diff --git a/notebooks/book2/03/linreg_post_pred_plot.ipynb b/notebooks/book2/03/linreg_post_pred_plot.ipynb index 747f7d8b45b..4435033c403 100644 --- a/notebooks/book2/03/linreg_post_pred_plot.ipynb +++ b/notebooks/book2/03/linreg_post_pred_plot.ipynb @@ -2,14 +2,335 @@ "cells": [ { "cell_type": "markdown", - "id": "bd6e730c", + "id": "b90f2d09", "metadata": {}, "source": [ - "Source of this notebook is here: https://colab.research.google.com/github/probml/pyprobml/blob/master/notebooks/book1/11/linreg_post_pred_plot.ipynb" + "# Bayesian Linear regression vs Plugin approximation" ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b3f25d29", + "metadata": {}, + "outputs": [], + "source": [ + "import jax\n", + "import jax.numpy as jnp\n", + "import matplotlib.pyplot as plt\n", + "\n", + "try:\n", + " import probml_utils as pml\n", + "except ModuleNotFoundError:\n", + " %pip install -qq git+https://github.com/probml/probml-utils.git\n", + " import probml_utils as pml\n", + "from probml_utils import savefig, latexify, is_latexify_enabled\n", + "\n", + "try:\n", + " from sklearn.linear_model import Ridge\n", + "except ModuleNotFoundError:\n", + " %pip install -qq scikit-learn\n", + " from sklearn.linear_model import Ridge\n", + "from scipy.stats import multivariate_normal\n", + "import warnings\n", + "\n", + "warnings.filterwarnings(\"ignore\")\n", + "jax.config.update(\"jax_platform_name\", \"cpu\")" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "1c51adc2", + "metadata": {}, + "outputs": [], + "source": [ + "latexify(width_scale_factor=2)" + ] + }, + { + "cell_type": "markdown", + "id": "bcda670b", + "metadata": {}, + "source": [ + "## Generate Data" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "36cb139a", + "metadata": {}, + "outputs": [], + "source": [ + "polydeg = 2 # Degree of design matrix\n", + "alph = 0.001 # Alpha of ridge regression\n", + "num_samples = 10 # Number of sample coefficients to draw and use for prediction\n", + "visibility = 0.5 # Transparency of plotted lines - in case we wish to plot a bunch.\n", + "\n", + "\n", + "key = jax.random.PRNGKey(1)\n", + "xtrain = jnp.array([-3, -2, 0, 2, 3])\n", + "xtest = jnp.linspace(-7, 7, 141)\n", + "sigma2 = 25\n", + "\n", + "\n", + "def fun(x):\n", + " return 10 + x + x**2\n", + "\n", + "\n", + "ytrain = fun(xtrain) + jax.random.normal(key=key, shape=[xtrain.shape[0]]) * jnp.sqrt(sigma2)\n", + "ytest = fun(xtest) + jax.random.normal(key=key, shape=[xtest.shape[0]]) * jnp.sqrt(sigma2)\n", + "\n", + "\n", + "def reshape(x):\n", + " return jnp.asarray(x).reshape(-1, 1)\n", + "\n", + "\n", + "xtrain = reshape(xtrain)\n", + "xtest = reshape(xtest)\n", + "ytrain = reshape(ytrain)\n", + "ytest = reshape(ytest)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "31e83c85", + "metadata": {}, + "outputs": [], + "source": [ + "def poly_basis(x, deg):\n", + " # Expands a vector to a polynomial design matrix: from a constant to the deg-power\n", + " return jnp.column_stack([x**deg for deg in range(0, deg + 1)])" + ] + }, + { + "cell_type": "markdown", + "id": "0e3795e6", + "metadata": {}, + "source": [ + "## Train both models" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "efd707fc", + "metadata": {}, + "outputs": [], + "source": [ + "xtrainp = poly_basis(xtrain, polydeg)\n", + "xtestp = poly_basis(xtest, polydeg)\n", + "\n", + "# Declare and fit linear regression model\n", + "linreg = Ridge(alpha=alph, fit_intercept=False)\n", + "linreg.fit(xtrainp, ytrain)\n", + "\n", + "# Determine coefficient distribution\n", + "wmle = linreg.coef_.reshape(\n", + " -1,\n", + ") # Mean of coefficients\n", + "wcov = sigma2 * jnp.linalg.inv(\n", + " jnp.diag(jnp.array([alph] * (polydeg + 