{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Non-Zero Prior Mean for Gaussian Process Regression\n", "\n", "Often users simply use a GP prior with zero mean. The model formulation is simple and meets most use cases. However, it can be useful to set a non-zero prior mean. This notebook walks through the use of squidward to fit a Gaussian process with a non-zero prior mean. I intentionally use a very informative prior over the covariance of each GP below to highlight the difference between the informative prior mean and the zero prior mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Setting Up An Example Problem" ] }, { "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, validation\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 = 10\n", "\n", "# train data\n", "x_train = np.random.uniform(0,15,samples)\n", "noise = np.random.normal(0,250,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,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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\n", "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": "markdown", "metadata": {}, "source": [ "## Fit Model with Zero Mean" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "d = distance.Linear(0.0, 10**2, 10**2)\n", "kernel = kernel_base.Kernel(d, 'k1')\n", "model = gpr.GaussianProcessInversion(kernel=kernel, var_l=172**2, show_warnings=False)\n", "model.fit(x_train, y_train)\n", "\n", "# 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=(20,5))\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.plot(x_true,y_true,label='True Mean of Data Generating Distribution', c='y')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Fit Model with Non-Zero Mean" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def prior_mean(x):\n", " return 200.0*x\n", "\n", "d = distance.Linear(0.0, 10**2, 10**2)\n", "kernel = kernel_base.Kernel(d, 'k1')\n", "model = gpr.GaussianProcessInversion(kernel=kernel, prior_mean=prior_mean, var_l=172**2, show_warnings=False)\n", "model.fit(x_train, y_train)\n", "\n", "# 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=(20,5))\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.plot(x_true,y_true,label='True Mean of Data Generating Distribution', c='y')\n", "plt.legend()\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 }