{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Published at http://msdresearch.blogspot.com/2015/01/learn-about-gaussian-processes.html" ] }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ " Learning Gaussian Processes by Demonstration and Exhibition" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The purpose of this document is to help learn about Gaussian processes (GP) by showing relevant formulas in code and demonstrating their calculation. This document is based off of Nano de Freitas's [code](http://www.cs.ubc.ca/~nando/540-2013/lectures/gp.py). Unfortunately, I could not understand every detail of the code but I made an effort to annotate as best as I could understand.\n", "\n", "Read an introductory text before going over this document. Not much effort is made to explain the concepts. The canonical text for Gaussian processes seems to be [Gaussian Processes for Machine Learning](http://www.gaussianprocess.org/gpml/) by Carl Rasmussen.\n", "\n", "For completeness, I'm just going to say that a Gaussian process is a genalization of a Gaussian distribution where the mean, $m$, and covariance, $k$, are _functions_ (as opposed to vectors).\n", "\n", "$$ f \\sim \\mathcal{GP}(m(x),k(x,x'))$$\n", "\n", "However, 0 _prior_ mean is going to be assumed here." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from __future__ import division #why?\n", "import numpy as np\n", "import matplotlib.pyplot as pl\n", "%matplotlib inline\n", "\"\"\" This is code for simple GP regression. \n", "It assumes a zero mean GP Prior \"\"\";" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# This is the true unknown function we are trying to approximate\n", "f = lambda x: np.sin(0.9*x).flatten() #flatten makes it 1-D\n", "#f = lambda x: (0.25*(x**2)).flatten()\n", "np.random.seed(123) #comment out for a consistent experience" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Kernel Function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Squared exponential kernel\n", "\n", "$$ k(x,x') = \\exp\\left(-\\frac{1}{2\\theta}|x-x'|^2\\right) $$" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Define the kernel\n", "def kernel(x, xp):\n", " \"\"\" GP squared exponential kernel \"\"\"\n", " theta = 0.1\n", " sqdist = np.sum(x**2,1).reshape(-1,1) + np.sum(xp**2,1) - 2*np.dot(x, xp.T)\n", " return np.exp(-.5 * (1/theta) * sqdist)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "The NumPy code was written in such a way as to return a matrix for all pairs of $x$ and $x'$." ] }, { "cell_type": "code", "collapsed": false, "input": [ "kernel(np.array([[1],[2]]),np.array([[3],[2],[1]]))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 4, "text": [ "array([[ 2.06115362e-09, 6.73794700e-03, 1.00000000e+00],\n", " [ 6.73794700e-03, 1.00000000e+00, 6.73794700e-03]])" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "What's VERY cool is that the same code allows the calculation of inputs of arbitrary dimension!" ] }, { "cell_type": "code", "collapsed": false, "input": [ "kernel(np.array([[1,0,0],[2,0,0]]),np.array([[3,0,0],[2,0,0],[1,0,0]]))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 5, "text": [ "array([[ 2.06115362e-09, 6.73794700e-03, 1.00000000e+00],\n", " [ 6.73794700e-03, 1.00000000e+00, 6.73794700e-03]])" ] } ], "prompt_number": 5 }, { "cell_type": "markdown", "metadata": {}, "source": [ "By computing the squared distances as $x^2 + x'^2 - 2xx'$ we can use NumPy to vectorize quantities that will come in handy for creating a matrix. The code uses array broadcasting to create an ['outer addition'](http://docs.scipy.org/doc/numpy/user/basics.broadcasting.html) which creates an association between all pairs.