49 2.468 27 35 6.434 27 5 1.000 27 69 5.405 27 54 2.468 27 67 5.405 27 48 2.468 27 66 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5.122 31 19 3.937 31 20 5.122 31 62 5.655 31 4 5.122 31 5 5.122 31 51 5.122 31 23 5.878 31 11 5.122 31 13 5.122 31 27 5.405 31 3 4.796 31 15 5.122 31 24 5.655 32 35 4.796 32 30 5.405 32 63 5.878 32 61 5.405 32 1 2.468 32 38 1.000 32 60 3.327 32 34 1.000 32 2 1.000 32 36 4.409 32 37 5.122 32 4 2.468 32 6 1.000 32 7 2.468 32 18 1.000 32 43 5.122 32 64 5.122 32 47 5.655 32 41 4.796 32 16 1.000 32 22 2.468 32 39 5.405 32 42 5.655 32 29 4.796 32 65 5.405 33 59 4.796 33 33 4.409 33 6 4.409 33 20 5.405 33 62 1.000 33 45 2.468 33 65 4.409 33 56 4.796 33 35 4.796 33 37 5.655 33 51 4.796 33 23 5.405 33 69 5.122 33 48 3.327 33 11 4.796 33 43 4.796 33 68 4.796 33 18 5.655 33 39 5.405 33 52 1.000 33 16 3.327 33 70 4.796 34 1 2.468 34 32 1.000 34 13 1.000 34 33 3.937 34 49 2.468 34 2 1.000 34 22 1.000 34 36 2.468 34 5 2.468 34 7 4.409 34 18 3.937 34 8 4.409 34 12 5.405 34 25 3.937 34 15 1.000 34 38 3.327 34 28 3.327 34 42 3.327 35 30 4.409 35 63 3.327 35 61 3.327 35 1 4.409 35 32 5.405 35 62 4.409 35 34 3.937 35 2 4.409 35 65 3.327 35 22 5.878 35 17 4.796 35 37 4.409 35 6 4.796 35 49 5.122 35 7 4.409 35 8 3.937 35 67 4.409 35 51 2.468 35 69 4.409 35 57 3.937 35 48 3.937 35 12 5.405 35 26 1.000 35 29 5.655 35 44 2.468 35 38 2.468 35 39 1.000 35 52 5.122 35 53 5.655 35 41 4.409 35 58 3.937 35 16 1.000 35 64 3.327 35 42 5.405 35 18 4.796 35 36 4.796 36 32 1.000 36 33 7.123 36 19 1.000 36 34 1.000 36 2 1.000 36 22 1.000 36 17 4.796 36 35 5.655 36 8 1.000 36 4 1.000 36 3 1.000 36 5 1.000 36 7 1.000 36 18 1.000 36 23 1.000 36 9 1.000 36 10 1.000 36 12 6.591 36 25 5.878 36 52 1.000 36 15 2.468 36 27 6.591 36 28 5.122 36 16 4.796 36 24 6.434 36 42 5.655 36 29 6.591 37 1 2.468 37 38 1.000 37 62 2.468 37 34 1.000 37 2 1.000 37 22 1.000 37 32 2.468 37 5 1.000 37 15 2.468 37 49 2.468 37 7 2.468 37 8 1.000 37 51 2.468 37 9 1.000 37 11 1.000 37 12 4.409 37 14 2.468 37 18 1.000 37 52 4.409 37 53 3.327 37 41 2.468 37 42 4.409 37 29 4.409 37 27 5.878 38 25 1.000 38 63 1.000 38 61 1.000 38 31 1.000 38 50 1.000 38 13 1.000 38 30 1.000 38 69 1.000 38 23 1.000 38 34 1.000 38 22 1.000 38 17 3.937 38 35 1.000 38 37 1.000 38 3 1.000 38 49 1.000 38 7 1.000 38 54 1.000 38 9 1.000 38 11 2.468 38 42 1.000 38 38 1.000 38 46 3.327 38 39 2.468 38 40 6.873 38 28 1.000 38 16 3.327 38 64 1.000 38 65 1.000 38 59 1.000 38 70 2.468 39 30 4.796 39 63 4.796 39 61 4.796 39 41 2.468 39 34 4.796 39 22 3.327 39 35 3.937 39 37 4.409 39 18 4.796 39 7 3.937 39 16 1.000 39 60 1.000 39 47 3.327 39 39 3.937 39 45 1.000 39 64 4.796 39 42 2.468 39 43 4.409 39 29 5.655 39 65 4.796 40 26 4.796 40 33 6.080 40 19 1.000 40 17 4.796 40 35 2.468 40 36 1.000 40 37 6.264 40 4 1.000 40 3 2.468 40 25 3.937 40 34 1.000 40 14 1.000 40 28 3.937 40 24 5.405 40 29 5.122 40 27 2.468 41 1 5.122 41 32 4.796 41 62 5.122 41 37 5.122 41 14 6.873 41 5 2.468 41 6 1.000 41 7 1.000 41 38 1.000 41 43 5.405 41 27 4.796 41 52 3.937 41 60 3.937 41 18 1.000 41 17 3.937 42 40 5.405 42 19 1.000 42 33 1.000 42 20 1.000 42 21 1.000 42 26 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47 4 3.937 47 33 1.000 47 28 1.000 47 34 2.468 47 22 1.000 47 37 5.655 47 6 2.468 47 51 3.327 47 23 1.000 47 69 3.937 47 39 1.000 47 12 1.000 47 66 4.409 47 13 2.468 47 26 4.409 47 29 1.000 47 24 3.937 47 10 2.468 47 60 2.468 48 1 5.655 48 32 3.327 48 40 3.937 48 7 3.937 48 8 3.937 48 23 3.327 48 10 2.468 48 11 1.000 48 13 1.000 48 14 1.000 48 26 6.264 48 27 8.342 48 52 2.468 48 24 7.002 48 39 7.123 49 1 1.000 49 33 6.080 49 19 1.000 49 20 3.937 49 35 4.409 49 32 4.796 49 5 5.878 49 8 4.796 49 25 5.122 49 13 5.122 49 12 5.655 49 18 5.122 49 2 4.796 49 22 4.796 49 24 3.937 50 5 5.655 50 32 5.878 50 52 1.000 50 2 6.264 50 22 5.878 50 31 3.937 50 4 4.409 50 49 5.405 50 12 6.080 50 38 2.468 50 18 7.002 50 36 5.655 50 53 5.655 50 28 5.405 50 15 6.434 50 35 1.000 50 42 5.655 51 1 3.327 51 32 4.409 51 2 5.405 51 22 5.122 51 35 3.937 51 7 4.796 51 8 3.937 51 23 4.409 51 12 5.655 51 26 4.796 51 38 1.000 51 18 5.405 51 39 5.655 51 42 3.937 52 30 4.796 52 63 4.796 52 61 4.409 52 1 1.000 52 31 1.000 52 50 1.000 52 20 1.000 52 42 1.000 52 62 1.000 52 21 1.000 52 34 1.000 52 37 1.000 52 6 1.000 52 49 1.000 52 51 5.122 52 9 1.000 52 11 2.468 52 26 7.002 52 18 1.000 52 39 6.080 52 40 6.737 52 45 1.000 52 16 2.468 52 64 4.409 52 29 3.937 53 35 3.937 53 50 5.405 53 41 1.000 53 62 1.000 53 34 4.409 53 17 4.796 53 43 4.409 53 44 1.000 53 46 3.937 53 39 4.409 53 45 2.468 53 64 3.327 53 18 5.655 54 35 3.327 54 4 3.937 54 1 3.937 54 32 3.327 54 62 1.000 54 7 3.327 54 34 3.937 54 2 4.409 54 8 5.655 54 23 1.000 54 12 5.122 54 25 4.409 54 26 5.878 54 44 1.000 54 38 1.000 54 39 3.937 54 36 2.468 54 52 5.122 54 53 3.327 54 28 3.327 54 45 2.468 54 16 2.468 54 22 4.796 54 24 5.405 54 10 1.000 54 18 7.548 55 25 5.405 55 1 3.327 55 33 2.468 55 20 3.937 55 62 1.000 55 26 5.655 55 8 2.468 55 11 4.796 55 34 1.000 55 29 5.122 55 27 6.264 55 16 2.468 55 24 5.878 55 12 1.000 56 32 2.468 56 34 3.327 56 2 1.000 56 22 1.000 56 17 3.937 56 8 1.000 56 69 3.937 56 10 1.000 56 12 5.122 56 38 1.000 56 15 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6.264 98 28 5.122 98 22 1.000 98 64 3.937 98 43 4.409 98 60 4.796 99 30 4.796 99 63 4.796 99 61 4.409 99 1 3.937 99 31 3.937 99 32 1.000 99 22 1.000 99 33 6.080 99 34 1.000 99 2 1.000 99 17 4.796 99 35 4.409 99 5 1.000 99 7 2.468 99 8 2.468 99 54 3.937 99 23 2.468 99 12 4.796 99 25 1.000 99 26 3.327 99 38 1.000 99 46 3.327 99 52 4.409 99 41 4.409 99 24 4.409 99 39 4.796 99 64 4.796 99 42 4.409 99 29 4.796 99 60 2.468 99 36 3.937 99 27 1.000 100 33 1.000 100 20 6.080 100 62 3.937 100 17 1.000 100 51 2.468 100 11 4.409 100 12 1.000 100 25 3.327 100 14 5.655 100 18 1.000 100 27 1.000 100 40 1.000 100 28 5.122 100 24 1.000 100 10 1.000 101 35 2.468 101 33 2.468 101 21 1.000 101 34 4.409 101 37 4.796 101 51 4.796 101 9 1.000 101 11 1.000 101 14 6.873 101 26 4.796 101 39 4.796 101 41 4.409 101 45 3.327 101 24 4.796 101 47 4.409 101 27 5.878 102 6 1.000 102 49 4.796 102 29 1.000 102 67 5.655 102 23 1.000 102 66 1.000 102 26 1.000 102 38 1.000 102 53 1.000 102 33 1.000 102 36 1.000 103 5 1.000 103 1 2.468 103 32 1.000 103 19 1.000 103 33 1.000 103 27 6.080 103 7 1.000 103 2 1.000 103 22 1.000 103 36 3.937 103 4 1.000 103 24 5.878 103 8 5.122 103 12 6.434 103 25 5.122 103 10 1.000 103 52 1.000 103 38 1.000 103 15 2.468 103 42 5.122 103 29 5.122 103 18 1.000 104 63 5.405 104 61 5.405 104 60 5.122 104 30 5.405 104 17 4.796 104 37 5.655 104 3 5.405 104 14 6.080 104 47 5.655 104 46 5.878 104 64 5.405 104 29 5.655 104 65 5.405 104 27 5.405 105 5 1.000 105 32 5.405 105 19 1.000 105 33 4.796 105 6 1.000 105 62 3.327 105 34 1.000 105 2 1.000 105 22 1.000 105 37 5.122 105 4 1.000 105 17 1.000 105 8 1.000 105 51 1.000 105 23 1.000 105 9 1.000 105 26 3.937 105 44 1.000 105 38 1.000 105 39 3.937 105 40 1.000 105 52 5.122 105 53 2.468 105 28 1.000 105 45 1.000 105 16 1.000 105 35 1.000 105 24 4.409 105 42 2.468 105 29 5.122 105 10 1.000 105 18 4.409 105 12 4.796 106 22 5.405 106 20 4.409 106 26 6.264 106 4 5.405 106 7 6.737 106 8 5.405 106 23 1.000 106 1 3.327 106 11 6.434 106 13 5.405 106 14 8.532 106 18 1.000 106 28 6.264 106 24 7.548 106 33 4.409 106 10 2.468 106 12 5.655 107 17 1.000 107 20 3.937 107 34 3.937 107 35 5.405 107 37 5.122 107 3 1.000 107 62 1.000 107 9 2.468 107 44 1.000 107 43 5.122 107 25 5.405 107 14 2.468 107 27 3.327 107 40 6.264 107 4 5.122 107 41 5.655 107 15 2.468 107 12 3.937 108 32 5.405 108 33 6.737 108 19 1.000 108 20 5.122 108 49 4.796 108 2 1.000 108 35 5.122 108 4 5.405 108 5 6.434 108 7 5.405 108 8 5.122 108 9 5.405 108 12 6.080 108 25 5.122 108 13 5.405 108 14 6.080 108 26 5.122 108 38 1.000 108 18 2.468 108 15 5.405 108 27 7.237 108 52 5.122 108 53 4.796 108 22 2.468 108 24 6.264 108 42 5.122 109 32 3.327 109 33 4.409 109 19 2.468 109 34 1.000 109 2 3.327 109 22 2.468 109 17 1.000 109 5 2.468 109 23 2.468 109 7 3.937 109 9 3.327 109 10 1.000 109 11 2.468 109 12 5.122 109 25 5.405 109 15 3.327 109 28 3.327 109 16 2.468 109 24 7.346 109 27 7.237 110 32 5.878 110 33 2.468 110 19 1.000 110 20 3.327 110 28 1.000 110 35 1.000 110 4 6.737 110 5 4.796 110 8 3.937 110 25 6.434 110 13 6.434 110 14 4.409 110 15 5.878 110 27 5.655 110 40 4.409 110 16 2.468 110 24 7.123 111 1 4.796 111 53 2.468 111 34 3.937 111 37 5.122 111 49 4.409 111 12 5.122 111 44 1.000 111 38 2.468 111 39 3.327 111 45 2.468 111 42 5.122 111 29 4.796 111 36 1.000 112 34 2.468 112 17 4.409 112 35 5.405 112 4 5.655 112 51 5.122 112 11 1.000 112 14 5.655 112 27 5.655 112 16 5.655 112 46 3.937 112 24 6.080 112 10 3.937 113 21 1.000 113 31 3.327 113 50 5.655 113 62 1.000 113 22 4.409 113 17 4.409 113 6 1.000 113 57 2.468 113 12 1.000 113 26 4.796 113 44 1.000 113 39 3.937 113 36 1.000 113 41 4.409 113 45 4.409 113 16 2.468 113 29 4.409 114 25 1.000 114 50 3.327 114 33 6.264 114 19 2.468 114 62 2.468 114 2 1.000 114 22 3.937 114 17 1.000 114 58 5.122 114 37 