Full Code of ctgk/PRML for AI

Repository: ctgk/PRML
Branch: main
Commit: b60a6853962d
Files: 184
Total size: 3.7 MB

Directory structure:
gitextract_qpn122o6/

├── .github/
│   ├── FUNDING.yml
│   └── workflows/
│       └── run-notebooks.yaml
├── .gitignore
├── .pre-commit-config.yaml
├── LICENSE
├── README.md
├── environment.yaml
├── notebooks/
│   ├── ch01_Introduction.ipynb
│   ├── ch02_Probability_Distributions.ipynb
│   ├── ch03_Linear_Models_for_Regression.ipynb
│   ├── ch04_Linear_Models_for_Classfication.ipynb
│   ├── ch05_Neural_Networks.ipynb
│   ├── ch06_Kernel_Methods.ipynb
│   ├── ch07_Sparse_Kernel_Machines.ipynb
│   ├── ch08_Graphical_Models.ipynb
│   ├── ch09_Mixture_Models_and_EM.ipynb
│   ├── ch10_Approximate_Inference.ipynb
│   ├── ch11_Sampling_Methods.ipynb
│   ├── ch12_Continuous_Latent_Variables.ipynb
│   └── ch13_Sequential_Data.ipynb
├── prml/
│   ├── __init__.py
│   ├── bayesnet/
│   │   ├── __init__.py
│   │   ├── discrete.py
│   │   ├── probability_function.py
│   │   └── random_variable.py
│   ├── clustering/
│   │   ├── __init__.py
│   │   └── k_means.py
│   ├── dimreduction/
│   │   ├── __init__.py
│   │   ├── autoencoder.py
│   │   ├── bayesian_pca.py
│   │   └── pca.py
│   ├── kernel/
│   │   ├── __init__.py
│   │   ├── gaussian_process_classifier.py
│   │   ├── gaussian_process_regressor.py
│   │   ├── kernel.py
│   │   ├── polynomial.py
│   │   ├── rbf.py
│   │   ├── relevance_vector_classifier.py
│   │   ├── relevance_vector_regressor.py
│   │   └── support_vector_classifier.py
│   ├── linear/
│   │   ├── __init__.py
│   │   ├── _bayesian_logistic_regression.py
│   │   ├── _bayesian_regression.py
│   │   ├── _classifier.py
│   │   ├── _empirical_bayes_regression.py
│   │   ├── _fishers_linear_discriminant.py
│   │   ├── _least_squares_classifier.py
│   │   ├── _linear_regression.py
│   │   ├── _logistic_regression.py
│   │   ├── _perceptron.py
│   │   ├── _regression.py
│   │   ├── _ridge_regression.py
│   │   ├── _softmax_regression.py
│   │   ├── _variational_linear_regression.py
│   │   └── _variational_logistic_regression.py
│   ├── markov/
│   │   ├── __init__.py
│   │   ├── categorical_hmm.py
│   │   ├── gaussian_hmm.py
│   │   ├── hmm.py
│   │   ├── kalman.py
│   │   ├── particle.py
│   │   └── state_space_model.py
│   ├── nn/
│   │   ├── __init__.py
│   │   ├── array/
│   │   │   ├── __init__.py
│   │   │   ├── array.py
│   │   │   ├── broadcast.py
│   │   │   ├── ones.py
│   │   │   ├── reshape.py
│   │   │   └── zeros.py
│   │   ├── config.py
│   │   ├── distribution/
│   │   │   ├── __init__.py
│   │   │   ├── bernoulli.py
│   │   │   ├── categorical.py
│   │   │   ├── distribution.py
│   │   │   └── gaussian.py
│   │   ├── function.py
│   │   ├── image/
│   │   │   ├── __init__.py
│   │   │   ├── convolve2d.py
│   │   │   ├── deconvolve2d.py
│   │   │   ├── max_pooling2d.py
│   │   │   └── util.py
│   │   ├── io/
│   │   │   ├── __init__.py
│   │   │   └── io.py
│   │   ├── loss/
│   │   │   ├── __init__.py
│   │   │   ├── kl.py
│   │   │   ├── sigmoid_cross_entropy.py
│   │   │   └── softmax_cross_entropy.py