1))) + xtrainp.T.dot(xtrainp)\n", + ") # Covariance of coefficients\n", + "posterior_bayes = multivariate_normal(mean=wmle, cov=wcov)\n", + "samples = posterior_bayes.rvs(num_samples)\n", + "\n", + "# Sample predictions according to samples of coefficients\n", + "prediction_samples = xtestp.dot(samples.T)\n", + "\n", + "ypred_mle = linreg.predict(xtestp) # MLE prediction\n", + "noise_mle = jnp.var(ytrain - linreg.predict(xtrainp), ddof=(polydeg + 1)) # MLE noise estimation" + ] + }, + { + "cell_type": "markdown", + "id": "f0b12d48", + "metadata": {}, + "source": [ + "## Plotting" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "356af39a", + "metadata": {}, + "outputs": [], + "source": [ + "def make_plot(ypreds, save_name, title, lowerb=None, upperb=None):\n", + " # Function for creating and saving plots\n", + " fig, ax = plt.subplots()\n", + " if not is_latexify_enabled():\n", + " SCATTER_SIZE = 140\n", + " else:\n", + " SCATTER_SIZE = 40\n", + "\n", + " ax.scatter(xtrain, ytrain, s=SCATTER_SIZE, facecolors=\"none\", edgecolors=\"r\", label=\"training data\")\n", + "\n", + " errlogi = lowerb is not None or upperb is not None # Determines where we will be plotting error bars as well\n", + " if errlogi:\n", + " errspacing = [int(round(s)) for s in jnp.linspace(0, xtest.shape[0] - 1, 30)]\n", + " errspacing_reshaped = jnp.reshape(jnp.array(errspacing), (1, len(errspacing)))\n", + " yerr = [list(lowerb[jnp.array(errspacing)]), list(upperb[jnp.array(errspacing)])]\n", + " ax.errorbar(\n", + " xtest[errspacing_reshaped][0, :, :],\n", + " ypreds[jnp.array(errspacing), 0],\n", + " yerr=yerr,\n", + " linewidth=0.5,\n", + " label=\"prediction\",\n", + " )\n", + " ax.fill_between(xtest[:, 0], ypreds[:, 0] + lowerb, ypreds[:, 0] - upperb, alpha=0.3)\n", + " else:\n", + " for j in range(ypreds.shape[1]):\n", + " ax.plot(xtest, ypreds[:, j], color=\"k\", linewidth=1.0, label=\"prediction\", alpha=visibility)\n", + " if errlogi:\n", + " plt.legend(loc=9, prop={\"size\": 7})\n", + "\n", + " ax.set_xlabel(\"x\")\n", + " ax.set_ylabel(\"y\")\n", + " ax.spines[\"right\"].set_visible(False)\n", + " ax.spines[\"top\"].set_visible(False)\n", + " pml.savefig(save_name + \"_latexified\")" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "5bdfea72", + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/", + "height": 1000 + }, + "id": "5bdfea72", + "outputId": "7829e9e5-14f8-40fe-e656-90ecfcd3595c", + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# plot a\n", + "noisevec = jnp.array([jnp.sqrt(noise_mle)] * ypred_mle.shape[0])\n", + "make_plot(ypred_mle, \"linregPostPredPlugin\", \"Plugin approximation\", noisevec, noisevec)\n", + "\n", + "# plot b\n", + "postnoise = jnp.array([jnp.sqrt(sigma2 + xtestp[i, :].T.dot(wcov.dot(xtestp[i, :]))) for i in range(xtestp.shape[0])])\n", + "make_plot(ypred_mle, \"linregPostPredBayes\", \"Posterior predictive\", postnoise, postnoise)\n", + "\n", + "# plot c\n", + "make_plot(ypred_mle, \"linregPostPredSamplesPlugin\", \"functions sampled from plugin approximation to posterior\")\n", + "\n", + "# plot d\n", + "make_plot(prediction_samples, \"linregPostPredSamples\", \"functions sampled from posterior\")\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f2c4a80b", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "60f4cbed", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "03bfe079", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "285114ae", + "metadata": {}, + "outputs": [], + "source": [] } ], - "metadata": {}, + "metadata": { + "colab": { + "name": "linreg_post_pred_plot.ipynb", + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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": "3.7.13" + } + }, "nbformat": 4, "nbformat_minor": 5 }