3.327 114 4 3.937 114 51 2.468 114 23 1.000 114 69 3.937 114 57 5.405 114 48 5.655 114 9 2.468 114 11 2.468 114 12 4.796 114 66 3.937 114 13 1.000 114 14 2.468 114 26 4.796 114 18 3.937 114 15 1.000 114 27 3.327 114 28 3.327 114 24 4.409 114 29 3.937 114 10 1.000 115 26 1.000 115 63 4.409 115 61 4.409 115 62 5.405 115 30 4.409 115 34 3.937 115 17 4.409 115 35 4.796 115 37 3.937 115 51 4.796 115 9 2.468 115 43 4.409 115 29 4.409 115 52 4.409 115 65 4.796 115 18 3.937 115 46 4.796 115 8 1.000 115 22 3.937 115 64 4.409 115 10 1.000 115 60 4.409 116 32 5.405 116 53 4.409 116 50 6.080 116 34 1.000 116 2 4.409 116 62 3.937 116 49 1.000 116 7 4.796 116 51 1.000 116 48 5.122 116 9 3.937 116 12 5.405 116 38 4.796 116 36 4.409 116 52 5.122 116 58 1.000 116 22 5.405 116 65 3.937 116 18 4.409 117 35 1.000 117 53 1.000 117 22 2.468 117 34 7.902 117 55 5.405 117 56 5.655 117 37 1.000 117 32 2.468 117 23 1.000 117 49 5.878 117 8 1.000 117 54 5.405 117 57 6.264 117 48 5.655 117 43 5.122 117 38 1.000 117 39 3.937 117 52 5.878 117 41 1.000 117 58 5.122 117 68 4.796 117 42 8.133 117 59 5.122 118 1 2.468 118 31 5.122 118 32 5.655 118 33 3.937 118 34 1.000 118 22 5.122 118 17 5.122 118 37 6.264 118 5 5.405 118 25 4.796 118 13 5.405 118 38 1.000 118 39 5.405 118 52 5.122 118 53 5.405 118 28 4.409 118 42 5.655 118 29 5.655 118 10 1.000 118 60 5.122 118 12 1.000 119 40 1.000 119 30 1.000 119 63 1.000 119 1 1.000 119 33 1.000 119 62 1.000 119 21 1.000 119 55 1.000 119 56 2.468 119 37 1.000 119 6 1.000 119 51 1.000 119 23 2.468 119 69 2.468 119 9 1.000 119 64 1.000 119 66 1.000 119 13 2.468 119 26 1.000 119 47 1.000 119 39 1.000 119 61 1.000 119 41 1.000 119 28 1.000 119 16 1.000 119 68 1.000 119 29 1.000 119 65 1.000 119 70 1.000 119 59 1.000 120 1 5.655 120 32 6.591 120 33 6.873 120 46 1.000 120 22 3.327 120 17 4.409 120 51 1.000 120 6 3.327 120 24 3.937 120 8 5.405 120 11 5.405 120 12 5.878 120 25 5.405 120 13 1.000 120 14 1.000 120 10 2.468 120 27 3.327 120 28 1.000 120 29 5.405 120 36 3.327 121 35 1.000 121 1 3.327 121 32 1.000 121 50 1.000 121 17 4.409 121 23 1.000 121 49 1.000 121 7 3.327 121 8 1.000 121 29 3.327 121 18 1.000 121 46 3.327 121 39 2.468 121 36 1.000 121 52 3.327 121 41 1.000 121 53 3.327 121 33 6.080 122 34 1.000 122 2 1.000 122 22 1.000 122 37 1.000 122 15 1.000 122 36 1.000 122 23 1.000 122 49 1.000 122 29 1.000 122 52 1.000 122 45 1.000 122 16 1.000 122 42 1.000 122 60 2.468 122 62 3.937 122 21 1.000 122 17 3.937 122 7 1.000 122 51 1.000 122 39 1.000 122 41 1.000 122 47 1.000 122 18 1.000 122 9 1.000 122 38 1.000 123 1 1.000 123 32 1.000 123 50 1.000 123 20 1.000 123 8 1.000 123 62 1.000 123 2 1.000 123 22 2.468 123 26 2.468 123 35 5.122 123 37 4.409 123 7 2.468 123 51 5.122 123 57 5.122 123 9 1.000 123 12 5.878 123 38 1.000 123 39 5.122 123 36 5.122 123 27 7.123 123 52 4.796 123 53 3.327 123 41 5.122 123 42 5.122 123 29 4.796 123 47 5.122 123 18 1.000 124 30 6.737 124 63 6.737 124 61 7.123 124 35 6.591 124 37 6.591 124 7 3.327 124 43 6.264 124 39 5.405 124 52 6.737 124 45 6.591 124 16 3.937 124 64 7.123 124 29 6.264 124 60 5.655 125 34 3.327 125 41 1.000 125 55 4.409 125 56 4.409 125 49 4.796 125 54 3.327 125 69 4.409 125 48 4.796 125 21 1.000 125 39 5.405 125 36 3.327 125 52 4.409 125 53 3.937 125 45 4.796 125 58 4.796 125 68 4.409 125 42 4.409 125 29 3.327 125 70 4.409 125 59 4.409 126 32 5.655 126 20 2.468 126 2 5.405 126 22 5.655 126 5 4.409 126 1 5.655 126 49 6.264 126 7 5.878 126 8 5.405 126 12 5.878 126 13 4.796 126 52 4.796 126 19 4.796 126 38 5.122 126 18 6.591 126 53 4.796 126 28 5.122 126 42 6.264 127 30 5.122 127 22 1.000 127 33 1.000 127 2 5.122 127 35 4.409 127 37 6.080 127 49 1.000 127 8 3.327 127 23 1.000 127 26 5.878 127 58 4.409 127 64 1.000 128 35 4.409 128 32 5.405 128 33 6.873 128 6 4.796 128 20 5.122 128 62 3.937 128 21 5.405 128 34 1.000 128 41 3.937 128 26 5.878 128 18 6.873 128 4 5.122 128 5 5.655 128 31 5.122 128 7 4.409 128 23 5.122 128 13 5.122 128 14 3.937 128 10 3.327 128 15 4.796 128 39 5.122 128 27 5.655 128 40 5.122 128 16 3.327 128 24 3.937 128 29 5.405 129 40 6.873 129 30 3.937 129 63 4.796 129 61 4.796 129 1 1.000 129 19 2.468 129 34 4.796 129 37 3.937 129 5 1.000 129 49 3.327 129 9 2.468 129 14 2.468 129 38 5.122 129 29 1.000 129 46 4.409 129 39 3.937 129 27 3.937 129 24 4.796 129 64 4.796 129 42 3.937 130 30 5.122 130 63 5.122 130 61 5.122 130 31 3.327 130 34 3.327 130 55 4.409 130 56 4.796 130 37 5.405 130 67 4.796 130 69 5.122 130 66 1.000 130 50 1.000 130 36 4.409 130 52 4.796 130 53 3.327 130 41 4.409 130 68 4.409 130 64 4.796 130 29 5.122 130 70 5.122 130 59 3.937 131 32 5.878 131 33 3.327 131 17 2.468 131 7 1.000 131 12 5.655 131 25 2.468 131 24 3.327 131 42 5.655 131 10 2.468 132 1 1.000 132 6 3.937 132 22 2.468 132 26 3.327 132 16 2.468 132 7 2.468 132 8 1.000 132 67 1.000 132 23 3.937 132 21 1.000 132 12 4.409 132 25 1.000 132 14 1.000 132 39 3.937 132 52 1.000 132 53 2.468 132 24 4.796 132 42 1.000 132 33 1.000 132 29 1.000 132 18 3.937 133 63 3.937 133 1 5.655 133 50 1.000 133 19 3.937 133 34 3.937 133 36 1.000 133 4 4.796 133 49 5.122 133 8 3.327 133 23 1.000 133 57 4.796 133 25 5.405 133 26 5.655 133 60 2.468 133 11 1.000 133 52 5.122 133 42 4.796 133 33 1.000 134 35 1.000 134 30 3.937 134 4 3.937 134 50 1.000 134 27 1.000 134 20 3.937 134 33 1.000 134 54 1.000 134 6 3.327 134 7 2.468 134 51 2.468 134 23 1.000 134 11 2.468 134 26 5.122 134 10 1.000 134 18 1.000 134 28 3.327 134 16 4.409 134 24 5.122 134 39 3.327 134 29 2.468 134 12 1.000 135 25 3.937 135 26 5.405 135 1 3.327 135 31 3.937 135 32 5.655 135 50 7.450 135 34 2.468 135 2 4.796 135 22 5.655 135 17 4.796 135 37 5.655 135 5 3.937 135 49 5.405 135 7 5.122 135 8 5.405 135 9 3.327 135 12 4.796 135 38 1.000 135 18 7.237 135 36 5.405 135 40 1.000 135 52 5.405 135 53 5.405 135 60 4.409 135 41 5.405 135 28 4.796 135 45 5.405 135 16 2.468 135 42 5.655 135 29 5.878 136 28 3.327 136 62 1.000 136 22 5.122 136 35 4.409 136 37 5.122 136 4 2.468 136 51 2.468 136 46 4.796 136 27 1.000 136 41 4.796 136 29 5.122 136 60 5.122 137 20 4.796 137 31 1.000 137 34 3.327 137 51 5.122 137 49 4.796 137 23 4.796 137 11 3.937 137 26 5.655 137 44 2.468 137 39 5.122 137 36 6.591 137 52 6.434 137 53 5.405 137 41 5.405 137 45 5.122 137 24 5.655 137 42 6.080 137 60 5.878 138 1 1.000 138 32 4.796 138 33 6.591 138 34 3.937 138 22 3.937 138 26 5.122 138 17 5.122 138 35 2.468 138 37 6.737 138 6 5.878 138 8 4.796 138 51 3.327 138 9 3.937 138 12 5.122 138 44 1.000 138 39 5.122 138 42 2.468 138 18 4.409 139 20 6.264 139 26 6.264 139 4 5.405 139 8 5.405 139 15 6.591 139 10 1.000 139 23 3.937 139 14 6.264 139 16 3.937 139 37 7.450 139 12 2.468 139 27 6.737 139 40 9.156 139 3 3.327 139 17 4.796 139 11 3.327 140 33 6.591 140 19 4.796 140 20 5.122 140 62 5.122 140 17 4.796 140 35 4.796 140 51 1.000 140 4 4.796 140 3 5.122 140 7 4.796 140 9 4.796 140 11 2.468 140 12 4.796 140 25 5.405 140 13 5.122 140 14 5.122 140 26 5.122 140 18 5.405 140 27 5.122 140 40 6.737 140 28 5.122 140 16 5.122 140 29 4.796 140 10 1.000 141 1 1.000 141 33 6.264 141 19 3.937 141 20 4.409 141 8 6.080 141 7 5.655 141 26 3.327 141 23 5.405 141 9 4.409 141 11 5.122 141 12 3.327 141 15 3.327 141 28 4.796 141 16 3.327 141 22 5.405 141 24 6.080 141 10 1.000 141 17 5.878 142 30 3.937 142 63 3.937 142 61 3.937 142 1 3.937 142 31 5.405 142 32 5.405 142 33 6.434 142 62 5.122 142 34 3.937 142 22 5.122 142 35 4.796 142 37 5.878 142 51 5.122 142 3 5.122 142 5 5.405 142 49 5.122 142 8 5.878 142 54 5.122 142 11 4.409 142 26 5.405 142 10 1.000 142 19 3.327 142 38 2.468 142 18 5.878 142 39 5.122 142 40 6.080 142 52 5.405 142 28 5.405 142 29 5.405 142 53 4.409 142 64 3.937 142 42 5.122 142 65 3.937 142 27 3.937 143 30 2.468 143 1 5.122 143 31 2.468 143 32 6.873 143 50 6.591 143 38 5.655 143 33 6.737 143 20 2.468 143 21 6.873 143 34 2.468 143 22 5.405 143 35 5.122 143 49 5.878 143 11 3.937 143 8 6.264 143 23 6.080 143 25 6.080 143 26 7.237 143 18 7.819 143 2 6.264 143 36 6.873 143 40 6.737 143 52 6.434 143 53 6.264 143 41 5.655 143 45 5.655 143 16 6.264 143 42 5.655 143 29 6.080 144 33 1.000 144 62 1.000 144 34 1.000 144 17 5.405 144 35 5.122 144 37 3.937 144 44 1.000 144 46 1.000 144 39 2.468 144 27 4.796 144 40 2.468 144 43 4.409 144 10 2.468 144 60 3.937 144 18 1.000 144 12 2.468 145 1 5.405 145 33 1.000 145 45 2.468 145 37 3.937 145 18 5.122 145 44 2.468 145 6 5.655 145 49 5.878 145 8 5.655 145 11 1.000 145 26 8.275 145 38 6.080 145 39 3.937 145 52 5.655 145 53 5.878 145 42 5.878 145 36 6.080 146 1 4.409 146 31 4.409 146 32 1.000 146 2 1.000 146 49 5.405 146 7 3.937 146 23 3.327 146 67 1.000 146 44 1.000 146 38 5.405 146 39 1.000 146 41 5.122 146 16 1.000 146 22 1.000 146 42 6.264 146 29 5.405 147 32 5.405 147 2 3.327 147 22 6.591 147 35 2.468 147 1 4.796 147 49 5.878 147 7 4.409 147 8 6.434 147 11 3.327 147 12 5.878 147 26 5.655 147 44 1.000 147 38 5.878 147 15 3.327 147 52 6.080 147 53 3.327 147 24 1.000 147 42 6.591 147 29 1.000 147 18 6.737 147 36 3.937 148 19 2.468 148 33 6.080 148 49 2.468 148 34 1.000 148 22 1.000 148 55 2.468 