│   │   ├── math/
│   │   │   ├── __init__.py
│   │   │   ├── add.py
│   │   │   ├── divide.py
│   │   │   ├── exp.py
│   │   │   ├── log.py
│   │   │   ├── matmul.py
│   │   │   ├── mean.py
│   │   │   ├── multiply.py
│   │   │   ├── negative.py
│   │   │   ├── power.py
│   │   │   ├── product.py
│   │   │   ├── sqrt.py
│   │   │   ├── square.py
│   │   │   ├── subtract.py
│   │   │   └── sum.py
│   │   ├── network.py
│   │   ├── nonlinear/
│   │   │   ├── __init__.py
│   │   │   ├── log_softmax.py
│   │   │   ├── logit.py
│   │   │   ├── relu.py
│   │   │   ├── sigmoid.py
│   │   │   ├── softmax.py
│   │   │   ├── softplus.py
│   │   │   └── tanh.py
│   │   ├── normalization/
│   │   │   ├── __init__.py
│   │   │   └── batch_normalization.py
│   │   ├── optimizer/
│   │   │   ├── __init__.py
│   │   │   ├── ada_delta.py
│   │   │   ├── ada_grad.py
│   │   │   ├── adam.py
│   │   │   ├── gradient.py
│   │   │   ├── momentum.py
│   │   │   ├── optimizer.py
│   │   │   └── rmsprop.py
│   │   ├── queue.py
│   │   └── random/
│   │       ├── __init__.py
│   │       ├── dropout.py
│   │       ├── normal.py
│   │       ├── random.py
│   │       └── uniform.py
│   ├── preprocess/
│   │   ├── __init__.py
│   │   ├── gaussian.py
│   │   ├── label_transformer.py
│   │   ├── polynomial.py
│   │   └── sigmoidal.py
│   ├── rv/
│   │   ├── __init__.py
│   │   ├── bernoulli.py
│   │   ├── bernoulli_mixture.py
│   │   ├── beta.py
│   │   ├── categorical.py
│   │   ├── dirichlet.py
│   │   ├── gamma.py
│   │   ├── gaussian.py
│   │   ├── multivariate_gaussian.py
│   │   ├── multivariate_gaussian_mixture.py
│   │   ├── rv.py
│   │   ├── students_t.py
│   │   ├── uniform.py
│   │   └── variational_gaussian_mixture.py
│   └── sampling/
│       ├── __init__.py
│       ├── metropolis.py
│       ├── metropolis_hastings.py
│       ├── rejection_sampling.py
│       └── sir.py
├── setup.cfg
├── setup.py
└── test/
    ├── __init__.py
    ├── test_bayesnet/
    │   ├── __init__.py
    │   └── test_discrete.py
    ├── test_linear/
    │   ├── __init__.py
    │   ├── test_bayesian_regression.py
    │   ├── test_linear_regression.py
    │   ├── test_logistic_regression.py
    │   └── test_ridge_regression.py
    └── test_nn/
        ├── __init__.py
        ├── test_backward.py
        ├── test_distribution/
        │   ├── __init__.py
        │   ├── test_bernoulli.py
        │   └── test_gaussian.py
        ├── test_image/
        │   ├── __init__.py
        │   ├── test_convolve2d.py
        │   ├── test_deconvolve2d.py
        │   └── test_max_pooling2d.py
        ├── test_loss/
        │   ├── __init__.py
        │   └── test_sigmoid_cross_entropy.py
        ├── test_math/
        │   ├── __init__.py
        │   ├── test_add.py
        │   ├── test_log.py
        │   ├── test_matmul.py
        │   ├── test_multiply.py
        │   └── test_negative.py
        ├── test_nonlinear/
        │   ├── __init__.py
        │   ├── test_log_softmax.py
        │   ├── test_sigmoid.py
        │   ├── test_softmax.py
        │   └── test_tanh.py
        └── test_random/
            └── __init__.py

