{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 10. Approximate Inference" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.animation as animation\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "%matplotlib inline\n", "\n", "from prml.rv import VariationalGaussianMixture\n", "from prml.preprocess import PolynomialFeature\n", "from prml.linear import (\n", " VariationalLinearRegression,\n", " VariationalLogisticRegression\n", ")\n", "\n", "np.random.seed(1234)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 10.2 Illustration: Variational Mixture of Gaussians" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "x1 = np.random.normal(size=(100, 2))\n", "x1 += np.array([-5, -5])\n", "x2 = np.random.normal(size=(100, 2))\n", "x2 += np.array([5, -5])\n", "x3 = np.random.normal(size=(100, 2))\n", "x3 += np.array([0, 5])\n", "x_train = np.vstack((x1, x2, x3))\n", "\n", "x0, x1 = np.meshgrid(np.linspace(-10, 10, 100), np.linspace(-10, 10, 100))\n", "x = np.array([x0, x1]).reshape(2, -1).T" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vgmm = VariationalGaussianMixture(n_components=6)\n", "vgmm.fit(x_train)\n", "\n", "plt.scatter(x_train[:, 0], x_train[:, 1], c=vgmm.classify(x_train))\n", "plt.contour(x0, x1, vgmm.pdf(x).reshape(100, 100))\n", "plt.xlim(-10, 10)\n", "plt.ylim(-10, 10)\n", "plt.gca().set_aspect('equal', adjustable='box')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "vgmm = VariationalGaussianMixture(n_components=6)\n", "vgmm._init_params(x_train)\n", "params = np.hstack([param.flatten() for param in vgmm.get_params()])\n", "fig = plt.figure()\n", "colors = np.array([\"r\", \"orange\", \"y\", \"g\", \"b\", \"purple\"])\n", "frames = []\n", "for _ in range(100):\n", " plt.xlim(-10, 10)\n", " plt.ylim(-10, 10)\n", " plt.gca().set_aspect('equal', adjustable='box')\n", " r = vgmm._variational_expectation(x_train)\n", " imgs = [plt.scatter(x_train[:, 0], x_train[:, 1], c=colors[np.argmax(r, -1)])]\n", " for i in range(vgmm.n_components):\n", " if vgmm.component_size[i] > 1:\n", " imgs.append(plt.scatter(vgmm.mu[i, 0], vgmm.mu[i, 1], 100, colors[i], \"X\", lw=2, edgecolors=\"white\"))\n", " frames.append(imgs)\n", " vgmm._variational_maximization(x_train, r)\n", " new_params = np.hstack([param.flatten() for param in vgmm.get_params()])\n", " if np.allclose(new_params, params):\n", " break\n", " else:\n", " params = np.copy(new_params)\n", "plt.close()\n", "plt.rcParams['animation.html'] = 'html5'\n", "anim = animation.ArtistAnimation(fig, frames)\n", "anim" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 10.3 Variational Linear Regression" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "def create_toy_data(func, sample_size, std, domain=[0, 1]):\n", " x = np.linspace(domain[0], domain[1], sample_size)\n", " np.random.shuffle(x)\n", " t = func(x) + np.random.normal(scale=std, size=x.shape)\n", " return x, t\n", "\n", "def cubic(x):\n", " return x * (x - 5) * (x + 5)\n", "\n", "x_train, y_train = create_toy_data(cubic, 10, 10., [-5, 5])\n", "x = np.linspace(-5, 5, 100)\n", "y = cubic(x)\n", "\n", "feature = PolynomialFeature(degree=3)\n", "X_train = feature.transform(x_train)\n", "X = feature.transform(x)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vlr = VariationalLinearRegression(beta=0.01)\n", "vlr.fit(X_train, y_train)\n", "y_mean, y_std = vlr.predict(X, return_std=True)\n", "plt.scatter(x_train, y_train, s=100, facecolor=\"none\", edgecolor=\"b\")\n", "plt.plot(x, y, c=\"g\", label=\"$\\sin(2\\pi x)$\")\n", "plt.plot(x, y_mean, c=\"r\", label=\"prediction\") \n", "plt.fill_between(x, y_mean - y_std, y_mean + y_std, alpha=0.2, color=\"pink\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 10.6 Variational Logistic Regression" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "def create_toy_data(add_outliers=False, add_class=False):\n", " x0 = np.random.normal(size=50).reshape(-1, 2) - 3.\n", " x1 = np.random.normal(size=50).reshape(-1, 2) + 3.\n", " return np.concatenate([x0, x1]), np.concatenate([np.zeros(25), np.ones(25)]).astype(int)\n", "x_train, y_train = create_toy_data()\n", "x0, x1 = np.meshgrid(np.linspace(-7, 7, 100), np.linspace(-7, 7, 100))\n", "x = np.array([x0, x1]).reshape(2, -1).T\n", "feature = PolynomialFeature(degree=1)\n", "X_train = feature.transform(x_train)\n", "X = feature.transform(x)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vlr = VariationalLogisticRegression()\n", "vlr.fit(X_train, y_train)\n", "y = vlr.proba(X).reshape(100, 100)\n", "\n", "plt.scatter(x_train[:, 0], x_train[:, 1], c=y_train)\n", "plt.contourf(x0, x1, y, np.array([0., 0.01, 0.1, 0.25, 0.5, 0.75, 0.9, 0.99, 1.]), alpha=0.2)\n", "plt.colorbar()\n", "plt.xlim(-7, 7)\n", "plt.ylim(-7, 7)\n", "plt.gca().set_aspect('equal', adjustable='box')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "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": "3.11.7" } }, "nbformat": 4, "nbformat_minor": 4 }