{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "name": "BayesianRegression.ipynb", "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "SVOCZvFgNhn8" }, "source": [ "# Bayesian Regression\n", "\n", "Code implementing basic Bayesian regression (fixed basis) based on chapter 3of [Bishop's PRML](https://www.microsoft.com/en-us/research/people/cmbishop/prml-book/). \n", "\n", "(adapted from [https://github.com/amber-kshz/PRML](https://github.com/amber-kshz/PRML))" ] }, { "cell_type": "code", "metadata": { "id": "dBf6pRkcwHle" }, "source": [ "import numpy as np\n", "from scipy.optimize import minimize\n", "from matplotlib import pyplot as plt\n", "\n", "\n", "# Defining epsilon for limits\n", "eps = 1e-15\n", " \n", "# Configuring matplotlib\n", "import matplotlib.pyplot as plt\n", "plt.rcParams[\"figure.figsize\"] = (8,8)\n", "plt.rcParams['axes.labelsize'] = 14\n", "plt.rcParams['xtick.labelsize'] = 12\n", "plt.rcParams['ytick.labelsize'] = 12\n", "plt.rcParams['lines.linewidth'] = 3.0\n", "plt.style.use('dark_background')\n", "plt.rcParams[\"image.cmap\"] = 'Set3'\n", "\n", "# Fix np.random seed for replicability\n", "np.random.seed(0)" ], "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "y03A1fvItliD" }, "source": [ "## Generating ground truth data\n", "\n", "Sampling points from ground truth function with Gaussian noise" ] }, { "cell_type": "code", "metadata": { "id": "O8JGSyNzxCBF", "colab": { "base_uri": "https://localhost:8080/", "height": 613 }, "outputId": "5c37441c-4cf9-491f-d5fe-5022472f445a" }, "source": [ "def truef(x):\n", " return np.sin(2*x) + 2*np.cos(4*x) - 0.5*x\n", "\n", "x_min = -3\n", "x_max = 3\n", "\n", "N = 15\n", "X = np.random.uniform(x_min,x_max, N)\n", "\n", "beta_true = 4.0\n", "ep = np.sqrt(1.0/beta_true)*np.random.randn(N)\n", "t = truef(X) + ep\n", "\n", "# Generate grid for plotting\n", "Xcont = np.linspace(x_min,x_max,200) \n", "\n", "plt.figure(figsize=(12,10))\n", "plt.plot(X, t,'og', label='training data')\n", "plt.plot(Xcont, truef(Xcont), ':r',label='ground truth')\n", "plt.xlabel(r'$x$')\n", "plt.ylabel(r'$t$')\n", "plt.legend()\n", "plt.show()\n", "\n", "X = np.reshape(X,(len(X),1))\n", "Xtest = np.reshape(Xcont,(len(Xcont),1))" ], "execution_count": null, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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