================================================
FILE CONTENTS
================================================

================================================
FILE: .github/FUNDING.yml
================================================
# These are supported funding model platforms

github: ctgk # Replace with up to 4 GitHub Sponsors-enabled usernames e.g., [user1, user2]


================================================
FILE: .github/workflows/run-notebooks.yaml
================================================
# This workflow will install Python dependencies, run full checks defined in `.pre-commit-config.yaml` with a variety of Python versions
# For more information see: https://help.github.com/actions/language-and-framework-guides/using-python-with-github-actions

name: Jupyter Notebooks

on:
  push:
    branches: [ main, develop ]
  pull_request:
    branches: [ main, develop ]
  schedule:
    # run every month on 6th day
    - cron: '0 0 6 * *'

jobs:
  jupyter-notebooks:

    runs-on: ubuntu-latest
    strategy:
      matrix:
        python-version: ['3.9', '3.10', '3.11', '3.12']

    steps:
    - uses: actions/checkout@v2
    - name: Set up Python ${{ matrix.python-version }}
      uses: actions/setup-python@v2
      with:
        python-version: ${{ matrix.python-version }}
    - name: Upgrade pip
      run: python -m pip install --upgrade pip
    - name: Install packages
      run: pip install .[develop]
    - name: Run Jupyter notebooks
      run: for note in `ls notebooks/*.ipynb`; do jupyter nbconvert --to html --execute $note; if [ $? != 0 ]; then echo $note; exit 1; fi; done


================================================
FILE: .gitignore
================================================
# Byte-compiled / optimized / DLL files
__pycache__/
*.py[cod]
*$py.class

# C extensions
*.so

# Distribution / packaging
.Python
env/
build/
develop-eggs/
dist/
downloads/
eggs/
.eggs/
lib/
lib64/
parts/
sdist/
var/
*.egg-info/
.installed.cfg
*.egg

# 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/
.coverage
.coverage.*
.cache
nosetests.xml
coverage.xml
*,cover
.hypothesis/

# Translations
*.mo
*.pot

# Django stuff:
*.log
local_settings.py

# Flask stuff:
instance/
.webassets-cache

# Scrapy stuff:
.scrapy

# Sphinx documentation
docs/_build/

# PyBuilder
target/

# IPython Notebook
.ipynb_checkpoints

# pyenv
.python-version

# celery beat schedule file
celerybeat-schedule

# dotenv
.env

# virtualenv
venv/
ENV/

# Spyder project settings
.spyderproject

# Rope project settings
.ropeproject


# VSCode project settings
.vscode/


================================================
FILE: .pre-commit-config.yaml
================================================
# See https://pre-commit.com for more information
# See https://pre-commit.com/hooks.html for more hooks
repos:
-   repo: https://github.com/pre-commit/pre-commit-hooks
    rev: v3.2.0
    hooks:
    -   id: trailing-whitespace
    -   id: end-of-file-fixer
    -   id: check-yaml
    -   id: check-added-large-files
-   repo: local
    hooks:
    -   id: assert_ascii
        language: system
        name: Check file encoding
        entry: bash -c 'for file in "$@"; do file --mime-encoding $file | grep -q "ascii\|binary"; if [ $? != 0 ]; then echo $file; exit 1; fi; done' --
        types: [text]
    -   id: flake8
        name: Check Python format
        entry: flake8 --count --show-source --statistics
        language: system
        types: [python]
    -   id: unittest
        name: Run Python unittests
        language: system
        entry: python setup.py test
        pass_filenames: false


================================================
FILE: LICENSE
================================================
MIT License

Copyright (c) 2018 ctgk

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.


