├── GP_example.ipynb └── README.md /GP_example.ipynb: -------------------------------------------------------------------------------- 1 | { 2 | "cells": [ 3 | { 4 | "cell_type": "code", 5 | "execution_count": 1, 6 | "metadata": {}, 7 | "outputs": [ 8 | { 9 | "name": "stdout", 10 | "output_type": "stream", 11 | "text": [ 12 | "Populating the interactive namespace from numpy and matplotlib\n" 13 | ] 14 | }, 15 | { 16 | "data": { 17 | "image/png": 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A2/CLqSzqcRMDy6JZ6gfis4FjKfx8PTCP8p1T8ErqXhE5uDri+jhPk4NxbXZ2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\n+ZbpC4wznkGe5YWf5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18 | "text/plain": [ 19 | "" 20 | ] 21 | }, 22 | "metadata": {}, 23 | "output_type": "display_data" 24 | } 25 | ], 26 | "source": [ 27 | "import numpy as np\n", 28 | "from scipy.interpolate import spline\n", 29 | "from scipy.linalg import cho_solve\n", 30 | "from numpy.linalg import cholesky\n", 31 | "from itertools import cycle\n", 32 | "\n", 33 | "%pylab inline\n", 34 | "\n", 35 | "class SimpleGP():\n", 36 | " \"\"\" One dimensional Gaussian Process class. Uses\n", 37 | " squared exponential covariance form. \n", 38 | " \n", 39 | " parameters\n", 40 | " ----------\n", 41 | " width_scale : float, positive\n", 42 | " Same as sigma in (4) of post\n", 43 | "\n", 44 | " length_scale : float, positive\n", 45 | " Same as l in (4) of post\n", 46 | "\n", 47 | " noise : float\n", 48 | " Added to diagonal of covariance, useful for\n", 49 | " improving convergence\n", 50 | " \"\"\"\n", 51 | " def __init__(self, width_scale, length_scale, noise=10 ** (-6)):\n", 52 | " self.width_scale = width_scale\n", 53 | " self.length_scale = length_scale\n", 54 | " self.noise = noise\n", 55 | " \n", 56 | " def _exponential_cov(self, x1, x2):\n", 57 | " \"\"\"\n", 58 | " Return covariance matrix for two arrays,\n", 59 | " with i-j element = cov(x_1i, x_2j).\n", 60 | " \n", 61 | " parameters\n", 62 | " ----------\n", 63 | " x1, x2: np.array\n", 64 | " arrays containing x locations\n", 65 | " \"\"\"\n", 66 | " return (self.width_scale ** 2) * np.exp(\n", 67 | " - np.subtract.outer(x1, x2) ** 2 / (2 * self.length_scale ** 2))\n", 68 | "\n", 69 | " def fit(self, sample_x, sample_y, sample_s):\n", 70 | " \"\"\"\n", 71 | " Save for later use the Cholesky matrix \n", 72 | " associated with the inverse that appears\n", 73 | " in (5) of post. Also evaluate the weighted\n", 74 | " y vector that appears in that equation.\n", 75 | " \n", 76 | " parameters\n", 77 | " ----------\n", 78 | " sample_x : np.array\n", 79 | " locations where we have sampled\n", 80 | " \n", 81 | " sample_y : np.array\n", 82 | " y values observed at each sample location\n", 83 | " \n", 84 | " sample_s : np.array\n", 85 | " array of stds for each sample\n", 86 | " \"\"\"\n", 87 | " \n", 88 | " self.sample_x = np.array(sample_x)\n", 89 | " \n", 90 | " S = self._exponential_cov(sample_x, sample_x)\n", 91 | " d = np.diag(np.array(sample_s) ** 2 + self.noise)\n", 92 | " \n", 93 | " self.lower_cholesky = cholesky(S + d)\n", 94 | " self.weighted_sample_y = cho_solve(\n", 95 | " (self.lower_cholesky, True), sample_y)\n", 96 | "\n", 97 | " def interval(self, test_x):\n", 98 | " \"\"\"\n", 99 | " Obtain the one-sigam confidence