\n", "\n", "The line of code calculating `sqdist` is clever but difficult to decipher! It would have been clearer to write loops for its calculation using [Numba](http://numba.pydata.org/) when speed is an issue. " ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Computation of a Gaussian Process" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assuming a 0 mean prior, We write the joint distribution of the training and test (star) values as (following Rasmussen)\n", "\n", "$\n", "\\left[ \\begin{array}{c} {\\bf y} \\\\ {\\bf f_{*}} \\end{array} \\right] \n", "\\sim \n", "\\mathcal{N}\\left( {\\bf 0} , \\left[\\begin{array}{cc}\n", " K(X,X)+\\sigma_n I & K(X,X_*) \\\\\n", " K(X_*,X) & K(X_*,X_*)\n", " \\end{array}\n", " \\right]\n", " \\right)\n", "$(Eqn. 2.2 in Rasmussen)\n", "\n", "\n", "\n", "Primarily we want to compute mean values at our 'test' points given data.\n", "\n", "$ {\\bf\\bar{f_*}} = K(X_*,X)[K(X,X)+\\sigma_n^2I]^{-1}{\\bf y} $ (2.23)\n", "\n", "The covariance matrix allows us to draw samples from the distribution.\n", "\n", "$ \\text{cov}\\left({\\bf{f_*}}\\right) = K(X_*,X_*) - K(X_*,X)[K(X,X)+\\sigma_n^2I]^{-1}K(X,X_*) $ (2.24)\n", "\n", "Here is the correspondence between the math symbols and code variables. Keep in mind the $K$'s are matrices.\n", ". | code | shorthand |\n", "------------|-----------------|-----------|\n", "$K(X,X)$ | `K` | $K$ \n", "$K(X_*,X)$ | `Kstar` | $K_*$ \n", "$K(X_*,X_*)$| `Kstarstar` | $K_{**}$ \n", "$\\sigma_n$ | `s` |\n", "${\\bf{\\bar{f_*}}}$| `mu`| " ] }, { "cell_type": "code", "collapsed": false, "input": [ "n = 10 # number of training points.\n", "N = 200 # number of test points. (star)\n", "s = 0.05 # noise variance." ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "# Sample some input points and noisy versions of the function evaluated at\n", "# these points. \n", "X = np.random.uniform(-5, 5, size=(n,1)) # \"training\"\n", "y = f(X) + s*np.random.randn(n)\n", "\n", "K = kernel(X, X)\n", "# points we're going to make predictions at.\n", "Xtest = np.linspace(-5, 5, N ).reshape(-1,1)\n", "Ktest = kernel(X, Xtest)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 7 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Computing Mean and Variance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you see an inverted matrix in a text, it's probably a good idea [not to invert](http://www.johndcook.com/blog/2010/01/19/dont-invert-that-matrix/) it when implementing your calculations. You want to use some kind of matrix factorization. Here, a [Cholesky decomposition](http://en.wikipedia.org/wiki/Cholesky_decomposition) helps us calculate the mean vector and covariance matrix as well as draw samples from prior and posterior distributions.\n", "\n", "If we use Cholesky decomposition to factor $K_{**}$ as $LL^T$, we can write the mean as\n", "\n", "$ {\\bf\\bar{f_*}} = K_{*}^TK{\\bf y} = (K_*^{T} L^{-T}) (L^{-1} {\\bf y}) = u v $," ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "where $v$ in the linear system, $Lv={\\bf y}$, can be solved for (matrix inversion was avoided). Similary (as it seems in the code), $u$ can be solved for in $L^Tu=K_*^T$. Unfortunately, I'm not seeing the exact correspondence in the code.\n", "But another way to calculate the mean is to calculate $L^{-T}(L^{-1}{\\bf y})=L^{-T}v=w$ where $w$ is solved for in the linear system $L^Tw=v$.\n", "\n", "The (individual) variances are obtained by taking the diagonal of some covariance matrix. Again, I could not decipher the code (thank you NumPy!)." ] }, { "cell_type": "code", "collapsed": false, "input": [ "L = np.linalg.cholesky(K + s*np.eye(n)) # i(eye)dentity added...\n", "#...for numerical stabilization\n", "\n", "# compute the mean at our test points.\n", "u = np.linalg.solve(L, Ktest) # = something like LKstar\n", "v=np.linalg.solve(L, y)\n", "mu=np.dot(u.T, v)\n", "#another way to calculate is commented out\n", "#w=np.linalg.solve(L.T,v)\n", "#mu = np.dot( Ktest.T , w )\n", "\n", "# compute the variance at our test points.\n", "Kstarstar = kernel(Xtest, Xtest)\n", "s2 = np.diag(Kstarstar) - np.sum(u**2, axis=0) #I don't know how this works!\n", "ss = np.sqrt(s2)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "# PLOTS:\n", "import seaborn as sns\n", "pl.figure(1)\n", "pl.clf()\n", "\n", "pl.gca().fill_between(Xtest.flat, mu-2*ss, mu+2*ss, color=\"#dddddd\")\n", "pl.scatter(X, y, s=200, marker='+', c='black')\n", "pl.plot(Xtest, f(Xtest), 'b-')\n", "pl.plot(Xtest, mu, 'r--', lw=2)\n", "pl.title('Mean predictions plus 2 st.deviations')\n", "pl.axis([-5, 5, -3, 3])\n", "#pl.savefig('predictive.png', bbox_inches='tight')\n", "pl.