================================================
FILE: README.md
================================================
# PRML
Python codes implementing algorithms described in Bishop's book "Pattern Recognition and Machine Learning"

## Required Packages
- python 3
- numpy
- scipy
- jupyter (optional: to run jupyter notebooks)
- matplotlib (optional: to plot results in the notebooks)
- sklearn (optional: to fetch data)

## Notebooks

The notebooks in this repository can be viewed with nbviewer or other tools, or you can use [Amazon SageMaker Studio Lab](https://studiolab.sagemaker.aws/), a free computing environment on AWS (prior [registration with an email address](https://studiolab.sagemaker.aws/requestAccount) is required. Please refer to [this document](https://docs.aws.amazon.com/sagemaker/latest/dg/studio-lab-onboard.html) for usage).

From the table below, you can open the notebooks for each chapter in each of these environments.

|nbviewer|Amazon SageMaker Studio Lab|
|:-------|:--------------------------:|
|[ch1. Introduction](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch01_Introduction.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch01_Introduction.ipynb)|
|[ch2. Probability Distributions](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch02_Probability_Distributions.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch02_Probability_Distributions.ipynb)|
|[ch3. Linear Models for Regression](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch03_Linear_Models_for_Regression.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch03_Linear_Models_for_Regression.ipynb)|
|[ch4. Linear Models for Classification](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch04_Linear_Models_for_Classfication.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch04_Linear_Models_for_Classfication.ipynb)|
|[ch5. Neural Networks](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch05_Neural_Networks.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch05_Neural_Networks.ipynb)|
|[ch6. Kernel Methods](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch06_Kernel_Methods.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch06_Kernel_Methods.ipynb)|
|[ch7. Sparse Kernel Machines](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch07_Sparse_Kernel_Machines.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch07_Sparse_Kernel_Machines.ipynb)|
|[ch8. Graphical Models](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch08_Graphical_Models.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch08_Graphical_Models.ipynb)|
|[ch9. Mixture Models and EM](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch09_Mixture_Models_and_EM.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch09_Mixture_Models_and_EM.ipynb)|
|[ch10. Approximate Inference](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch10_Approximate_Inference.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch10_Approximate_Inference.ipynb)|
|[ch11. Sampling Methods](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch11_Sampling_Methods.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch11_Sampling_Methods.ipynb)|
|[ch12. Continuous Latent Variables](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch12_Continuous_Latent_Variables.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch12_Continuous_Latent_Variables.ipynb)|
|[ch13. Sequential Data](https://nbviewer.jupyter.org/github/ctgk/PRML/blob/main/notebooks/ch13_Sequential_Data.ipynb)|[![Open in SageMaker Studio Lab](https://studiolab.sagemaker.aws/studiolab.svg)](https://studiolab.sagemaker.aws/import/github/ctgk/PRML/blob/main/notebooks/ch13_Sequential_Data.ipynb)|

If you use the SageMaker Studio Lab, open a terminal and execute the following commands to install the required libraries.

```bash
conda env create -f environment.yaml  # might be optional
conda activate prml
python setup.py install
```


================================================
FILE: environment.yaml
================================================
# run: conda env create -n environment.yaml
#      conda activate prml
#      python setup.py install
name: prml
dependencies:
  - numpy
  - pandas
  - scipy
  - scikit-learn
  - matplotlib
  - ipykernel
  - ffmpeg