interval\n", 100 | " for a set of test points\n", 101 | " \n", 102 | " parameters\n", 103 | " ----------\n", 104 | " test_x : np.array\n", 105 | " locations where we want to test\n", 106 | " \"\"\"\n", 107 | " test_x = np.array([test_x]).flatten()\n", 108 | " means, stds = [], []\n", 109 | " for row in test_x:\n", 110 | " S0 = self._exponential_cov(row, self.sample_x)\n", 111 | " v = cho_solve((self.lower_cholesky, True), S0)\n", 112 | " means.append(np.dot(S0, self.weighted_sample_y))\n", 113 | " stds.append(np.sqrt(self.width_scale ** 2 - np.dot(S0, v)))\n", 114 | " return means, stds\n", 115 | " \n", 116 | " def sample(self, test_x, samples=1):\n", 117 | " \"\"\"\n", 118 | " Obtain function samples from the posterior\n", 119 | " \n", 120 | " parameters\n", 121 | " ----------\n", 122 | " test_x : np.array\n", 123 | " locations where we want to test\n", 124 | " \n", 125 | " samples : int\n", 126 | " Number of samples to take\n", 127 | " \"\"\"\n", 128 | " S0 = self._exponential_cov(test_x, self.sample_x)\n", 129 | " # construct covariance matrix of sampled points.\n", 130 | " m = []\n", 131 | " for row in S0:\n", 132 | " m.append(cho_solve((self.lower_cholesky, True), row))\n", 133 | " cov = self._exponential_cov(test_x, test_x) - np.dot(S0, np.array(m).T)\n", 134 | " mean = np.dot(S0, self.weighted_sample_y)\n", 135 | " return np.random.multivariate_normal(mean, cov, samples)\n", 136 | "\n", 137 | " \n", 138 | "# Insert data here. \n", 139 | "sample_x = [0.5, 2, -2]\n", 140 | "sample_y = [2, 1.5, -0.5]\n", 141 | "sample_s = [0.01, 0.05, 0.125]\n", 142 | "\n", 143 | "WIDTH_SCALE = 1\n", 144 | "LENGTH_SCALE = 1\n", 145 | "SAMPLES = 8\n", 146 | "model = SimpleGP(WIDTH_SCALE, LENGTH_SCALE)\n", 147 | "model.fit(sample_x, sample_y, sample_s)\n", 148 | "\n", 149 | "test_x = np.arange(-5, 5, .1)\n", 150 | "means, stds = model.interval(test_x)\n", 151 | "samples = model.sample(test_x, SAMPLES)\n", 152 | "\n", 153 | "# plots here.\n", 154 | "fig, ax = plt.subplots(figsize=(12, 5))\n", 155 | "ax.set_ylim([-3, 3])\n", 156 | "ax.axis('off')\n", 157 | "\n", 158 | "colors = cycle(['g', 'b', 'k', 'y', 'c', 'r', 'm'])\n", 159 | "plt.errorbar(test_x, means, yerr=stds,\n", 160 | " ecolor='g', linewidth=1.5,\n", 161 | " elinewidth=0.5, alpha=0.75)\n", 162 | "\n", 163 | "for sample, c in zip(samples, colors): \n", 164 | " plt.plot(test_x, sample, c, linewidth=2.*np.random.rand(), alpha=0.5)" 165 | ] 166 | }, 167 | { 168 | "cell_type": "code", 169 | "execution_count": null, 170 | "metadata": { 171 | "collapsed": true 172 | }, 173 | "outputs": [], 174 | "source": [ 175 | " " 176 | ] 177 | } 178 | ], 179 | "metadata": { 180 | "kernelspec": { 181 | "display_name": "Python 2", 182 | "language": "python", 183 | "name": "python2" 184 | }, 185 | "language_info": { 186 | "codemirror_mode": { 187 | "name": "ipython", 188 | "version": 2 189 | }, 190 | "file_extension": ".py", 191 | "mimetype": "text/x-python", 192 | "name": "python", 193 | "nbconvert_exporter": "python", 194 | "pygments_lexer": "ipython2", 195 | "version": "2.7.10" 196 | } 197 | }, 198 | "nbformat": 4, 199 | "nbformat_minor": 2 200 | } 201 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # gaussian_processes 2 | --------------------------------------------------------------------------------