148 56 2.468 148 37 3.327 148 32 1.000 148 3 2.468 148 8 2.468 148 23 2.468 148 9 2.468 148 10 1.000 148 11 1.000 148 26 1.000 148 29 3.327 148 38 1.000 148 18 3.327 148 40 2.468 148 52 5.655 148 41 3.327 148 28 3.327 148 16 3.327 148 68 3.327 148 42 2.468 148 60 2.468 148 36 3.327 148 59 2.468 149 2 4.409 149 17 4.409 149 8 3.937 149 12 1.000 149 25 4.409 149 14 3.327 149 26 4.409 149 9 4.796 149 18 5.122 149 27 5.878 149 40 6.434 149 28 2.468 149 16 3.937 149 29 5.655 150 5 1.000 150 30 4.409 150 63 5.122 150 1 4.409 150 31 4.409 150 32 1.000 150 33 6.434 150 19 1.000 150 46 4.409 150 34 1.000 150 22 1.000 150 17 5.122 150 35 3.327 150 3 1.000 150 7 1.000 150 18 1.000 150 8 1.000 150 54 1.000 150 9 3.327 150 43 5.122 150 25 4.409 150 13 3.327 150 44 1.000 150 65 5.122 150 38 1.000 150 15 3.327 150 27 2.468 150 40 5.655 150 53 5.122 150 16 2.468 150 24 5.122 150 39 3.937 150 64 5.122 150 42 4.796 150 29 5.122 150 10 1.000 150 60 5.122 151 40 6.434 151 50 1.000 151 41 1.000 151 34 2.468 151 17 4.796 151 37 3.327 151 3 1.000 151 8 2.468 151 14 2.468 151 26 3.937 151 16 4.409 151 27 3.327 152 30 5.122 152 63 5.122 152 61 5.122 152 1 5.122 152 32 1.000 152 33 1.000 152 7 2.468 152 2 1.000 152 22 1.000 152 17 4.796 152 35 5.405 152 47 3.327 152 37 5.122 152 4 2.468 152 5 1.000 152 18 1.000 152 8 1.000 152 43 4.796 152 12 6.080 152 25 4.409 152 26 5.122 152 9 1.000 152 65 5.122 152 38 1.000 152 46 5.122 152 39 5.122 152 27 6.264 152 52 4.796 152 53 4.796 152 16 3.327 152 24 5.122 152 64 5.405 152 42 6.080 152 29 5.405 152 60 5.122 152 36 4.409 153 1 3.327 153 32 1.000 153 21 1.000 153 22 2.468 153 8 1.000 153 4 1.000 153 5 1.000 153 7 2.468 153 23 2.468 153 57 4.796 153 9 1.000 153 10 1.000 153 12 5.878 153 25 4.796 153 38 1.000 153 18 1.000 153 15 1.000 153 24 5.122 153 42 7.548 153 29 5.122 153 60 4.409 154 5 2.468 154 1 3.327 154 32 3.327 154 7 3.327 154 34 3.327 154 2 2.468 154 6 1.000 154 22 6.264 154 8 2.468 154 4 2.468 154 9 2.468 154 11 1.000 154 25 8.205 154 15 3.327 154 36 7.819 154 27 8.059 154 40 7.548 154 52 7.732 154 28 6.080 154 16 4.796 154 24 7.732 154 42 7.902 154 18 3.327 155 33 6.434 155 2 4.796 155 22 5.122 155 7 5.655 155 8 3.327 155 11 1.000 155 12 5.122 155 25 1.000 155 14 3.327 155 26 5.878 155 18 6.264 156 19 5.405 156 33 6.264 156 26 5.655 156 62 1.000 156 21 3.327 156 4 1.000 156 5 5.655 156 23 5.655 156 11 5.122 156 12 3.937 156 13 6.080 156 44 2.468 156 15 7.002 156 40 3.327 156 10 2.468 157 63 6.737 157 61 6.737 157 20 1.000 157 62 3.327 157 30 4.796 157 17 1.000 157 37 7.902 157 21 2.468 157 5 2.468 157 7 7.237 157 8 5.878 157 9 1.000 157 11 3.327 157 14 3.937 157 26 4.796 157 29 7.002 157 2 1.000 157 46 5.655 157 15 6.873 157 39 3.937 157 27 5.122 157 52 6.873 157 16 3.937 157 24 3.937 157 64 4.409 157 42 7.450 157 33 3.327 157 10 2.468 158 30 3.937 158 63 3.937 158 61 3.937 158 34 3.327 158 37 6.737 158 29 3.937 158 32 3.937 158 35 5.122 158 6 1.000 158 45 5.122 158 60 1.000 158 62 1.000 158 51 1.000 158 43 5.122 158 39 3.937 158 40 5.878 158 41 1.000 158 64 4.409 158 47 1.000 159 32 5.405 159 8 1.000 159 62 4.796 159 34 2.468 159 35 1.000 159 37 4.796 159 43 2.468 159 26 5.405 159 44 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35 1.000 211 37 2.468 211 8 1.000 211 11 1.000 211 12 6.080 211 14 3.937 211 26 3.327 211 38 3.327 211 27 1.000 211 16 3.327 211 24 4.796 211 29 3.937 211 18 1.000 211 70 3.937 212 1 8.059 212 36 8.059 212 49 4.796 212 7 6.264 212 29 4.409 212 11 2.468 212 25 6.591 212 13 6.264 212 18 9.565 212 52 2.468 212 28 6.434 212 24 6.873 212 42 8.133 212 10 2.468 212 60 6.080 213 31 3.937 213 33 6.591 213 19 2.468 213 20 1.000 213 34 1.000 213 35 4.409 213 62 1.000 213 17 3.937 213 23 1.000 213 11 1.000 213 12 3.937 213 13 3.937 213 10 1.000 213 39 2.468 213 41 4.409 213 24 5.405 213 47 3.327 213 27 1.000 214 33 1.000 214 62 5.405 214 35 3.937 214 37 3.937 214 54 5.405 214 51 5.122 214 14 6.080 214 46 4.409 214 40 3.937 214 28 1.000 215 30 3.937 215 63 3.937 215 61 4.796 215 62 4.796 215 17 4.409 215 37 5.655 215 3 2.468 215 8 1.000 215 43 3.937 215 27 1.000 215 58 2.468 215 64 5.122 215 65 3.937 215 18 2.468 216 30 5.405 216 63 5.122 216 61 5.122 216 31 5.405 216 19 2.468 216 34 1.000 216 55 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111 29 4.796 111 36 1.000 112 34 2.468 112 17 4.409 112 35 5.405 112 4 5.655 112 51 5.122 112 11 1.000 112 14 5.655 112 27 5.655 112 16 5.655 112 46 3.937 112 24 6.080 112 10 3.937 113 21 1.000 113 31 3.327 113 50 5.655 113 62 1.000 113 22 4.409 113 17 4.409 113 6 1.000 113 57 2.468 113 12 1.000 113 26 4.796 113 44 1.000 113 39 3.937 113 36 1.000 113 41 4.409 113 45 4.409 113 16 2.468 113 29 4.409 114 25 1.000 114 50 3.327 114 33 6.264 114 19 2.468 114 62 2.468 114 2 1.000 114 22 3.937 114 17 1.000 114 58 5.122 114 37 3.327 114 4 3.937 114 51 2.468 114 23 1.000 114 69 3.937 114 57 5.405 114 48 5.655 114 9 2.468 114 11 2.468 114 12 4.796 114 66 3.937 114 13 1.000 114 14 2.468 114 26 4.796 114 18 3.937 114 15 1.000 114 27 3.327 114 28 3.327 114 24 4.409 114 29 3.937 114 10 1.000 115 26 1.000 115 63 4.409 115 61 4.409 115 62 5.405 115 30 4.409 115 34 3.937 115 17 4.409 115 35 4.796 115 37 3.937 115 51 4.796 115 9 2.468 115 43 4.409 115 29 4.409 115 52 4.409 115 65 4.796 115 18 3.937 115 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126 13 4.796 126 52 4.796 126 19 4.796 126 38 5.122 126 18 6.591 126 53 4.796 126 28 5.122 126 42 6.264 127 30 5.122 127 22 1.000 127 33 1.000 127 2 5.122 127 35 4.409 127 37 6.080 127 49 1.000 127 8 3.327 127 23 1.000 127 26 5.878 127 58 4.409 127 64 1.000 128 35 4.409 128 32 5.405 128 33 6.873 128 6 4.796 128 20 5.122 128 62 3.937 128 21 5.405 128 34 1.000 128 41 3.937 128 26 5.878 128 18 6.873 128 4 5.122 128 5 5.655 128 31 5.122 128 7 4.409 128 23 5.122 128 13 5.122 128 14 3.937 128 10 3.327 128 15 4.796 128 39 5.122 128 27 5.655 128 40 5.122 128 16 3.327 128 24 3.937 128 29 5.405 129 40 6.873 129 30 3.937 129 63 4.796 129 61 4.796 129 1 1.000 129 19 2.468 129 34 4.796 129 37 3.937 129 5 1.000 129 49 3.327 129 9 2.468 129 14 2.468 129 38 5.122 129 29 1.000 129 46 4.409 129 39 3.937 129 27 3.937 129 24 4.796 129 64 4.796 129 42 3.937 130 30 5.122 130 63 5.122 130 61 5.122 130 31 3.327 130 34 3.327 130 55 4.409 130 56 4.796 130 37 5.405 130 67 4.796 130 69 5.122 130 66 1.000 130 50 1.000 130 36 4.409 130 52 4.796 130 53 3.327 130 41 4.409 130 68 4.409 130 64 4.796 130 29 5.122 130 70 5.122 130 59 3.937 131 32 5.878 131 33 3.327 131 17 2.468 131 7 1.000 131 12 5.655 131 25 2.468 131 24 3.327 131 42 5.655 131 10 2.468 132 1 1.000 132 6 3.937 132 22 2.468 132 26 3.327 132 16 2.468 132 7 2.468 132 8 1.000 132 67 1.000 132 23 3.937 132 21 1.000 132 12 4.409 132 25 1.000 132 14 1.000 132 39 3.937 132 52 1.000 132 53 2.468 132 24 4.796 132 42 1.000 132 33 1.000 132 29 1.000 132 18 3.937 133 63 3.937 133 1 5.655 133 50 1.000 133 19 3.937 133 34 3.937 133 36 1.000 133 4 4.796 133 49 5.122 133 8 3.327 133 23 1.000 133 57 4.796 133 25 5.405 133 26 5.655 133 60 2.468 133 11 1.000 133 52 5.122 133 42 4.796 133 33 1.000 134 35 1.000 134 30 3.937 134 4 3.937 134 50 1.000 134 27 1.000 134 20 3.937 134 33 1.000 134 54 1.000 134 6 3.327 134 7 2.468 134 51 2.468 134 23 1.000 134 11 2.468 134 26 5.122 134 10 1.000 134 18 1.000 134 28 3.327 134 16 4.409 134 24 5.122 134 39 3.327 134 29 2.468 134 12 1.000 135 25 3.937 135 26 5.405 135 1 3.327 135 31 3.937 135 32 5.655 135 50 7.450 135 34 2.468 135 2 4.796 135 22 5.655 135 17 4.796 135 37 5.655 135 5 3.937 135 49 5.405 135 7 5.122 135 8 5.405 135 9 3.327 135 12 4.796 135 38 1.000 135 18 7.237 135 36 5.405 135 40 1.000 135 52 5.405 135 53 5.405 135 60 4.409 135 41 5.405 135 28 4.796 135 45 5.405 135 16 2.468 135 42 5.655 135 29 5.878 136 28 3.327 136 62 1.000 136 22 5.122 136 35 4.409 136 37 5.122 136 4 2.468 136 51 2.468 136 46 4.796 136 27 1.000 136 41 4.796 136 29 5.122 136 60 5.122 137 20 4.796 137 31 1.000 137 34 3.327 137 51 5.122 137 49 4.796 137 23 4.796 137 11 3.937 137 26 5.655 137 44 2.468 137 39 5.122 137 36 6.591 137 52 6.434 137 53 5.405 137 41 5.405 137 45 5.122 137 24 5.655 137 42 6.080 137 60 5.878 138 1 1.000 138 32 4.796 138 33 6.591 138 34 3.937 138 22 3.937 138 26 5.122 138 17 5.122 138 35 2.468 138 37 6.737 138 6 5.878 138 8 4.796 138 51 3.327 138 9 3.937 138 12 5.122 138 44 1.000 138 39 5.122 138 42 2.468 138 18 4.409 139 20 6.264 139 26 6.264 139 4 5.405 139 8 5.405 139 15 6.591 139 10 1.000 139 23 3.937 139 14 6.264 139 16 3.937 139 37 7.450 139 12 2.468 139 27 6.737 139 40 9.156 139 3 3.327 139 17 4.796 139 11 3.327 140 33 6.591 140 19 4.796 140 20 5.122 140 62 5.122 140 17 4.796 140 35 4.796 140 51 1.000 140 4 4.796 140 3 5.122 140 7 4.796 140 9 4.796 140 11 2.468 140 12 4.796 140 25 5.405 140 13 5.122 140 14 5.122 140 26 5.122 140 18 5.405 140 27 5.122 140 40 6.737 140 28 5.122 140 16 5.122 140 29 4.796 140 10 1.000 141 1 1.000 141 33 6.264 141 19 3.937 141 20 4.409 141 8 6.080 141 7 5.655 141 26 3.327 141 23 5.405 141 9 4.409 141 11 5.122 141 12 3.327 141 15 3.327 141 28 