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Repository: probabilisticai/probai-2022
Branch: main
Commit: 7e64c1316e9f
Files: 12
Total size: 28.9 MB
Directory structure:
gitextract_qz6qchcq/
├── README.md
├── day_1/
│ └── 1_antonio/
│ └── probAI2022.ipynb
├── day_3/
│ └── 3_didrik/
│ ├── bnn.ipynb
│ ├── bnn_solution.ipynb
│ ├── realnvp.ipynb
│ └── realnvp_solution.ipynb
├── day_4/
│ ├── 4_cagatay/
│ │ └── ODE2VAE.ipynb
│ └── 4_henri/
│ └── elfitutorialprobAI2022.ipynb
└── day_5/
└── 5_yingzhen/
├── classification.ipynb
├── classification_solution.ipynb
├── regression.ipynb
└── regression_solution.ipynb
================================================
FILE CONTENTS
================================================
================================================
FILE: README.md
================================================
# ProbAI 2022
Materials of the Nordic Probabilistic AI School ([ProbAI](https://www.probabilistic.ai)) 2022.
## Lectures and Tutorials
* Day 1 (June 13):
- [[recording](https://youtu.be/qQsaJH-VRbM), [slides](day_1/1_luigi/day1-probai2022-luigi.pdf)] Luigi Acerbi - Opening of ProbAI 2022
- [[recording](https://youtu.be/i59_eqiw0K8), [slides](day_1/1_arto/IntroLectureKlami.pdf)] Arto Klami - Probabilistic AI: What is it?
- [[recording](https://youtu.be/2faAkcS8R0c), [slides](day_1/1_antonio/inference-probai.pdf), [materials](day_1/1_antonio)] Antonio Salmerón - Introduction to Probabilistic Models
- [[recording](https://youtu.be/X5-5ykQsuWQ), [materials and slides](https://github.com/PGM-Lab/2022-ProbAI)] Andrés R. Masegosa & Thomas D. Nielsen - Introduction to Probabilistic Programming
- [[recording](https://youtu.be/-GRdaXTRCko), [slides](day_1/1_elizaveta/elizaveta_probai2022.pdf), [materials](https://github.com/elizavetasemenova/ProbAI-2022)] Elizaveta Semenova - Bayesian Workflow
* Day 2 (June 14):
- [[recording](https://youtu.be/bvhCkDmWVQw), [materials](https://github.com/PGM-Lab/2022-ProbAI)] Andrés R. Masegosa, Helge Langseth & Thomas D. Nielsen - Variational Inference 1
- [[recording](https://youtu.be/5jyVatgCzr0), [materials](https://github.com/PGM-Lab/2022-ProbAI)] Andrés R. Masegosa, Helge Langseth & Thomas D. Nielsen - Variational Inference 2
- [~~recording~~, [materials](https://github.com/PGM-Lab/2022-ProbAI)] Andrés R. Masegosa, Helge Langseth & Thomas D. Nielsen - Variational Inference 3
* Day 3 (June 15):
- [[recording](https://youtu.be/wOxDHVVurIg), [slides](day_3/3_rianne/Deep%20Generative%20Models_helsinki_15_6-2022_cut.pdf)] Rianne van den Berg - Deep Generative Models
- [[recording](https://youtu.be/bu9WZ0RFG0U), [slides](day_3/3_didrik/nf_slides.pdf)], [[RealVNP task](day_3/3_didrik/realnvp.ipynb), [solution](day_3/3_didrik/realnvp_solution.ipynb)], [[BNNs task](day_3/3_didrik/bnn.ipynb), [solution](day_3/3_didrik/bnn_solution.ipynb)], [[Colab - RealVNP](https://colab.research.google.com/github/probabilisticai/probai-2022/blob/main/day_3/3_didrik/realnvp.ipynb)] Didrik Nielsen - Normalizing Flows
- [[recording](https://youtu.be/_80NmKf7H0k), [slides](day_3/3_arno/gps.pdf)] Arno Solin - Gaussian Processes
* Day 4 (June 16):
- [[recording](https://youtu.be/oh2X89rmMdQ), [materials](https://onedrive.live.com/?authkey=%21AJSvUQkSLNITlrU&id=9D9AFECB41FCA080%21271190&cid=9D9AFECB41FCA080), [notebook](day_4/4_cagatay/ODE2VAE.ipynb), [colab](https://drive.google.com/file/d/1PjwNLeLCUcam9BjeddwDRDSyTIdX2h6o/view?usp=sharing)] - Cagatay Yildiz - Neural ODEs