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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d2opBIIhFIGTgkgpybQgEeeOVCxoQth0MHjwY//zzD0aOHIkFCxaI1TcCgUAgEIIWry1g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\nNJy9eDHY+no0jBpluuDbjsOBE5eOw92H7sbMmd1RU8Nh3rw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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Analytical solutions are nice but to really believe we are working with random variables we can draw samples from the GP. Here is where the Cholesky decomposition comes handy. We can generate samples of $ \\mathcal{N}({\\bf m},K) $ by using a scalar Gaussian generator and scaling it like\n", "\n", "$ {\\bf m} + L\\mathcal{N}(0,I) $\n", "\n", "Some details are in [Appendix A.2](http://www.gaussianprocess.org/gpml/chapters/RWA.pdf) in Rasmussen. Now we could use just use `numpy.random.multivariate_normal` but then it wouldn't be as fun!\n" ] }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Prior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Notice the prior only involves 'test' points and no data." ] }, { "cell_type": "code", "collapsed": false, "input": [ "# draw samples from the prior at our test points.\n", "npr_samples=20\n", "L = np.linalg.cholesky(Kstarstar + 1e-6*np.eye( N ))\n", "f_prior = np.dot(L, np.random.normal(size=(N,npr_samples)))\n", "#notice no data goes in f_prior" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "pl.figure(2)\n", "pl.clf()\n", "\n", "#pl.plot(Xtest, f_prior)\n", "sns.tsplot(f_prior.T, time=Xtest, err_style='unit_points')\n", "pl.title(str(npr_samples)+' samples from the GP prior')\n", "pl.axis([-5, 5, -3, 3])\n", "#pl.savefig('prior.png', bbox_inches='tight')\n", "pl.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ymQbNwMDAUB8wDbjJwXy5DAwMDM0JpgFf4GDR0AwMDAz1AdOAL3AwDZqBgYGhPmAaMAMD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\n9E6cNmo5Shj0YaFfMn+oCvgwslepRRsAvGhSpmG1oe20IxynrFx6VmqyP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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "heading", "level": 3, "metadata": {}, "source": [ "Posterior" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the posterior sampling, the 'data' are used to calculate the covariance function as\n", "\n", "$$\\text{cov}({\\bf f_*})=K_{**}-K_*^TK^{-1}K_* = K_{**} - u^Tu $$\n", "(verify)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# draw samples from the posterior at test points.\n", "\n", "#commented out is a more direct way to get L\n", "#L = np.linalg.cholesky(K_ \n", "#- np.dot( np.dot( kernel(X,Xtest).T\n", "# , np.linalg.inv(K) \n", "#) \n", "# , kernel(X,Xtest) ) \n", "#+ 1e-6*np.eye(N)\n", "#)\n", "nps_samples=20\n", "L = np.linalg.cholesky(Kstarstar + 1e-6*np.eye(N) - np.dot(u.T, u))\n", "f_post = mu.reshape(-1,1) + np.dot(L, np.random.normal(size=(N,npr_samples)))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "pl.figure(3)\n", "pl.clf()\n", "\n", "pl.plot(Xtest, f(Xtest), 'b-')\n", "#pl.plot(Xtest, f_post) #mpl plot\n", "sns.tsplot(f_post.T, time=Xtest , err_style='unit_points')\n", "pl.scatter(X, y, s=1000, marker='+', c='red',alpha=1) #how do you make the markers more visible??\n", "#pl.plot(Xtest, mu, 'r--', lw=2)\n", "#^^^turns out the theoretical mu is close to the estimated mu from tsplot \n", "pl.title(str(npr_samples)+' samples from the GP posterior')\n", "pl.axis([-5, 5, -3, 3])\n", "#pl.savefig('post.png', bbox_inches='tight')\n", "\n", "pl.show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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JvudjNtnC3FhbdaWXt47NqZ/sd1rXdbQnQI3HDoJZs/krZMWr9LHPBSrGBG3l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XSRSsXWwTXN5q5HzbKcxsNGZ9QHb03wuCbw1Lf6+MAHfPzio6PMJnPIski+qNHb4eftdw1fNJDg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\nEpJ9nuenN0zLZSITZ2okweWm/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9sRLjHlqsXV9RL5UoOzV7fxPA/Pg1rdYnQgynvun+Gh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