4.796 141 16 3.327 141 22 5.405 141 24 6.080 141 10 1.000 141 17 5.878 142 30 3.937 142 63 3.937 142 61 3.937 142 1 3.937 142 31 5.405 142 32 5.405 142 33 6.434 142 62 5.122 142 34 3.937 142 22 5.122 142 35 4.796 142 37 5.878 142 51 5.122 142 3 5.122 142 5 5.405 142 49 5.122 142 8 5.878 142 54 5.122 142 11 4.409 142 26 5.405 142 10 1.000 142 19 3.327 142 38 2.468 142 18 5.878 142 39 5.122 142 40 6.080 142 52 5.405 142 28 5.405 142 29 5.405 142 53 4.409 142 64 3.937 142 42 5.122 142 65 3.937 142 27 3.937 143 30 2.468 143 1 5.122 143 31 2.468 143 32 6.873 143 50 6.591 143 38 5.655 143 33 6.737 143 20 2.468 143 21 6.873 143 34 2.468 143 22 5.405 143 35 5.122 143 49 5.878 143 11 3.937 143 8 6.264 143 23 6.080 143 25 6.080 143 26 7.237 143 18 7.819 143 2 6.264 143 36 6.873 143 40 6.737 143 52 6.434 143 53 6.264 143 41 5.655 143 45 5.655 143 16 6.264 143 42 5.655 143 29 6.080 144 33 1.000 144 62 1.000 144 34 1.000 144 17 5.405 144 35 5.122 144 37 3.937 144 44 1.000 144 46 1.000 144 39 2.468 144 27 4.796 144 40 2.468 144 43 4.409 144 10 2.468 144 60 3.937 144 18 1.000 144 12 2.468 145 1 5.405 145 33 1.000 145 45 2.468 145 37 3.937 145 18 5.122 145 44 2.468 145 6 5.655 145 49 5.878 145 8 5.655 145 11 1.000 145 26 8.275 145 38 6.080 145 39 3.937 145 52 5.655 145 53 5.878 145 42 5.878 145 36 6.080 146 1 4.409 146 31 4.409 146 32 1.000 146 2 1.000 146 49 5.405 146 7 3.937 146 23 3.327 146 67 1.000 146 44 1.000 146 38 5.405 146 39 1.000 146 41 5.122 146 16 1.000 146 22 1.000 146 42 6.264 146 29 5.405 147 32 5.405 147 2 3.327 147 22 6.591 147 35 2.468 147 1 4.796 147 49 5.878 147 7 4.409 147 8 6.434 147 11 3.327 147 12 5.878 147 26 5.655 147 44 1.000 147 38 5.878 147 15 3.327 147 52 6.080 147 53 3.327 147 24 1.000 147 42 6.591 147 29 1.000 147 18 6.737 147 36 3.937 148 19 2.468 148 33 6.080 148 49 2.468 148 34 1.000 148 22 1.000 148 55 2.468 148 56 2.468 148 37 3.327 148 32 1.000 148 3 2.468 148 8 2.468 148 23 2.468 148 9 2.468 148 10 1.000 148 11 1.000 148 26 1.000 148 29 3.327 148 38 1.000 148 18 3.327 148 40 2.468 148 52 5.655 148 41 3.327 148 28 3.327 148 16 3.327 148 68 3.327 148 42 2.468 148 60 2.468 148 36 3.327 148 59 2.468 149 2 4.409 149 17 4.409 149 8 3.937 149 12 1.000 149 25 4.409 149 14 3.327 149 26 4.409 149 9 4.796 149 18 5.122 149 27 5.878 149 40 6.434 149 28 2.468 149 16 3.937 149 29 5.655 150 5 1.000 150 30 4.409 150 63 5.122 150 1 4.409 150 31 4.409 150 32 1.000 150 33 6.434 150 19 1.000 150 46 4.409 150 34 1.000 150 22 1.000 150 17 5.122 150 35 3.327 150 3 1.000 150 7 1.000 150 18 1.000 150 8 1.000 150 54 1.000 150 9 3.327 150 43 5.122 150 25 4.409 150 13 3.327 150 44 1.000 150 65 5.122 150 38 1.000 150 15 3.327 150 27 2.468 150 40 5.655 150 53 5.122 150 16 2.468 150 24 5.122 150 39 3.937 150 64 5.122 150 42 4.796 150 29 5.122 150 10 1.000 150 60 5.122 151 40 6.434 151 50 1.000 151 41 1.000 151 34 2.468 151 17 4.796 151 37 3.327 151 3 1.000 151 8 2.468 151 14 2.468 151 26 3.937 151 16 4.409 151 27 3.327 152 30 5.122 152 63 5.122 152 61 5.122 152 1 5.122 152 32 1.000 152 33 1.000 152 7 2.468 152 2 1.000 152 22 1.000 152 17 4.796 152 35 5.405 152 47 3.327 152 37 5.122 152 4 2.468 152 5 1.000 152 18 1.000 152 8 1.000 152 43 4.796 152 12 6.080 152 25 4.409 152 26 5.122 152 9 1.000 152 65 5.122 152 38 1.000 152 46 5.122 152 39 5.122 152 27 6.264 152 52 4.796 152 53 4.796 152 16 3.327 152 24 5.122 152 64 5.405 152 42 6.080 152 29 5.405 152 60 5.122 152 36 4.409 153 1 3.327 153 32 1.000 153 21 1.000 153 22 2.468 153 8 1.000 153 4 1.000 153 5 1.000 153 7 2.468 153 23 2.468 153 57 4.796 153 9 1.000 153 10 1.000 153 12 5.878 153 25 4.796 153 38 1.000 153 18 1.000 153 15 1.000 153 24 5.122 153 42 7.548 153 29 5.122 153 60 4.409 154 5 2.468 154 1 3.327 154 32 3.327 154 7 3.327 154 34 3.327 154 2 2.468 154 6 1.000 154 22 6.264 154 8 2.468 154 4 2.468 154 9 2.468 154 11 1.000 154 25 8.205 154 15 3.327 154 36 7.819 154 27 8.059 154 40 7.548 154 52 7.732 154 28 6.080 154 16 4.796 154 24 7.732 154 42 7.902 154 18 3.327 155 33 6.434 155 2 4.796 155 22 5.122 155 7 5.655 155 8 3.327 155 11 1.000 155 12 5.122 155 25 1.000 155 14 3.327 155 26 5.878 155 18 6.264 156 19 5.405 156 33 6.264 156 26 5.655 156 62 1.000 156 21 3.327 156 4 1.000 156 5 5.655 156 23 5.655 156 11 5.122 156 12 3.937 156 13 6.080 156 44 2.468 156 15 7.002 156 40 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4.409 162 10 1.000 162 18 6.434 162 12 4.796 163 1 1.000 163 32 6.434 163 50 9.450 163 34 3.327 163 2 3.327 163 36 7.237 163 33 1.000 163 5 3.327 163 8 6.264 163 48 7.642 163 12 7.732 163 25 8.275 163 38 3.937 163 18 6.264 163 15 3.327 163 27 7.819 163 52 6.591 163 53 7.237 163 28 7.819 163 22 4.796 163 24 7.346 163 42 8.133 163 29 7.819 163 60 7.123 164 1 2.468 164 32 5.122 164 50 5.655 164 19 4.409 164 28 1.000 164 22 4.409 164 24 4.409 164 7 5.122 164 8 5.122 164 57 5.122 164 48 5.405 164 9 1.000 164 12 4.409 164 13 4.796 164 14 3.327 164 38 2.468 164 2 1.000 164 15 1.000 164 27 5.405 164 53 5.122 164 58 5.122 164 42 3.937 164 29 1.000 164 18 5.122 165 63 3.327 165 34 3.937 165 35 4.409 165 49 2.468 165 26 4.796 165 40 6.264 165 39 4.796 165 64 3.937 165 43 1.000 165 29 4.409 165 60 4.409 166 32 3.937 166 33 6.873 166 19 5.405 166 20 5.405 166 62 5.405 166 37 3.937 166 51 5.122 166 23 5.122 166 9 5.405 166 11 5.122 166 43 4.409 166 25 5.122 166 26 6.434 166 46 4.796 166 15 5.878 166 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41 1.000 5 1 1.000 5 20 2.468 5 28 1.000 5 21 5.122 5 16 4.409 5 37 5.122 5 23 1.000 5 48 1.000 5 26 1.000 5 39 3.327 5 27 2.468 5 40 1.000 5 29 1.000 6 26 3.327 6 33 1.000 6 46 4.796 6 21 1.000 6 34 1.000 6 49 4.409 6 3 4.409 6 17 3.937 6 43 3.327 6 39 4.409 6 27 3.937 6 40 4.409 6 24 4.409 6 29 1.000 6 47 4.409 7 18 1.000 7 1 3.327 7 32 4.409 7 50 6.264 7 2 1.000 7 26 3.327 7 37 5.405 7 17 4.796 7 6 3.327 7 7 5.122 7 8 3.327 7 51 3.327 7 48 4.796 7 12 4.796 7 25 3.937 7 14 6.873 7 38 1.000 7 39 5.122 7 36 5.122 7 27 5.122 7 52 5.122 7 41 3.937 7 28 4.796 7 45 4.796 7 16 2.468 7 22 1.000 7 24 4.409 7 42 5.122 7 29 5.122 7 47 4.796 8 25 5.122 8 1 4.796 8 32 4.409 8 22 4.796 8 27 4.409 8 34 4.409 8 37 5.122 8 51 4.409 8 5 4.409 8 49 4.796 8 8 4.796 8 44 1.000 8 11 4.409 8 26 4.409 8 38 2.468 8 52 4.409 8 28 4.409 8 42 4.409 8 29 5.122 8 17 3.937 9 25 2.468 9 26 3.937 9 1 2.468 9 53 5.405 9 19 1.000 9 8 5.405 9 4 5.405 9 3 5.405 9 5 5.122 9 7 4.796 9 18 1.000 9 12 5.878 9 13 6.080 9 14 2.468 9 9 5.655 9 38 1.000 9 2 3.327 9 15 1.000 9 52 5.655 9 28 3.937 9 45 5.655 9 22 1.000 9 24 6.080 9 10 1.000 10 1 1.000 10 32 5.405 10 33 1.000 10 54 1.000 10 19 4.796 10 20 1.000 10 34 3.937 10 2 5.405 10 22 5.405 10 35 5.122 10 37 5.655 10 5 4.409 10 49 3.327 10 7 4.796 10 8 5.405 10 11 4.409 10 12 5.405 10 26 4.796 10 10 3.937 10 38 1.000 10 46 4.409 10 27 1.000 10 24 5.122 10 42 5.405 10 29 3.937 10 18 2.468 11 36 1.000 11 50 2.468 11 33 5.122 11 6 3.937 11 23 1.000 11 21 3.937 11 55 1.000 11 56 1.000 11 57 2.468 11 48 2.468 11 26 3.937 11 44 3.327 11 53 4.409 11 41 3.937 11 45 1.000 11 58 2.468 11 16 2.468 11 39 4.409 11 42 3.327 11 59 1.000 12 5 3.327 12 35 4.796 12 1 3.937 12 31 5.878 12 32 5.655 12 52 1.000 12 50 4.409 12 19 4.409 12 41 2.468 12 22 2.468 12 37 6.434 12 7 3.327 12 11 1.000 12 12 1.000 12 10 3.327 12 44 2.468 12 15 1.000 12 53 3.937 12 28 4.409 12 45 4.796 12 39 5.122 12 42 5.122 12 60 2.468 12 18 3.327 12 36 5.122 13 4 3.937 13 6 3.937 13 7 3.327 13 51 4.409 13 12 1.000 13 34 1.000 13 29 4.409 13 44 1.000 13 38 1.000 13 39 3.327 13 52 4.409 13 53 2.468 13 41 3.327 13 28 3.327 13 60 4.796 13 18 6.264 14 33 6.264 14 19 1.000 14 20 3.327 14 22 4.796 14 35 4.796 14 4 5.405 14 3 2.468 14 8 5.655 14 51 5.122 14 11 4.409 14 12 4.409 14 25 1.000 14 13 4.796 14 14 6.434 14 46 6.264 14 27 8.649 14 28 3.327 14 45 1.000 14 24 6.591 15 30 5.122 15 61 6.080 15 31 5.655 15 32 2.468 15 33 6.737 15 62 4.796 15 21 1.000 15 63 5.655 15 34 1.000 15 35 4.796 15 8 1.000 15 37 3.327 15 23 5.122 15 13 4.409 15 26 4.409 15 10 2.468 15 44 3.327 15 47 5.405 15 46 5.878 15 40 5.405 15 45 2.468 15 64 5.122 15 65 5.122 15 18 3.327 16 25 4.796 16 33 3.327 16 19 2.468 16 20 5.122 16 2 1.000 16 4 4.409 16 23 4.409 16 11 3.327 16 13 4.796 16 26 3.937 16 9 4.409 16 28 3.937 16 3 2.468 16 24 5.122 16 10 1.000 17 1 2.468 17 32 6.264 17 33 6.080 17 19 1.000 17 20 6.264 17 49 3.937 17 2 4.796 17 22 5.878 17 17 5.655 17 5 6.080 17 7 6.080 17 8 6.264 17 51 6.080 17 23 3.937 17 12 6.434 17 25 5.655 17 13 6.264 17 14 6.080 17 18 7.346 17 15 6.434 17 27 6.591 17 52 6.080 17 28 6.080 17 24 6.737 17 29 3.937 17 10 1.000 18 25 7.002 18 26 6.873 18 1 5.122 18 32 7.902 18 33 4.796 18 6 1.000 18 62 1.000 18 7 7.123 18 2 8.867 18 22 6.873 18 17 1.000 18 49 1.000 18 8 7.450 18 10 1.000 18 12 7.450 18 13 7.123 18 38 2.468 18 18 8.205 18 42 4.409 19 30 4.409 19 32 5.655 19 62 1.000 19 34 3.327 19 22 4.409 19 35 3.327 19 37 3.937 19 31 1.000 19 49 3.327 19 7 3.937 19 12 4.796 19 25 3.327 19 14 3.327 19 26 4.796 19 44 1.000 19 18 3.937 19 27 3.937 19 40 2.468 19 28 1.000 19 45 2.468 19 39 3.327 20 66 3.937 