- [[recording](https://youtu.be/un7t9UIavRU), [slides](https://hpesonen.github.io/assets/presentations/pesonen_probAI2022_slides/index.html#0), [slides in pdf](day_4/4_henri/pesonen_probAI2022.pdf), [colab](https://colab.research.google.com/drive/1Dg9FZe07DJdGw5tZI5PIxNuAuszULsNP?usp=sharing), [notebook](day_4/4_henri/elfitutorialprobAI2022.ipynb)] - Henri Eerikki Pesonen - ELFI-tutorial
- [[recording](https://youtu.be/iDv1REzbRzg)] - Fani Deligianni - Human-Centric ML
* Day 5 (June 17):
- [[recording](https://youtu.be/cRzNWVjnD6I), [slides](day_5/5_yingzhen/ProbAI2022_vi_bnn_tutorial.pdf), [notes](day_5/5_yingzhen/notes.pdf)], [regression task: [colab](https://colab.research.google.com/drive/1jvJE-P0zye95ICSS5bG2qL35lpr63zxm?usp=sharing) / [notebook](day_5/5_yingzhen/regression.ipynb) / [solution](day_5/5_yingzhen/regression_solution.ipynb)], [classification task: [colab](https://colab.research.google.com/drive/1d-7S7bsu8XE7rYikg5wuRkHyHZo8Pn8v?usp=sharing) / [notebook](day_5/5_yingzhen/classification.ipynb) / [solution](day_5/5_yingzhen/classification_solution.ipynb)] Yingzhen Li - Bayesian Neural Networks - Hands-on tutorial
- [[recording](https://youtu.be/MoJVCc9QDf8), [slides](day_5/5_jose/slides_helsinki.pdf)] José Miguel Hernández–Lobato - Advanced Bayesian Neural Networks
- [[recording](https://youtu.be/L13EYwDec4w)] Luigi Acerbi - Closing of ProbAI 2022
================================================
FILE: day_1/1_antonio/probAI2022.ipynb
================================================
{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "probAI2022.ipynb",
"provenance": [],
"collapsed_sections": []
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "code",
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import math\n",
"import scipy.stats as stats\n",
"from sklearn.linear_model import LinearRegression\n"
],
"metadata": {
"id": "crndOuUQMEUi"
},
"execution_count": 1,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"# **Can simple linear regression be considered a ML method?**"
],
"metadata": {
"id": "893lv1PipFcG"
}
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"id": "_xJElH11Ko1j"
},
"outputs": [],
"source": [
"t = [2,4,6,10,100,500,1000]\n",
"rmse = [0]*len(t) \n",
"\n",
"x = np.random.uniform(-3,3,1000)\n",
"\n",
"y = 2*x + 3 + np.random.normal(0,2, 1000)\n"
]
},
{
"cell_type": "code",
"source": [
"\n",
"plt.figure(figsize=(15,10))\n",
"plt.scatter(x,y, s=5, color=\"grey\")\n",
"\n",
"co = [\"black\",\"red\",\"green\",\"blue\",\"yellow\",\"cyan\",\"brown\"]\n",
"\n",
"for i in range(0, len(t)):\n",
"\n",
"\n",
"\n",
" x_partial, y_partial = x[:t[i]].reshape(1, -1) ,y[:t[i]].reshape(1, -1)\n",
"\n",
"\n",
"\n",
" m = LinearRegression().fit(x_partial.T, y_partial.T)\n",
"\n",
" b = m.coef_[0][0] \n",
" a = m.intercept_[0]\n",
"\n",
" y_estimate = a + b * x\n",
" rmse[i] = math.sqrt(np.mean((y - y_estimate)**2))\n",
"\n",
" f = lambda xi : a + b*xi\n",
" if ((i==0) or (i==(len(t)-1))):\n",
" plt.plot([-3,3],[f(-3), f(3)], c = co[i],linewidth=5)\n",
" else:\n",
" plt.plot([-3,3],[f(-3), f(3)], c = co[i])\n",
"\n",
"\n",
"plt.show()\n",
"\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 592