================================================
FILE: notebooks/ch01_Introduction.ipynb
================================================
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Introduction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from prml.preprocess import PolynomialFeature\n",
    "from prml.linear import (\n",
    "    LinearRegression,\n",
    "    RidgeRegression,\n",
    "    BayesianRegression\n",
    ")\n",
    "\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1. Example: Polynomial Curve Fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def create_toy_data(func, sample_size, std):\n",
    "    x = np.linspace(0, 1, sample_size)\n",
    "    t = func(x) + np.random.normal(scale=std, size=x.shape)\n",
    "    return x, t\n",
    "\n",
    "def func(x):\n",
    "    return np.sin(2 * np.pi * x)\n",
    "\n",
    "x_train, y_train = create_toy_data(func, 10, 0.25)\n",
    "x_test = np.linspace(0, 1, 100)\n",
    "y_test = func(x_test)\n",
    "\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", s=50, label=\"training data\")\n",
    "plt.plot(x_test, y_test, c=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i, degree in enumerate([0, 1, 3, 9]):\n",
    "    plt.subplot(2, 2, i + 1)\n",
    "    feature = PolynomialFeature(degree)\n",
    "    X_train = feature.transform(x_train)\n",
    "    X_test = feature.transform(x_test)\n",
    "\n",
    "    model = LinearRegression()\n",
    "    model.fit(X_train, y_train)\n",
    "    y = model.predict(X_test)\n",
    "\n",
    "    plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", s=50, label=\"training data\")\n",
    "    plt.plot(x_test, y_test, c=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "    plt.plot(x_test, y, c=\"r\", label=\"fitting\")\n",
    "    plt.ylim(-1.5, 1.5)\n",
    "    plt.annotate(\"M={}\".format(degree), xy=(-0.15, 1))\n",
    "plt.legend(bbox_to_anchor=(1.05, 0.64), loc=2, borderaxespad=0.)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def rmse(a, b):\n",
    "    return np.sqrt(np.mean(np.square(a - b)))\n",
    "\n",
    "training_errors = []\n",
    "test_errors = []\n",
    "\n",
    "for i in range(10):\n",
    "    feature = PolynomialFeature(i)\n",
    "    X_train = feature.transform(x_train)\n",
    "    X_test = feature.transform(x_test)\n",
    "\n",
    "    model = LinearRegression()\n",
    "    model.fit(X_train, y_train)\n",
    "    y = model.predict(X_test)\n",
    "    training_errors.append(rmse(model.predict(X_train), y_train))\n",
    "    test_errors.append(rmse(model.predict(X_test), y_test + np.random.normal(scale=0.25, size=len(y_test))))\n",
    "\n",
    "plt.plot(training_errors, 'o-', mfc=\"none\", mec=\"b\", ms=10, c=\"b\", label=\"Training\")\n",
    "plt.plot(test_errors, 'o-', mfc=\"none\", mec=\"r\", ms=10, c=\"r\", label=\"Test\")\n",
    "plt.legend()\n",
    "plt.xlabel(\"degree\")\n",
    "plt.ylabel(\"RMSE\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Regularization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "feature = PolynomialFeature(9)\n",
    "X_train = feature.transform(x_train)\n",
    "X_test = feature.transform(x_test)\n",
    "\n",
    "model = RidgeRegression(alpha=1e-3)\n",
    "model.fit(X_train, y_train)\n",
    "y = model.predict(X_test)\n",
    "\n",
    "y = model.predict(X_test)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", s=50, label=\"training data\")\n",
    "plt.plot(x_test, y_test, c=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.plot(x_test, y, c=\"r\", label=\"fitting\")\n",
    "plt.ylim(-1.5, 1.5)\n",
    "plt.legend()\n",
    "plt.annotate(\"M=9\", xy=(-0.15, 1))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2.6 Bayesian curve fitting"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = BayesianRegression(alpha=2e-3, beta=2)\n",
    "model.fit(X_train, y_train)\n",
    "\n",
    "y, y_err = model.predict(X_test, return_std=True)\n",
    "plt.scatter(x_train, y_train, facecolor=\"none\", edgecolor=\"b\", s=50, label=\"training data\")\n",
    "plt.plot(x_test, y_test, c=\"g\", label=\"$\\sin(2\\pi x)$\")\n",
    "plt.plot(x_test, y, c=\"r\", label=\"mean\")\n",
    "plt.fill_between(x_test, y - y_err, y + y_err, color=\"pink\", label=\"std.\", alpha=0.5)\n",
    "plt.xlim(-0.1, 1.1)\n",
    "plt.ylim(-1.5, 1.5)\n",
    "plt.annotate(\"M=9\", xy=(0.8, 1))\n",
    "plt.legend(bbox_to_anchor=(1.05, 1.), loc=2, borderaxespad=0.)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}


