{ "nbformat": 4, "nbformat_minor": 0, "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" }, "colab": { "name": "ch01_Introduction.ipynb", "provenance": [], "toc_visible": true, "include_colab_link": true } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "ceRmVgOq6XmY" }, "source": [ "# 1. Introduction" ] }, { "cell_type": "markdown", "metadata": { "id": "Wj_RTULpriir" }, "source": [ "\n", " \n", " \n", "
\n", " Run in Google Colab\n", "
" ] }, { "cell_type": "code", "metadata": { "id": "TMxmVuag7eyA", "outputId": "e7a14285-f2ef-4457-e802-f2f488679beb", "colab": { "base_uri": "https://localhost:8080/", "height": 34 } }, "source": [ "from google.colab import drive\n", "drive.mount('/content/drive')" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "Mounted at /content/drive\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "id": "F3rYRMAD6ynO" }, "source": [ "# You need to adjust the directory names below for your own account\n", "# e.g. you may elect to create ms-notebooks dir or not\n", "\n", "# Execute this cell once\n", "\n", "# 1. Download the repo and set it as the current directory\n", "%cd /content/drive/My Drive/Colab Notebooks/ml-notebooks\n", "!git clone https://github.com/pantelis/PRML\n", "%cd /content/drive/My Drive/Colab Notebooks/ml-notebooks/PRML\n", "\n", "# 2. install the project/module\n", "!python setup.py install\n", "\n" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "iv9ADzLqiNsU", "outputId": "4be99758-4704-43df-cfca-5b190e0f7043", "colab": { "base_uri": "https://localhost:8080/", "height": 34 } }, "source": [ "# 3. Add the project directory to the path\n", "%cd /content/drive/My Drive/Colab Notebooks/ml-notebooks/PRML\n", "import os, sys\n", "sys.path.append(os.getcwd())" ], "execution_count": null, "outputs": [ { "output_type": "stream", "text": [ "/content/drive/My Drive/Colab Notebooks/ml-notebooks/PRML\n" ], "name": "stdout" } ] }, { "cell_type": "code", "metadata": { "id": "qwxjFZSR_vuX" }, "source": [ "# Import seaborn\n", "import seaborn as sns\n", "\n", "# Apply the default theme\n", "sns.set_theme()\n" ], "execution_count": null, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "pxBLdL3r6XmZ" }, "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)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "TWjYKLNc6Xmd" }, "source": [ "## 1.1. Example: Polynomial Curve Fitting" ] }, { "cell_type": "markdown", "metadata": { "id": "6XPE-VC_-OYK" }, "source": [ "The cell below defines $p_{data}(y|x)$ and generates the $\\hat p_{data}(y|x)$" ] }, { "cell_type": "code", "metadata": { "id": "Tj4RTV3X6Xmd", "outputId": "0baceadf-7645-418a-c6eb-2a06134b4c00", "colab": { "base_uri": "https://localhost:8080/", "height": 285 } }, "source": [ "def create_toy_data(func, sample_size, std):\n", " x = np.linspace(0, 1, sample_size) # p(x)\n", " y = func(x) + np.random.normal(scale=std, size=x.shape) \n", " return x, y\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.xlabel('$x$')\n", "plt.ylabel('$y$')\n", "plt.show()" ], "execution_count": null, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "tags": [], "needs_background": "light" } } ] }, { "cell_type": "code", "metadata": { "scrolled": true, "id": "diJlsNGo6Xmg", "outputId": "f13b190d-24bd-4904-b9e7-fb3240dabe70", "colab": { "base_uri": "https://localhost:8080/", "height": 442 } }, "source": [ "plt.subplots(figsize=(20, 10))\n", "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=\"hypothesis\")\n", " plt.ylim(-1.5, 1.5)\n", " plt.annotate(\"M={}\".format(degree), xy=(-0.15, 1))\n", " plt.xlabel('$x$')\n", " plt.ylabel('$y$') \n", "plt.legend(bbox_to_anchor=(1.05, 0.64), loc=2, borderaxespad=0.)\n", "plt.show()" ], "execution_count": null, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "tags": [], "needs_background": "light" } } ] }, { "cell_type": "code", "metadata": { "id": "nfpg434z6Xmj", "outputId": "596e2af7-bb0c-4f96-dfcd-b5ab841107eb", "colab": { "base_uri": "https://localhost:8080/", "height": 285 } }, "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(\"model capacity (degree)\")\n", "plt.ylabel(\"RMSE\")\n", "plt.show()" ], "execution_count": null, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "tags": [], "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "PTOLlihm6Xml" }, "source": [ "#### Regularization" ] }, { "cell_type": "code", "metadata": { "id": "18aoGaUg6Xml", "outputId": "f144ee73-3e4c-4986-d1ac-2c9a61d9b337", "colab": { "base_uri": "https://localhost:8080/", "height": 289 } }, "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=\"hypothesis\")\n", "plt.ylim(-1.5, 1.5)\n", "plt.legend()\n", "plt.annotate(\"M=9\", xy=(-0.15, 1))\n", "plt.xlabel('$x$')\n", "plt.ylabel('$y$') \n", "plt.show()" ], "execution_count": null, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "tags": [], "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "kfmJy1-96Xmo" }, "source": [ "### 1.2.6 Bayesian curve fitting" ] }, { "cell_type": "code", "metadata": { "id": "GFCXxwiz6Xmo", "outputId": "85c564ea-96a2-4c9a-da36-b245f8dccfb2", "colab": { "base_uri": "https://localhost:8080/", "height": 289 } }, "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.xlabel('$x$')\n", "plt.ylabel('$y$') \n", "plt.legend(bbox_to_anchor=(1.05, 1.), loc=2, borderaxespad=0.)\n", "plt.show()" ], "execution_count": null, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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