},
"id": "uSdU_MeELNf2",
"outputId": "c99e04e7-748b-4d9d-e17e-deed929bad14"
},
"execution_count": 4,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"rmse"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "eLR8MmLjOx1G",
"outputId": "26ad82db-a0ff-47ae-e340-dd4d81cd2ac3"
},
"execution_count": 5,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[2.2659173638043635,\n",
" 1.9897077447865485,\n",
" 2.0499444428269564,\n",
" 2.16823631919792,\n",
" 1.955510871571366,\n",
" 1.950981441525572,\n",
" 1.950742126415348]"
]
},
"metadata": {},
"execution_count": 5
}
]
},
{
"cell_type": "code",
"source": [
"i=range(0,len(t))\n",
"plt.figure(figsize=(15,10))\n",
"plt.plot(i,rmse)\n",
"plt.show()"
],
"metadata": {
"id": "B13O6dAAPBOp",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 592
},
"outputId": "65c85ede-a2b7-4a61-d0b0-815389e500af"
},
"execution_count": 6,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"# **Conjugate analysis for a Beta-Binomial model**"
],
"metadata": {
"id": "vlkxfopGo7Bv"
}
},
{
"cell_type": "code",
"source": [
"data = np.random.binomial(1,0.4,1000)\n",
"x = np.linspace(0,1, 1000)\n",
"plt.figure(figsize=(15,10))\n",
"plt.plot(x, stats.beta.pdf(x,1,1))\n",
"\n",
"n=5\n",
"su = sum(data[1:n])\n",
"plt.plot(x, stats.beta.pdf(x,1+su,1+n-su),c=\"red\")\n",
"\n",
"n=10\n",
"su = sum(data[1:n])\n",
"plt.plot(x, stats.beta.pdf(x,1+su,1+n-su),c=\"blue\")\n",
"\n",
"n=50\n",
"su = sum(data[1:n])\n",
"plt.plot(x, stats.beta.pdf(x,1+su,1+n-su),c=\"green\")\n",
"\n",
"n=100\n",
"su = sum(data[1:n])\n",
"plt.plot(x, stats.beta.pdf(x,1+su,1+n-su),c=\"purple\")\n",
"\n",
"n=1000\n",
"su = sum(data[1:n])\n",
"plt.plot(x, stats.beta.pdf(x,1+su,1+n-su),c=\"brown\")\n",
"\n",
"\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 592
},
"id": "WkwnTPz46Pes",
"outputId": "1b398074-410f-46b9-e2d1-896dad29c03c"
},
"execution_count": 7,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
],
"image/png": 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\n"
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"# **Bayesian linear regression**"
],
"metadata": {
"id": "m1-iDOkE-jD_"
}
},
{
"cell_type": "code",
"source": [
"N = 5000\n",
"x = np.random.uniform(0,3,N)\n",
"y = 3*x + 1 + np.random.normal(0,1,N)"
],
"metadata": {
"id": "HiubYUtv-m2x"
},
"execution_count": 32,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"Now we define the prior on w0 to be a N(a0,b0), initially N(0,1)"
],
"metadata": {
"id": "RBt-0eCX_j8z"
}
},
{
"cell_type": "code",
"source": [
"a0 = 0\n",
"b0 = 1"
],
"metadata": {
"id": "01UzwIAt_rx0"
},
"execution_count": 33,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"The same for w1"
],
"metadata": {
"id": "FrjUa0pX_36N"
}
},
{
"cell_type": "code",
"source": [
"a1 = 0\n",
"b1 = 1"
],
"metadata": {
"id": "EC7NoG4u_55C"
},
"execution_count": 34,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"Sample size for each iteration: K"
],
"metadata": {
"id": "UWX9T-Ig__-3"
}
},
{
"cell_type": "code",
"source": [
"K = 1000\n",
"for i in range(0,N):\n",
" s_w0 = np.random.normal(a0,b0,K) \n",
" s_w1 = np.random.normal(a1,b1,K)\n",
" s_epsilon = np.random.normal(0,1,K)\n",
" var_yi = b0**2+b1**2*x[i]**2+1\n",
" \n",
" p = stats.norm.pdf(s_w0,a0,b0) * stats.norm.pdf(s_w1,a1,b1) * stats.norm.pdf(y[i],s_w0+s_w1*x[i]+s_epsilon,math.sqrt(var_yi))\n",