20 31 3.327 20 32 3.327 20 50 1.000 20 41 1.000 20 34 3.327 20 5 3.327 20 54 4.409 20 67 3.937 20 23 4.409 20 48 4.409 20 9 3.327 20 26 3.327 20 44 1.000 20 38 4.409 20 39 2.468 20 36 3.937 20 40 6.080 20 53 3.327 20 16 4.409 20 68 3.327 20 42 3.327 20 29 1.000 20 18 1.000 21 43 1.000 21 1 4.796 21 31 5.655 21 32 8.342 21 46 1.000 21 62 6.264 21 34 3.937 21 2 5.122 21 22 7.450 21 35 5.655 21 37 8.205 21 49 3.937 21 7 5.405 21 8 7.902 21 12 6.080 21 60 5.122 21 38 3.327 21 39 3.937 21 36 5.122 21 52 4.409 21 53 4.796 21 42 3.937 21 18 8.649 22 63 3.937 22 62 1.000 22 6 7.450 22 49 5.878 22 54 1.000 22 38 1.000 22 36 5.122 22 42 6.080 22 17 3.937 23 31 1.000 23 33 5.655 23 20 3.327 23 21 4.409 23 6 3.937 23 51 4.796 23 23 3.327 23 10 1.000 23 11 4.409 23 12 1.000 23 13 1.000 23 14 4.796 23 26 6.591 23 27 7.002 23 40 7.237 23 16 1.000 23 24 3.327 23 39 3.327 24 40 6.080 24 30 5.405 24 63 5.405 24 61 5.122 24 1 3.327 24 49 6.080 24 35 3.327 24 16 4.409 24 37 1.000 24 6 2.468 24 23 3.937 24 44 1.000 24 26 5.122 24 38 3.327 24 39 5.122 24 36 6.591 24 52 6.264 24 53 4.796 24 41 5.122 24 45 3.327 24 22 1.000 24 64 5.122 24 42 5.122 25 32 2.468 25 38 1.000 25 33 6.737 25 27 5.655 25 7 2.468 25 2 1.000 25 22 2.468 25 17 4.796 25 1 2.468 25 24 5.405 25 8 1.000 25 23 3.327 25 43 1.000 25 12 5.878 25 26 3.327 25 44 1.000 25 11 1.000 25 39 1.000 25 36 4.409 25 40 6.264 25 52 1.000 25 28 5.122 25 45 2.468 25 16 2.468 25 42 5.405 25 29 5.122 25 60 5.405 25 18 1.000 26 1 1.000 26 15 2.468 26 2 1.000 26 22 2.468 26 32 2.468 26 36 3.937 26 8 1.000 26 5 1.000 26 7 1.000 26 18 1.000 26 25 4.796 26 52 1.000 26 38 1.000 26 28 3.937 26 42 5.405 26 47 1.000 27 30 7.548 27 63 7.002 27 61 7.002 27 31 5.655 27 19 1.000 27 34 2.468 27 2 1.000 27 22 2.468 27 37 4.409 27 4 2.468 27 36 3.937 27 10 2.468 27 32 2.468 27 49 2.468 27 35 6.434 27 5 1.000 27 69 5.405 27 54 2.468 27 67 5.405 27 48 2.468 27 66 5.405 27 29 5.405 27 52 1.000 27 45 2.468 27 58 3.327 27 16 3.327 27 60 6.873 27 33 6.264 27 23 3.327 27 62 1.000 27 21 1.000 27 44 1.000 27 7 1.000 27 57 2.468 27 43 5.405 27 12 5.655 27 38 1.000 27 46 5.405 27 39 5.405 27 27 5.405 27 40 5.405 27 28 6.080 27 24 5.878 27 64 7.002 27 65 7.346 27 18 1.000 27 15 2.468 27 8 1.000 27 56 5.405 27 9 2.468 27 42 5.655 27 25 6.873 27 17 4.796 28 33 2.468 28 27 1.000 28 34 1.000 28 17 5.122 28 7 4.409 28 8 5.655 28 43 4.409 28 12 3.937 28 15 1.000 28 22 3.937 28 10 1.000 28 18 7.237 29 50 4.796 29 62 1.000 29 17 2.468 29 35 3.327 29 37 3.327 29 23 3.937 29 48 5.122 29 43 2.468 29 44 1.000 29 38 2.468 29 46 3.937 29 39 5.122 29 45 3.327 29 58 3.937 30 31 4.409 30 32 1.000 30 33 7.123 30 19 2.468 30 21 1.000 30 15 2.468 30 2 1.000 30 22 1.000 30 26 2.468 30 60 5.405 30 4 1.000 30 5 5.122 30 17 4.409 30 7 2.468 30 23 1.000 30 43 5.122 30 25 5.122 30 9 1.000 30 18 1.000 30 46 8.059 30 27 7.237 30 28 4.409 30 10 1.000 30 65 3.327 30 12 4.409 31 25 5.122 31 19 3.937 31 20 5.122 31 62 5.655 31 4 5.122 31 5 5.122 31 51 5.122 31 23 5.878 31 11 5.122 31 13 5.122 31 27 5.405 31 3 4.796 31 15 5.122 31 24 5.655 32 35 4.796 32 30 5.405 32 63 5.878 32 61 5.405 32 1 2.468 32 38 1.000 32 60 3.327 32 34 1.000 32 2 1.000 32 36 4.409 32 37 5.122 32 4 2.468 32 6 1.000 32 7 2.468 32 18 1.000 32 43 5.122 32 64 5.122 32 47 5.655 32 41 4.796 32 16 1.000 32 22 2.468 32 39 5.405 32 42 5.655 32 29 4.796 32 65 5.405 33 59 4.796 33 33 4.409 33 6 4.409 33 20 5.405 33 62 1.000 33 45 2.468 33 65 4.409 33 56 4.796 33 35 4.796 33 37 5.655 33 51 4.796 33 23 5.405 33 69 5.122 33 48 3.327 33 11 4.796 33 43 4.796 33 68 4.796 33 18 5.655 33 39 5.405 33 52 1.000 33 16 3.327 33 70 4.796 34 1 2.468 34 32 1.000 34 13 1.000 34 33 3.937 34 49 2.468 34 2 1.000 34 22 1.000 34 36 2.468 34 5 2.468 34 7 4.409 34 18 3.937 34 8 4.409 34 12 5.405 34 25 3.937 34 15 1.000 34 38 3.327 34 28 3.327 34 42 3.327 35 30 4.409 35 63 3.327 35 61 3.327 35 1 4.409 35 32 5.405 35 62 4.409 35 34 3.937 35 2 4.409 35 65 3.327 35 22 5.878 35 17 4.796 35 37 4.409 35 6 4.796 35 49 5.122 35 7 4.409 35 8 3.937 35 67 4.409 35 51 2.468 35 69 4.409 35 57 3.937 35 48 3.937 35 12 5.405 35 26 1.000 35 29 5.655 35 44 2.468 35 38 2.468 35 39 1.000 35 52 5.122 35 53 5.655 35 41 4.409 35 58 3.937 35 16 1.000 35 64 3.327 35 42 5.405 35 18 4.796 35 36 4.796 36 32 1.000 36 33 7.123 36 19 1.000 36 34 1.000 36 2 1.000 36 22 1.000 36 17 4.796 36 35 5.655 36 8 1.000 36 4 1.000 36 3 1.000 36 5 1.000 36 7 1.000 36 18 1.000 36 23 1.000 36 9 1.000 36 10 1.000 36 12 6.591 36 25 5.878 36 52 1.000 36 15 2.468 36 27 6.591 36 28 5.122 36 16 4.796 36 24 6.434 36 42 5.655 36 29 6.591 37 1 2.468 37 38 1.000 37 62 2.468 37 34 1.000 37 2 1.000 37 22 1.000 37 32 2.468 37 5 1.000 37 15 2.468 37 49 2.468 37 7 2.468 37 8 1.000 37 51 2.468 37 9 1.000 37 11 1.000 37 12 4.409 37 14 2.468 37 18 1.000 37 52 4.409 37 53 3.327 37 41 2.468 37 42 4.409 37 29 4.409 37 27 5.878 38 25 1.000 38 63 1.000 38 61 1.000 38 31 1.000 38 50 1.000 38 13 1.000 38 30 1.000 38 69 1.000 38 23 1.000 38 34 1.000 38 22 1.000 38 17 3.937 38 35 1.000 38 37 1.000 38 3 1.000 38 49 1.000 38 7 1.000 38 54 1.000 38 9 1.000 38 11 2.468 38 42 1.000 38 38 1.000 38 46 3.327 38 39 2.468 38 40 6.873 38 28 1.000 38 16 3.327 38 64 1.000 38 65 1.000 38 59 1.000 38 70 2.468 39 30 4.796 39 63 4.796 39 61 4.796 39 41 2.468 39 34 4.796 39 22 3.327 39 35 3.937 39 37 4.409 39 18 4.796 39 7 3.937 39 16 1.000 39 60 1.000 39 47 3.327 39 39 3.937 39 45 1.000 39 64 4.796 39 42 2.468 39 43 4.409 39 29 5.655 39 65 4.796 40 26 4.796 40 33 6.080 40 19 1.000 40 17 4.796 40 35 2.468 40 36 1.000 40 37 6.264 40 4 1.000 40 3 2.468 40 25 3.937 40 34 1.000 40 14 1.000 40 28 3.937 40 24 5.405 40 29 5.122 40 27 2.468 41 1 5.122 41 32 4.796 41 62 5.122 41 37 5.122 41 14 6.873 41 5 2.468 41 6 1.000 41 7 1.000 41 38 1.000 41 43 5.405 41 27 4.796 41 52 3.937 41 60 3.937 41 18 1.000 41 17 3.937 42 40 5.405 42 19 1.000 42 33 1.000 42 20 1.000 42 21 1.000 42 26 4.796 42 35 3.327 42 4 2.468 42 3 1.000 42 51 1.000 42 23 2.468 42 9 1.000 42 43 1.000 42 25 1.000 42 14 1.000 42 46 3.937 42 15 4.409 42 39 4.796 42 27 1.000 42 28 1.000 42 60 1.000 43 32 5.405 43 33 2.468 43 41 1.000 43 34 1.000 43 22 5.655 43 37 5.878 43 4 5.405 43 8 3.937 43 11 1.000 43 66 4.409 43 13 3.327 43 26 5.405 43 29 5.405 43 44 1.000 43 18 7.123 43 2 1.000 43 24 2.468 43 42 5.878 43 27 3.327 44 30 4.409 44 61 5.122 44 34 1.000 44 17 4.409 44 37 5.122 44 3 5.655 44 7 2.468 44 26 3.327 44 38 1.000 44 46 4.409 44 40 4.409 44 42 3.937 44 65 4.796 44 47 1.000 44 18 3.327 44 36 1.000 44 12 4.796 45 30 1.000 45 1 5.405 45 33 6.737 45 34 5.122 45 2 3.937 45 22 5.878 45 4 4.409 45 8 2.468 45 5 3.937 45 15 2.468 45 35 4.796 45 29 3.937 45 42 3.327 45 32 1.000 45 7 3.937 45 51 4.409 45 12 4.409 45 46 5.655 45 18 5.655 45 38 2.468 45 17 3.937 46 30 4.409 46 62 4.409 46 35 4.409 46 54 1.000 46 51 4.409 46 26 4.796 46 46 4.409 46 18 4.409 46 40 6.737 46 45 4.409 46 16 4.409 46 39 4.409 47 4 3.937 47 33 1.000 47 28 1.000 47 34 2.468 47 22 1.000 47 37 5.655 47 6 2.468 47 51 3.327 47 23 1.000 47 69 3.937 47 39 1.000 47 12 1.000 47 66 4.409 47 13 2.468 47 26 4.409 47 29 1.000 47 24 3.937 47 10 2.468 47 60 2.468 48 1 5.655 48 32 3.327 48 40 3.937 48 7 3.937 48 8 3.937 48 23 3.327 48 10 2.468 48 11 1.000 48 13 1.000 48 14 1.000 48 26 6.264 48 27 8.342 48 52 2.468 48 24 7.002 48 39 7.123 49 1 1.000 49 33 6.080 49 19 1.000 49 20 3.937 49 35 4.409 49 32 4.796 49 5 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54 2 4.409 54 8 5.655 54 23 1.000 54 12 5.122 54 25 4.409 54 26 5.878 54 44 1.000 54 38 1.000 54 39 3.937 54 36 2.468 54 52 5.122 54 53 3.327 54 28 3.327 54 45 2.468 54 16 2.468 54 22 4.796 54 24 5.405 54 10 1.000 54 18 7.548 55 25 5.405 55 1 3.327 55 33 2.468 55 20 3.937 55 62 1.000 55 26 5.655 55 8 2.468 55 11 4.796 55 34 1.000 55 29 5.122 55 27 6.264 55 16 2.468 55 24 5.878 55 12 1.000 56 32 2.468 56 34 3.327 56 2 1.000 56 22 1.000 56 17 3.937 56 8 1.000 56 69 3.937 56 10 1.000 56 12 5.122 56 38 1.000 56 15 5.122 56 39 1.000 56 52 2.468 56 42 1.000 56 18 3.327 56 27 3.327 57 25 1.000 57 1 3.327 57 32 1.000 57 34 1.000 57 22 1.000 57 35 1.000 57 37 1.000 57 4 1.000 57 3 1.000 57 8 1.000 57 11 1.000 57 39 1.000 57 45 1.000 57 16 2.468 57 42 4.796 58 31 6.080 58 62 5.878 58 34 5.122 58 37 4.796 58 3 1.000 58 5 1.000 58 43 5.405 58 46 5.655 58 15 2.468 58 39 4.409 58 27 5.655 58 40 5.405 58 45 1.000 59 5 1.000 59 1 3.937 59 32 2.468 59 33 6.591 59 62 5.122 59 21 3.327 59 34 1.000 59 2 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43 4.409 61 42 6.591 61 12 7.002 61 25 6.434 61 60 6.737 61 47 6.264 61 38 3.937 61 18 1.000 61 39 7.002 61 27 6.264 61 40 6.591 61 52 7.002 61 53 6.591 61 28 5.655 61 45 1.000 61 16 5.655 61 22 1.000 61 24 5.878 61 68 2.468 61 64 6.737 61 29 6.434 61 65 6.264 61 36 6.591 61 59 2.468 62 32 3.937 62 33 4.409 62 19 1.000 62 28 1.000 62 62 5.122 62 34 2.468 62 22 2.468 62 35 2.468 62 4 1.000 62 49 1.000 62 8 2.468 62 51 2.468 62 23 1.000 62 11 1.000 62 12 3.937 62 29 5.122 62 7 1.000 62 18 3.327 62 2 1.000 62 5 2.468 62 15 1.000 62 27 6.080 