{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Heteroscedastic Gaussian Process Regression\n", "\n", "## What Is Heteroscedastic GP Regression?\n", "\n", "Typically when doing Gaussian process regression it is assumed that the data noise (or \"likelihood\" variance) is constant across the feature space. This is called homoscedasticity. Sometimes this is a valid assumption and typical Gaussian process modeling packages are sufficient. \n", "\n", "However, sometimes the data noise varies across the feature space. One example that is often used in introductory statistics classes is that of predicting food expenditure based on income. Wealthy individuals sometimes buy cheaper food product and sometimes buy very expensive food products. Less wealthy individuals don't tend to buy very expensive food products because they are limited by their income. This results in an increase in variance in the target variable along the predictor. This is called heteroscedasticity.\n", "\n", "In this notebook we walk through a very simple example of fitting and using a heteroscedastic GP. For an example of fitting and using a homoscedastic GP see the regression example notebook." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example of 1D Heteroscedastic GP Regression" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# model with Squidward\n", "from squidward.kernels import distance, kernel_base\n", "from squidward import gpr\n", "\n", "# useful visualization functions\n", "import gp_viz\n", "\n", "# generate example data\n", "import numpy as np\n", "\n", "# plot example data\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "import warnings\n", "warnings.filterwarnings(\"ignore\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# generate noisy samples for dataset\n", "samples = 100\n", "\n", "# train data\n", "x_train = np.random.uniform(0,15,samples)\n", "noise = np.random.normal(0,250*x_train,samples)\n", "y_train = 200 * x_train + noise\n", "\n", "# test data\n", "x_test = np.random.uniform(0,15,samples)\n", "noise = np.random.normal(0,250*x_test,samples)\n", "y_test = 200 * x_test + noise\n", "\n", "# generate noiseless data to plot true mean\n", "x_true = np.linspace(0,15,1000)\n", "y_true = 200 * x_true" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# plot example dataset\n", "plt.figure(figsize=(20,5))\n", "plt.title('1D GP Regression Example Dataset')\n", "plt.scatter(x_train,y_train,label='Train Data', c='c')\n", "plt.scatter(x_test,y_test,label='Test Data', c='r')\n", "plt.plot(x_true,y_true,label='True Mean of Data Generating Distribution', c='k')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# first we define a model for our noise\n", "# here we know the function exactly\n", "# in practice this model would need to be learned/fit\n", "def likelihood_variance_fucntion(x):\n", " return (250*x)**2\n", "\n", "likelihood_variance = likelihood_variance_fucntion(x_train)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "# define the distance function used by the kernel\n", "d = distance.Linear(0.0, 1000**2, 1000**2)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# the kernel base class takes the distance measure of choice\n", "kernel = kernel_base.Kernel(d, 'k1')" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# the model is instantiated with the kernel\n", "model = gpr.GaussianProcessInversion(kernel=kernel, var_l=likelihood_variance, inv_method='solve', show_warnings=False)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "model.fit(x_train,y_train)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generate data to plot posterior of model\n", "x = np.linspace(0,15,100)\n", "\n", "# pull the parameters of the posterior distribution\n", "mean, var = model.posterior_predict(x)\n", "\n", "# plot posterior of model\n", "plt.figure(figsize=(20,10))\n", "plt.title(\"GP Posterior Distribution\")\n", "gp_viz.regression.plot_1d(x,mean,var[:,0])\n", "plt.scatter(x_train,y_train,label='Train Data', c='c')\n", "plt.scatter(x_test,y_test,label='Test Data', c='r')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One good test of fit for a GP model is comparing the posterior predictive to the actual data. Let's try that here." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, 15, 100)\n", "\n", "plt.figure(figsize=(20, 8))\n", "\n", "plt.subplot(121)\n", "plt.title(\"Posterior Predictive Samples\")\n", "\n", "for i in range(10):\n", "\n", " # draw a sample from the posterior\n", " posterior_sample = model.posterior_sample(x)\n", "\n", " # add likelihood noise \n", " liklihood_noise = likelihood_variance_fucntion(x)\n", " liklihood_noise = np.diag(liklihood_noise)\n", " posterior_predictive_sample = np.random.multivariate_normal(mean=posterior_sample, cov=liklihood_noise, size=1)\n", "\n", " plt.scatter(x, posterior_predictive_sample)\n", " \n", "plt.ylim(-15000, 15000)\n", " \n", "plt.subplot(122)\n", "plt.title('1D GP Regression Example Dataset')\n", "plt.scatter(x_train,y_train,label='Train Data', c='c')\n", "plt.scatter(x_test,y_test,label='Test Data', c='r')\n", "plt.ylim(-15000, 15000)\n", "plt.legend()\n", " \n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "squidward_env", "language": "python", "name": "squidward_env" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.8" } }, "nbformat": 4, "nbformat_minor": 2 }