" p_star = stats.norm.pdf(s_w0,a0,b0) * stats.norm.pdf(s_w1,a1,b1)\n",
" weights = p / p_star\n",
" sum_weights = sum(weights)\n",
" \n",
" est_a0 = 1/sum_weights*sum(weights*s_w0)\n",
" est_b0 = 1/sum_weights*sum(weights*s_w0**2)\n",
" a0 = est_a0\n",
" b0 = math.sqrt(est_b0-est_a0**2)\n",
" \n",
" est_a1 = 1/sum_weights*sum(weights*s_w1)\n",
" est_b1 = 1/sum_weights*sum(weights*s_w1**2)\n",
" a1 = est_a1\n",
" b1 = math.sqrt(est_b1-est_a1**2)\n"
],
"metadata": {
"id": "ybOYwRuZACYz"
},
"execution_count": 35,
"outputs": []
},
{
"cell_type": "code",
"source": [
"plt.figure(figsize=(15,10))\n",
"plt.scatter(x,y, s=5, color=\"grey\")\n",
"f_exact = lambda xi : 1 + 3*xi\n",
"f_estimated = lambda xi : a0 + a1*xi\n",
"plt.plot([0,3],[f_exact(0), f_exact(3)], c = \"blue\")\n",
"plt.plot([0,3],[f_estimated(0), f_estimated(3)], c = \"red\")\n",
"m = LinearRegression().fit(x.reshape(1,-1).T,y.reshape(1,-1).T)\n",
"\n",
"b = m.coef_[0][0] \n",
"a = m.intercept_[0]\n",
"f_lr = lambda xi : a + b*xi\n",
"plt.plot([0,3],[f_lr(0), f_lr(3)], c = \"green\")\n",
"\n",
"plt.show()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 592
},
"id": "woPwIICWlptb",
"outputId": "49d15cf9-fb3a-41cc-a5d3-bfccbf3c92e7"
},
"execution_count": 31,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 1080x720 with 1 Axes>"
],
"image/png": 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
gitextract_qz6qchcq/
├── README.md
├── day_1/
│ └── 1_antonio/
│ └── probAI2022.ipynb
├── day_3/
│ └── 3_didrik/
│ ├── bnn.ipynb
│ ├── bnn_solution.ipynb
│ ├── realnvp.ipynb
│ └── realnvp_solution.ipynb
├── day_4/
│ ├── 4_cagatay/
│ │ └── ODE2VAE.ipynb
│ └── 4_henri/
│ └── elfitutorialprobAI2022.ipynb
└── day_5/
└── 5_yingzhen/
├── classification.ipynb
├── classification_solution.ipynb
├── regression.ipynb
└── regression_solution.ipynb
Condensed preview — 12 files, each showing path, character count, and a content snippet. Download the .json file or copy for the full structured content (4,125K chars).
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"path": "README.md",
"chars": 4044,
"preview": "# ProbAI 2022\n\nMaterials of the Nordic Probabilistic AI School ([ProbAI](https://www.probabilistic.ai)) 2022.\n\n## Lectur"
},
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"chars": 41738,
"preview": "{\n \"nbformat\": 4,\n \"nbformat_minor\": 0,\n \"metadata\": {\n \"colab\": {\n \"name\": \"ProbAI 2022 BNN Tutorial - class"
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"path": "day_5/5_yingzhen/regression_solution.ipynb",
"chars": 879161,
"preview": "{\n \"cells\": [\n {\n \"cell_type\": \"markdown\",\n \"metadata\": {\n \"id\": \"Z97rDy1VjK4I\"\n },\n \"source\": [\n \"# A Ha"
}
]
// ... and 1 more files (download for full content)
About this extraction
This page contains the full source code of the probabilisticai/probai-2022 GitHub repository, extracted and formatted as plain text for AI agents and large language models (LLMs). The extraction includes 12 files (28.9 MB), approximately 1.0M tokens. Use this with OpenClaw, Claude, ChatGPT, Cursor, Windsurf, or any other AI tool that accepts text input. You can copy the full output to your clipboard or download it as a .txt file.
Extracted by GitExtract — free GitHub repo to text converter for AI. Built by Nikandr Surkov.