62 53 2.468 62 24 3.937 63 30 4.409 63 63 3.937 63 61 4.409 63 1 3.937 63 32 1.000 63 22 1.000 63 34 5.405 63 2 1.000 63 47 5.405 63 8 1.000 63 18 2.468 63 4 1.000 63 3 4.409 63 49 2.468 63 23 2.468 63 26 3.937 63 44 1.000 63 38 1.000 63 39 5.405 63 36 5.405 63 40 3.937 63 52 5.122 63 45 1.000 63 64 4.409 63 65 4.409 64 30 4.409 64 61 3.327 64 1 3.937 64 33 6.080 64 34 2.468 64 22 2.468 64 37 5.405 64 5 5.122 64 44 1.000 64 31 4.796 64 49 3.327 64 18 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4.409 69 44 1.000 69 2 1.000 69 39 6.264 70 1 5.122 70 32 2.468 70 33 6.737 70 19 2.468 70 21 5.405 70 7 1.000 70 22 3.327 70 4 2.468 70 5 1.000 70 18 1.000 70 8 5.655 70 12 6.873 70 2 3.937 70 15 2.468 70 24 6.873 70 27 1.000 71 31 5.122 71 34 3.937 71 22 1.000 71 17 5.122 71 35 4.409 71 8 3.327 71 37 1.000 71 3 2.468 71 46 3.937 71 43 4.796 71 45 5.122 71 29 5.405 72 40 6.080 72 1 3.937 72 22 1.000 72 2 1.000 72 35 3.327 72 32 1.000 72 37 3.937 72 17 4.409 72 49 3.937 72 8 1.000 72 11 1.000 72 43 3.937 72 14 1.000 72 26 3.327 72 38 3.327 72 46 3.937 72 39 2.468 72 36 3.937 72 52 3.937 72 53 5.122 72 41 2.468 72 24 4.409 72 42 3.937 72 29 3.937 72 18 1.000 72 12 5.405 73 5 1.000 73 1 4.409 73 33 3.937 73 4 4.409 73 12 5.122 73 13 3.327 73 10 1.000 73 53 4.796 73 42 5.405 73 27 2.468 74 32 6.591 74 33 7.123 74 34 4.409 74 22 4.796 74 35 1.000 74 7 6.434 74 8 6.737 74 9 6.080 74 11 3.327 74 13 5.405 74 12 6.873 74 14 7.002 74 18 4.409 74 2 4.796 74 3 3.327 74 24 6.737 74 10 1.000 74 17 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85 7 1.000 85 8 5.405 85 12 1.000 85 24 1.000 86 25 3.937 86 30 3.327 86 63 3.327 86 61 3.327 86 50 5.405 86 33 6.264 86 20 4.409 86 34 5.122 86 65 3.327 86 35 3.327 86 26 3.937 86 37 6.264 86 51 4.409 86 23 3.327 86 57 3.937 86 9 3.327 86 11 3.327 86 66 4.796 86 13 3.327 86 14 3.327 86 29 3.327 86 41 3.937 86 28 4.409 86 45 1.000 86 15 4.409 86 58 3.937 86 39 3.327 86 64 3.327 87 30 5.655 87 61 5.122 87 1 4.796 87 53 4.409 87 33 6.264 87 49 5.655 87 34 4.409 87 2 5.122 87 35 4.796 87 8 5.405 87 32 5.122 87 51 5.878 87 4 4.796 87 26 5.655 87 12 5.405 87 25 4.796 87 38 5.405 87 39 5.122 87 40 4.796 87 22 5.405 87 24 4.409 87 42 4.409 87 18 3.937 87 36 5.122 88 66 7.002 88 32 5.655 88 50 5.655 88 54 5.655 88 21 5.878 88 16 5.655 88 56 5.655 88 37 6.264 88 6 5.655 88 49 7.237 88 23 5.655 88 51 5.655 88 69 7.346 88 57 5.655 88 9 5.655 88 68 5.655 88 25 5.655 88 13 5.655 88 14 5.655 88 26 6.080 88 38 5.878 88 52 5.655 88 53 5.655 88 28 5.655 88 3 5.655 88 42 5.878 88 60 5.655 88 47 6.434 88 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100 51 2.468 100 11 4.409 100 12 1.000 100 25 3.327 100 14 5.655 100 18 1.000 100 27 1.000 100 40 1.000 100 28 5.122 100 24 1.000 100 10 1.000 101 35 2.468 101 33 2.468 101 21 1.000 101 34 4.409 101 37 4.796 101 51 4.796 101 9 1.000 101 11 1.000 101 14 6.873 101 26 4.796 101 39 4.796 101 41 4.409 101 45 3.327 101 24 4.796 101 47 4.409 101 27 5.878 102 6 1.000 102 49 4.796 102 29 1.000 102 67 5.655 102 23 1.000 102 66 1.000 102 26 1.000 102 38 1.000 102 53 1.000 102 33 1.000 102 36 1.000 103 5 1.000 103 1 2.468 103 32 1.000 103 19 1.000 103 33 1.000 103 27 6.080 103 7 1.000 103 2 1.000 103 22 1.000 103 36 3.937 103 4 1.000 103 24 5.878 103 8 5.122 103 12 6.434 103 25 5.122 103 10 1.000 103 52 1.000 103 38 1.000 103 15 2.468 103 42 5.122 103 29 5.122 103 18 1.000 104 63 5.405 104 61 5.405 104 60 5.122 104 30 5.405 104 17 4.796 104 37 5.655 104 3 5.405 104 14 6.080 104 47 5.655 104 46 5.878 104 64 5.405 104 29 5.655 104 65 5.405 104 27 5.405 105 5 1.000 105 32 5.405 105 19 1.000 105 33 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5.122 108 13 5.405 108 14 6.080 108 26 5.122 108 38 1.000 108 18 2.468 108 15 5.405 108 27 7.237 108 52 5.122 108 53 4.796 108 22 2.468 108 24 6.264 108 42 5.122 109 32 3.327 109 33 4.409 109 19 2.468 109 34 1.000 109 2 3.327 109 22 2.468 109 17 1.000 109 5 2.468 109 23 2.468 109 7 3.937 109 9 3.327 109 10 1.000 109 11 2.468 109 12 5.122 109 25 5.405 109 15 3.327 109 28 3.327 109 16 2.468 109 24 7.346 109 27 7.237 110 32 5.878 110 33 2.468 110 19 1.000 110 20 3.327 110 28 1.000 110 35 1.000 110 4 6.737 110 5 4.796 110 8 3.937 110 25 6.434 110 13 6.434 110 14 4.409 110 15 5.878 110 27 5.655 110 40 4.409 110 16 2.468 110 24 7.123 111 1 4.796 111 53 2.468 111 34 3.937 111 37 5.122 111 49 4.409 111 12 5.122 111 44 1.000 111 38 2.468 111 39 3.327 111 45 2.468 111 42 5.122 111 29 4.796 111 36 1.000 112 34 2.468 112 17 4.409 112 35 5.405 112 4 5.655 112 51 5.122 112 11 1.000 112 14 5.655 112 27 5.655 112 16 5.655 112 46 3.937 112 24 6.080 112 10 3.937 113 21 1.000 113 31 3.327 113 50 5.655 113 62 1.000 113 22 4.409 113 17 4.409 113 6 1.000 113 57 2.468 113 12 1.000 113 26 4.796 113 44 1.000 113 39 3.937 113 36 1.000 113 41 4.409 113 45 4.409 113 16 2.468 113 29 4.409 114 25 1.000 114 50 3.327 114 33 6.264 114 19 2.468 114 62 2.468 114 2 1.000 114 22 3.937 114 17 1.000 114 58 5.122 114 37 3.327 114 4 3.937 114 51 2.468 114 23 1.000 114 69 3.937 114 57 5.405 114 48 5.655 114 9 2.468 114 11 2.468 114 12 4.796 114 66 3.937 114 13 1.000 114 14 2.468 114 26 4.796 114 18 3.937 114 15 1.000 114 27 3.327 114 28 3.327 114 24 4.409 114 29 3.937 114 10 1.000 115 26 1.000 115 63 4.409 115 61 4.409 115 62 5.405 115 30 4.409 115 34 3.937 115 17 4.409 115 35 4.796 115 37 3.937 115 51 4.796 115 9 2.468 115 43 4.409 115 29 4.409 115 52 4.409 115 65 4.796 115 18 3.937 115 46 4.796 115 8 1.000 115 22 3.937 115 64 4.409 115 10 1.000 115 60 4.409 116 32 5.405 116 53 4.409 116 50 6.080 116 34 1.000 116 2 4.409 116 62 3.937 116 49 1.000 116 7 4.796 116 51 1.000 116 48 5.122 116 9 3.937 116 12 5.405 116 38 4.796 116 36 4.409 116 52 5.122 116 58 1.000 116 22 5.405 116 65 3.937 116 18 4.409 117 35 1.000 117 53 1.000 117 22 2.468 117 34 7.902 117 55 5.405 117 56 5.655 117 37 1.000 117 32 2.468 117 23 1.000 117 49 5.878 117 8 1.000 117 54 5.405 117 57 6.264 117 48 5.655 117 43 5.122 117 38 1.000 117 39 3.937 117 52 5.878 117 41 1.000 117 58 5.122 117 68 4.796 117 42 8.133 117 59 5.122 118 1 2.468 118 31 5.122 118 32 5.655 118 33 3.937 118 34 1.000 118 22 5.122 118 17 5.122 118 37 6.264 118 5 5.405 118 25 4.796 118 13 5.405 118 38 1.000 118 39 5.405 118 52 5.122 118 53 5.405 118 28 4.409 118 42 5.655 118 29 5.655 118 10 1.000 118 60 5.122 118 12 1.000 119 40 1.000 119 30 1.000 119 63 1.000 119 1 1.000 119 33 1.000 119 62 1.000 119 21 1.000 119 55 1.000 119 56 2.468 119 37 1.000 119 6 1.000 119 51 1.000 119 23 2.468 119 69 2.468 119 9 1.000 119 64 1.000 119 66 1.000 119 13 2.468 119 26 1.000 119 47 1.000 119 39 1.000 119 61 1.000 119 41 1.000 119 28 1.000 119 16 1.000 119 68 1.000 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26 5.878 127 58 4.409 127 64 1.000 128 35 4.409 128 32 5.405 128 33 6.873 128 6 4.796 128 20 5.122 128 62 3.937 128 21 5.405 128 34 1.000 128 41 3.937 128 26 5.878 128 18 6.873 128 4 5.122 128 5 5.655 128 31 5.122 128 7 4.409 128 23 5.122 128 13 5.122 128 14 3.937 128 10 3.327 128 15 4.796 128 39 5.122 128 27 5.655 128 40 5.122 128 16 3.327 128 24 3.937 128 29 5.405 129 40 6.873 129 30 3.937 129 63 4.796 129 61 4.796 129 1 1.000 129 19 2.468 129 34 4.796 129 37 3.937 129 5 1.000 129 49 3.327 129 9 2.468 129 14 2.468 129 38 5.122 129 29 1.000 129 46 4.409 129 39 3.937 129 27 3.937 129 24 4.796 129 64 4.796 129 42 3.937 130 30 5.122 130 63 5.122 130 61 5.122 130 31 3.327 130 34 3.327 130 55 4.409 130 56 4.796 130 37 5.405 130 67 4.796 130 69 5.122 130 66 1.000 130 50 1.000 130 36 4.409 130 52 4.796 130 53 3.327 130 41 4.409 130 68 4.409 130 64 4.796 130 29 5.122 130 70 5.122 130 59 3.937 131 32 5.878 131 33 3.327 131 17 2.468 131 7 1.000 131 12 5.655 131 25 2.468 131 24 3.327 131 42 5.655 131 10 2.468 132 1 1.000 132 6 3.937 132 22 2.468 132 26 3.327 132 16 2.468 132 7 2.468 132 8 1.000 132 67 1.000 132 23 3.937 132 21 1.000 132 12 4.409 132 25 1.000 132 14 1.000 132 39 3.937 132 52 1.000 132 53 2.468 132 24 4.796 132 42 1.000 132 33 1.000 132 29 1.000 132 18 3.937 133 63 3.937 133 1 5.655 133 50 1.000 133 19 3.937 133 34 3.937 133 36 1.000 133 4 4.796 133 49 5.122 133 8 3.327 133 23 1.000 133 57 4.796 133 25 5.405 133 26 5.655 133 60 2.468 133 11 1.000 133 52 5.122 133 42 4.796 133 33 1.000 134 35 1.000 134 30 3.937 134 4 3.937 134 50 1.000 134 27 1.000 134 20 3.937 134 33 1.000 134 54 1.000 134 6 3.327 134 7 2.468 134 51 2.468 134 23 1.000 134 11 2.468 134 26 5.122 134 10 1.000 134 18 1.000 134 28 3.327 134 16 4.409 134 24 5.122 134 39 3.327 134 29 2.468 134 12 1.000 135 25 3.937 135 26 5.405 135 1 3.327 135 31 3.937 135 32 5.655 135 50 7.450 135 34 2.468 135 2 4.796 135 22 5.655 135 17 4.796 135 37 5.655 135 5 3.937 135 49 5.405 135 7 5.122 135 8 5.405 135 9 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139 11 3.327 140 33 6.591 140 19 4.796 140 20 5.122 140 62 5.122 140 17 4.796 140 35 4.796 140 51 1.000 140 4 4.796 140 3 5.122 140 7 4.796 140 9 4.796 140 11 2.468 140 12 4.796 140 25 5.405 140 13 5.122 140 14 5.122 140 26 5.122 140 18 5.405 140 27 5.122 140 40 