================================================
FILE: notebooks/ch02_Probability_Distributions.ipynb
================================================
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Probability Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "from prml.rv import (\n",
    "    Bernoulli,\n",
    "    Beta,\n",
    "    Categorical,\n",
    "    Dirichlet,\n",
    "    Gamma,\n",
    "    Gaussian,\n",
    "    MultivariateGaussian,\n",
    "    MultivariateGaussianMixture,\n",
    "    StudentsT,\n",
    "    Uniform\n",
    ")\n",
    "\n",
    "np.random.seed(1234)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Binary Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Bernoulli(\n",
      "    mu=0.75\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "model = Bernoulli()\n",
    "model.fit(np.array([0., 1., 1., 1.]))\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1.1 The beta distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(0, 1, 100)\n",
    "for i, [a, b] in enumerate([[0.1, 0.1], [1, 1], [2, 3], [8, 4]]):\n",
    "    plt.subplot(2, 2, i + 1)\n",
    "    beta = Beta(a, b)\n",
    "    plt.xlim(0, 1)\n",
    "    plt.ylim(0, 3)\n",
    "    plt.plot(x, beta.pdf(x))\n",
    "    plt.annotate(\"a={}\".format(a), (0.1, 2.5))\n",
    "    plt.annotate(\"b={}\".format(b), (0.1, 2.1))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta = Beta(2, 2)\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 2)\n",
    "plt.plot(x, beta.pdf(x))\n",
    "plt.annotate(\"prior\", (0.1, 1.5))\n",
    "\n",
    "model = Bernoulli(mu=beta)\n",
    "model.fit(np.array([1]))\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.xlim(0, 1)\n",
    "plt.ylim(0, 2)\n",
    "plt.plot(x, model.mu.pdf(x))\n",
    "plt.annotate(\"posterior\", (0.1, 1.5))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Maximum likelihood estimation\n",
      "10000 out of 10000 is 1\n",
      "Bayesian estimation\n",
      "6649 out of 10000 is 1\n"
     ]
    }
   ],
   "source": [
    "print(\"Maximum likelihood estimation\")\n",
    "model = Bernoulli()\n",
    "model.fit(np.array([1]))\n",
    "print(\"{} out of 10000 is 1\".format(model.draw(10000).sum()))\n",
    "\n",
    "print(\"Bayesian estimation\")\n",
    "model = Bernoulli(mu=Beta(1, 1))\n",
    "model.fit(np.array([1]))\n",
    "print(\"{} out of 10000 is 1\".format(model.draw(10000).sum()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Multinomial Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Categorical(\n",
      "    mu=[0.5  0.25 0.25]\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "model = Categorical()\n",
    "model.fit(np.array([[0, 1, 0], [1, 0, 0], [1, 0, 0], [0, 0, 1]]))\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2.1 The Dirichlet distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Categorical(\n",
      "    mu=Dirichlet(\n",
      "        alpha=[1. 1. 1.]\n",
      "    )\n",
      ")\n",
      "Categorical(\n",
      "    mu=Dirichlet(\n",
      "        alpha=[3. 2. 1.]\n",
      "    )\n",
      ")\n"
     ]
    }
   ],
   "source": [
    "mu = Dirichlet(alpha=np.ones(3))\n",
    "model = Categorical(mu=mu)\n",
    "print(model)\n",
    "\n",
    "model.fit(np.array([[1., 0., 0.], [1., 0., 0.], [0., 1., 0.]]))\n",
    "print(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 The Gaussian Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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