6.737 140 28 5.122 140 16 5.122 140 29 4.796 140 10 1.000 141 1 1.000 141 33 6.264 141 19 3.937 141 20 4.409 141 8 6.080 141 7 5.655 141 26 3.327 141 23 5.405 141 9 4.409 141 11 5.122 141 12 3.327 141 15 3.327 141 28 4.796 141 16 3.327 141 22 5.405 141 24 6.080 141 10 1.000 141 17 5.878 142 30 3.937 142 63 3.937 142 61 3.937 142 1 3.937 142 31 5.405 142 32 5.405 142 33 6.434 142 62 5.122 142 34 3.937 142 22 5.122 142 35 4.796 142 37 5.878 142 51 5.122 142 3 5.122 142 5 5.405 142 49 5.122 142 8 5.878 142 54 5.122 142 11 4.409 142 26 5.405 142 10 1.000 142 19 3.327 142 38 2.468 142 18 5.878 142 39 5.122 142 40 6.080 142 52 5.405 142 28 5.405 142 29 5.405 142 53 4.409 142 64 3.937 142 42 5.122 142 65 3.937 142 27 3.937 143 30 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147 32 5.405 147 2 3.327 147 22 6.591 147 35 2.468 147 1 4.796 147 49 5.878 147 7 4.409 147 8 6.434 147 11 3.327 147 12 5.878 147 26 5.655 147 44 1.000 147 38 5.878 147 15 3.327 147 52 6.080 147 53 3.327 147 24 1.000 147 42 6.591 147 29 1.000 147 18 6.737 147 36 3.937 148 19 2.468 148 33 6.080 148 49 2.468 148 34 1.000 148 22 1.000 148 55 2.468 148 56 2.468 148 37 3.327 148 32 1.000 148 3 2.468 148 8 2.468 148 23 2.468 148 9 2.468 148 10 1.000 148 11 1.000 148 26 1.000 148 29 3.327 148 38 1.000 148 18 3.327 148 40 2.468 148 52 5.655 148 41 3.327 148 28 3.327 148 16 3.327 148 68 3.327 148 42 2.468 148 60 2.468 148 36 3.327 148 59 2.468 149 2 4.409 149 17 4.409 149 8 3.937 149 12 1.000 149 25 4.409 149 14 3.327 149 26 4.409 149 9 4.796 149 18 5.122 149 27 5.878 149 40 6.434 149 28 2.468 149 16 3.937 149 29 5.655 150 5 1.000 150 30 4.409 150 63 5.122 150 1 4.409 150 31 4.409 150 32 1.000 150 33 6.434 150 19 1.000 150 46 4.409 150 34 1.000 150 22 1.000 150 17 5.122 150 35 3.327 150 3 1.000 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29 7.002 157 2 1.000 157 46 5.655 157 15 6.873 157 39 3.937 157 27 5.122 157 52 6.873 157 16 3.937 157 24 3.937 157 64 4.409 157 42 7.450 157 33 3.327 157 10 2.468 158 30 3.937 158 63 3.937 158 61 3.937 158 34 3.327 158 37 6.737 158 29 3.937 158 32 3.937 158 35 5.122 158 6 1.000 158 45 5.122 158 60 1.000 158 62 1.000 158 51 1.000 158 43 5.122 158 39 3.937 158 40 5.878 158 41 1.000 158 64 4.409 158 47 1.000 159 32 5.405 159 8 1.000 159 62 4.796 159 34 2.468 159 35 1.000 159 37 4.796 159 43 2.468 159 26 5.405 159 44 1.000 159 39 4.409 159 16 3.937 159 65 2.468 159 18 1.000 160 1 2.468 160 15 2.468 160 36 3.937 160 67 1.000 160 42 4.796 160 60 2.468 160 23 3.937 160 7 3.937 160 18 4.409 160 55 2.468 160 56 3.937 160 17 4.796 160 33 6.591 160 20 2.468 160 22 4.796 160 37 5.405 160 70 3.327 160 59 2.468 160 50 4.796 160 21 3.327 160 49 2.468 160 54 3.327 160 68 2.468 160 32 4.409 160 12 6.080 160 46 4.409 160 39 4.796 160 25 3.327 160 31 1.000 160 34 2.468 160 2 2.468 160 8 4.409 160 19 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5.405 269 59 5.122 270 30 1.000 270 63 1.000 270 61 1.000 270 20 1.000 270 22 1.000 270 37 1.000 270 3 1.000 270 8 1.000 270 26 1.000 270 29 1.000 270 32 1.000 270 50 1.000 270 35 1.000 270 6 1.000 270 49 1.000 270 14 1.000 270 52 1.000 270 53 1.000 270 45 1.000 270 16 1.000 270 62 1.000 270 7 1.000 270 51 1.000 270 43 1.000 270 46 1.000 270 39 1.000 270 40 1.000 270 41 1.000 270 64 1.000 270 65 1.000 270 11 1.000 270 25 1.000 270 38 1.000 271 1 2.468 271 31 5.405 271 9 1.000 271 40 7.450 271 34 1.000 271 2 1.000 271 22 1.000 271 17 4.796 271 35 5.878 271 37 5.405 271 5 1.000 271 44 1.000 271 7 2.468 271 18 1.000 271 32 1.000 271 69 4.796 271 12 5.878 271 4 1.000 271 38 1.000 271 36 3.937 271 52 1.000 271 39 5.122 271 42 5.122 271 29 4.796 271 60 5.655 271 70 4.796 272 63 6.080 272 61 5.655 272 1 1.000 272 31 6.434 272 32 5.655 272 19 1.000 272 23 3.327 272 28 5.405 272 30 5.405 272 34 1.000 272 2 1.000 272 17 4.796 272 37 1.000 272 4 4.796 272 25 6.080 272 38 1.000 272 65 5.655 272 39 5.405 272 40 6.434 272 52 1.000 272 41 6.080 272 22 2.468 272 64 5.655 272 42 6.264 272 29 5.878 272 60 5.878 272 47 5.405 272 36 4.796 273 5 1.000 273 31 4.796 273 33 6.591 273 19 1.000 273 20 3.937 273 21 4.409 273 22 2.468 273 26 1.000 273 17 3.937 273 35 1.000 273 37 3.327 273 4 1.000 273 3 1.000 273 18 3.937 273 8 2.468 273 51 2.468 273 23 1.000 273 9 1.000 273 25 5.122 273 13 1.000 273 34 1.000 273 14 1.000 273 60 1.000 273 38 2.468 273 15 1.000 273 52 1.000 273 53 1.000 273 24 4.796 273 29 3.327 273 12 3.937 274 32 5.405 274 33 2.468 274 54 2.468 274 19 1.000 274 21 1.000 274 7 1.000 274 2 5.405 274 22 3.327 274 35 1.000 274 37 2.468 274 4 1.000 274 3 1.000 274 5 1.000 274 8 5.655 274 23 2.468 274 9 1.000 274 11 1.000 274 12 5.122 274 25 5.405 274 13 9.370 274 29 5.405 274 65 3.937 274 38 1.000 274 15 2.468 274 27 5.405 274 53 4.409 274 41 5.122 274 28 3.937 274 45 1.000 274 16 4.409 274 24 5.122 274 42 5.405 274 60 5.405 274 47 5.122 274 18 5.878 274 36 4.796 275 31 3.937 275 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296 35 3.937 296 37 5.122 296 51 5.655 296 5 2.468 296 7 1.000 296 18 1.000 296 23 2.468 296 9 1.000 296 12 5.122 296 25 5.122 296 13 1.000 296 26 3.937 296 38 1.000 296 60 3.937 296 15 1.000 296 52 1.000 296 28 4.796 296 16 3.327 296 24 5.122 296 42 5.122 296 29 5.405 296 36 5.122 297 7 1.000 297 32 2.468 297 38 2.468 297 1 2.468 297 33 5.122 297 2 2.468 297 22 2.468 297 8 8.059 297 37 6.873 297 4 2.468 297 49 7.002 297 36 6.873 297 52 6.873 297 53 6.873 297 24 6.737 297 42 7.002 297 29 6.737 297 18 1.000 298 30 4.796 298 63 4.796 298 61 4.409 298 20 1.000 298 34 3.327 298 26 2.468 298 17 3.937 298 35 3.327 298 55 4.796 298 56 4.796 298 6 2.468 298 49 3.327 298 51 2.468 298 9 1.000 298 14 3.327 298 44 1.000 298 47 2.468 298 46 3.327 298 27 3.937 298 40 2.468 298 41 2.468 298 45 1.000 298 39 3.327 298 3 1.000 298 64 4.796 298 43 3.937 298 65 4.796 299 25 1.000 299 30 5.122 299 63 5.122 299 61 5.122 299 33 6.264 299 20 1.000 299 4 5.405 299 49 1.000 299 8 1.000 299 12 6.080 299 14 1.000 299 24 7.237 299 64 5.122 299 29 5.122 299 10 1.000 299 65 5.122 299 27 5.655 300 66 3.937 300 63 4.796 300 61 4.796 300 33 6.737 300 20 3.327 300 30 4.796 300 34 1.000 300 26 1.000 300 17 4.796 300 35 4.796 300 37 5.405 300 31 4.409 300 7 1.000 300 62 1.000 300 8 1.000 300 54 2.468 300 11 3.327 300 14 1.000 300 29 5.405 300 65 4.796 300 46 5.122 300 27 5.405 300 40 6.264 300 41 4.796 300 28 3.327 300 22 1.000 300 64 4.796 300 60 5.122 300 70 5.405 30 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 ================================================ FILE: programming_assignments/mini_reco/testcase/output/output000.txt ================================================ 3 6 1 6 ================================================ FILE: programming_assignments/mini_reco/testcase/output/output001.txt ================================================ 50 49 35 6 48 25 21 30 15 42 26 41 28 3 30 42 28 20 3 26 31 15 30 35 41 19 28 31 35 40 25 21 29 28 41 15 30 25 14 41 45 1 35 20 25 41 11 40 3 30 15 41 29 47 44 45 35 20 11 14 24 6 12 35 50 25 20 11 6 15 20 15 33 31 28 24 30 25 35 41 14 24 40 46 20 25 35 11 38 15 50 50 25 35 6 20 15 28 20 33 6 28 30 29 50 25 11 33 20 29 30 38 25 49 48 35 1 20 28 25 42 30 1 44 15 45 20 35 3 25 24 28 41 30 42 14 44 41 1 45 30 25 1 42 28 26 41 50 35 6 24 1 46 45 25 28 30 26 46 41 29 28 20 31 26 29 36 44 6 15 25 20 28 50 31 50 25 35 28 33 30 6 28 25 3 41 14 24 4 35 25 20 28 3 14 21 35 15 28 19 26 21 42 14 11 20 28 35 12 21 ================================================ FILE: programming_assignments/mini_reco/testcase/output/output002.txt ================================================ 25 26 15 8 28 3 38 9 14 24 39 48 16 12 31 32 26 35 8 1 15 3 38 9 34 24 33 29 16 48 30 23 19 41 33 26 35 28 11 6 16 42 50 46 44 25 35 20 21 48 50 15 38 1 9 19 31 10 45 33 38 11 50 1 44 26 29 45 28 14 46 7 2 30 42 20 21 35 11 48 46 29 50 32 19 37 6 41 47 43 43 15 30 1 41 12 21 47 36 3 38 49 44 26 45 42 20 35 30 29 26 15 38 36 24 31 32 3 27 9 50 38 49 40 37 2 31 26 32 13 3 8 35 4 45 15 32 23 44 33 21 28 38 14 29 35 6 25 31 20 41 46 1 44 50 45 28 3 14 48 35 25 28 29 14 26 24 12 1 38 15 44 33 2 19 30 42 31 28 26 29 48 6 25 20 4 44 1 19 5 40 20 25 3 21 35 6 33 41 50 38 11 36 48 19 20 35 31 25 1 44 45 29 3 28 14 11 36 21 47 35 21 50 6 47 25 34 12 3 41 8 40 39 37 49 41 48 25 3 1 44 15 14 46 26 45 42 24 2 31 35 6 49 29 20 38 31 16 33 32 26 41 34 14 18 20 40 25 35 14 33 3 21 41 38 11 6 36 2 48 30 20 28 42 3 25 24 36 1 2 8 43 38 26 45 30 20 3 42 24 48 33 41 14 38 21 36 47 12 2 35 6 24 21 29 45 12 44 38 3 49 36 16 27 4 25 35 26 15 24 21 3 31 34 14 38 46 39 17 13 49 46 6 11 30 41 48 14 20 1 28 29 26 38 8 3 26 29 15 28 46 25 32 31 38 24 9 5 11 27 30 35 19 21 29 26 15 6 5 42 48 1 31 9 24 15 1 35 32 6 21 14 38 16 34 25 9 48 29 33 14 35 33 41 11 46 19 42 38 40 49 12 4 21 5 40 30 48 25 41 50 29 3 44 1 35 15 46 16 33 30 26 6 1 41 44 28 47 50 29 45 15 32 42 39 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33 41 30 14 1 44 41 21 42 3 45 36 ================================================ FILE: programming_assignments/mini_reco/testcase/output/output004.txt ================================================ 40 24 47 45 66 32 41 69 27 42 40 46 42 30 49 47 61 63 64 43 24 70 64 56 63 65 60 66 47 61 24 48 12 42 50 63 30 64 67 52 24 63 46 30 61 42 64 47 17 65 55 56 67 12 42 36 53 58 37 63 40 66 33 46 53 60 30 13 57 64 50 24 12 66 48 36 53 57 14 40 37 64 27 56 47 46 29 66 39 48 47 48 58 50 66 56 52 39 14 40 27 40 24 17 52 12 65 60 37 46 14 26 24 27 48 70 29 66 33 40 24 37 27 69 47 48 50 70 35 36 48 57 40 58 42 47 69 32 7 29 12 24 67 39 56 43 17 29 28 25 48 31 57 27 58 6 37 66 46 69 40 47 66 41 42 43 37 67 31 53 47 66 41 69 30 24 37 27 52 28 69 66 68 56 59 50 24 55 48 42 33 12 17 27 24 60 63 64 47 61 66 50 21 14 48 33 67 26 47 24 27 40 12 70 24 25 67 29 30 28 30 46 17 36 63 61 64 37 70 42 15 12 70 24 47 17 28 43 25 65 56 70 66 31 69 47 30 50 63 64 57 27 43 24 50 48 12 30 63 66 50 53 70 47 68 6 55 41 26 1 69 24 32 64 67 40 63 28 60 52 24 40 27 26 12 33 63 30 61 42 50 24 42 40 6 63 64 36 30 70 ================================================ FILE: programming_assignments/mini_reco/testcase/output/output005.txt ================================================ 55 66 17 40 52 12 48 46 36 70 60 57 53 42 30 27 40 12 60 42 17 63 70 30 43 24 61 56 69 64 40 50 57 69 48 30 37 47 64 63 60 28 61 35 65 12 24 40 66 39 42 43 67 70 56 28 31 53 35 51 58 47 48 50 27 66 36 64 56 70 30 25 31 46 60 48 57 58 30 32 70 66 69 43 27 29 31 40 39 42 24 69 42 30 63 70 65 64 66 46 31 33 61 36 67 40 37 46 66 48 58 64 29 56 70 41 17 36 50 43 40 42 47 29 46 50 41 13 36 14 43 8 60 31 65 68 56 69 59 66 42 47 12 41 29 30 61 63 64 36 70 27 40 24 52 25 31 60 35 6 47 26 30 57 69 69 42 40 37 12 26 67 70 36 29 63 30 43 33 64 24 27 33 40 66 48 58 42 46 14 53 60 43 63 28 40 30 42 46 47 61 63 64 65 36 56 31 60 70 43 12 24 42 40 53 39 36 31 66 25 27 67 70 69 47 37 27 66 24 8 42 56 26 13 57 60 25 14 21 41 12 27 40 33 24 17 26 30 63 60 36 61 46 1 70 24 50 48 40 27 58 70 36 66 26 6 56 47 64 30 27 12 17 46 24 36 42 43 67 25 53 60 11 58 31 40 50 30 48 47 42 60 31 37 26 61 43 65 20 41 12 24 42 40 27 47 63 58 37 64 43 26 60 48 61 27 24 12 33 40 50 70 14 66 26 35 53 32 43 58 24 40 63 30 64 33 61 66 65 70 60 31 25 13 14 12 24 40 46 65 56 36 42 27 67 47 17 69 55 53 12 27 40 24 17 30 33 63 65 61 26 60 64 43 25 37 66 33 50 27 48 57 69 24 25 67 14 36 41 31 48 12 40 52 39 66 24 29 61 63 65 42 32 46 7 12 46 66 58 36 17 42 37 56 70 43 25 48 47 60 12 66 65 56 36 43 17 47 67 31 53 35 52 26 55 12 42 27 24 40 65 17 25 46 39 43 28 35 13 47 ================================================ FILE: programming_assignments/mini_reco/testcase/output/output006.txt ================================================ 48 57 37 66 24 30 42 26 41 13 63 64 37 66 48 69 24 41 50 30 33 42 5 14 46 43 39 60 53 69 6 66 26 49 51 13 70 55 68 56 12 42 69 27 67 40 39 53 12 24 27 46 40 66 31 30 43 36 42 52 47 56 66 48 58 41 33 29 42 68 14 50 46 52 24 42 63 30 17 59 67 61 64 12 24 12 42 31 40 36 70 52 53 56 69 47 12 27 66 25 24 36 17 63 42 70 67 46 12 27 40 24 70 36 13 15 30 65 43 46 48 40 58 47 57 42 66 36 56 17 46 63 27 68 56 59 40 57 69 46 48 12 66 37 42 40 70 29 56 46 55 63 30 6 53 26 36 24 66 27 43 26 39 70 29 17 67 12 12 24 42 40 66 46 67 39 52 29 70 69 12 24 27 70 42 28 36 25 67 29 35 66 46 40 56 66 48 58 42 37 17 47 29 68 47 37 48 66 57 14 24 21 56 42 27 28 12 24 52 56 27 67 17 25 42 28 66 55 70 50 69 60 66 46 13 47 33 25 31 35 27 24 40 12 25 29 63 14 61 37 64 50 47 33 24 66 13 48 58 56 50 57 27 36 40 24 12 66 50 31 39 35 25 67 47 27 37 50 24 66 48 27 14 26 7 41 53 25 40 57 58 48 42 33 47 36 66 69 60 46 24 12 17 27 66 36 64 46 47 33 70 63 48 37 58 27 66 56 52 14 8 43 49 39 47 48 24 66 57 33 56 13 26 25 14 49 27 37 48 24 33 70 28 29 41 60 57 13 48 58 37 50 66 26 47 14 42 27 60 57 ================================================ FILE: publications/sigir2023-update-period/README.md ================================================ ## Summary We publish these real industry data sets across various domains from one of the largest web services companies in Korea. The dataset is crawled from the user-item interaction log at specific intervals. Each dataset is a sequence of matrices based on a specific period. The matrix is formed in [Matrix Market](https://math.nist.gov/MatrixMarket/formats.html) format. Training data and evaluation data are designed to form cycles, which is described as follows. If it is explained based on one interval, matrix data was created as logs for various periods of training data, and matrix data was created as evaluation data from data after the training data period. In the next section, training data includes the past evaluation data period, and in the current section, new evaluation data is generated with data after the training data period. In this way, a data set was generated as a matrix sequence of training and evaluation data at 8 intervals per cycle. ``` {A Service} ├── train-matrix │ ├── 0 │ ├── 1 │ ├── 2 ... │ └── 8 └── validation-matrix ├── 0 ├── 1 ├── 2 ... └── 8 ``` > Note that Each time period denotes one days other than Article domain. In Article domain, each time period denotes 4 hours. An interval contains a matrix with [Matrix Market](https://math.nist.gov/MatrixMarket/formats.html) format, and files containing user ID and item ID information. The actual pseudonymized id values in the `uid` and `iid` files are written to the lines corresponding to the id values of users and entries used in the Matrix Martix format. ``` {A Service/[train|validation]-matrix} └── {interval-index} ├── iid ├── main.mtx └── uid ``` > Please note that datasets are item click logs, not purchase information. Additionally, users/products are pseudonymized with random numbers to avoid restoration. ## Download Link Datasets are publicly available for download at [link: https://kko.to/data-sigir2023](https://kko.to/data-sigir2023) ## Citation To acknowledge use of the dataset in publications, please cite the following paper: Hyunsung Lee*, Sungwook Yoo*, Dongjun Lee, and Jaekwang Kim. **How Important is Periodic Model Update in Recommender Systems?** In Proceedings of the 46th International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR ’23), July 23–27, 2023, Taipei, Tai-wan. https://doi.org/10.1145/3539618.3591934 ## Article ### Description This dataset consists of click logs collected from the home feed of articles such as news and other kinds of web pages in South Korea. Please note that the time period for each interval in Article is 4 hours. This is because, in Article domain, old items become obsolete fast. ## Blog ### Description This dataset consists of click logs from a blog service. The logs contain click logs of recommended blog postings from users presented on the main page of the web page of the service. ## Comics ### Description This dataset consists of click logs from a comics service. New episodes of comics are uploaded mostly once a week. Different comics are updated on different weekdays. ## Commerce ### Description This domain is to buy gifts for other people in a social network service. Logs contain view logs of users to items. ## Statistics of Datasets The Average Data statistics of different domains over different time periods are as follows. We only include statistics of average values over training datasets and validation datasets. Dataset characteristics do not show abrupt changes in different time periods. |domain|log_type|users|items|interactions|sparsity| |---|-------|------|-----|------------|--------| |article|train|493.9K|14.2K|117.8M|0.2544| |article|validation| 193.2K |3.9K | 2.39M |0.3150| |blog| train| 54.5K| 164.5K | 515K | 0.0057| |blog|validation| 6.3K| 32.6K| 52K |0.0262| |comics|train| 279.2K| 1.65K| 2819K |0.6120| |comics|validation|77.6K| 1.6K| 471K |0.3796| |commerce |train| 779.1K| 278.9K |5560K| 0.0026| |commerce|validation|58.3K| 93.1K| 329K |0.0061| ## License This is a statement regarding the license to release the dataset. The following bullet points outline the terms and conditions of use: * Ownership: Kakao Corporation is the rightful owner of the dataset. Availability: The dataset is available for non-commercial use only. * User's responsibilities: The user is responsible for following all copyright and legal regulations when using the dataset. * Prior approval: If the dataset is being used for commercial purposes or being cited or redistributed, it requires approval from Kakao Corporation. * Accuracy: Kakao Corporation does not guarantee the accuracy, suitability, or validity of the dataset for any other purpose. * No warranties: Kakao Corporation provides no warranties or representations regarding the dataset, and the user may not indicate any endorsement from the company. * Limitation of liability: The user assumes all responsibility for using the dataset and is solely responsible for any consequences arising from its use. Kakao Corporation is exempted from liability for use. * The user must acknowledge the use of the data set in publications resulting from the use of the data set (see the citation information above).