{ "cells": [ { "cell_type": "markdown", "id": "65f3d80a", "metadata": {}, "source": [ "Title: Normal Distributions\n", "Author: Thomas Breuel\n", "Institution: UniKL" ] }, { "cell_type": "code", "execution_count": 31, "id": "a673fd59", "metadata": { "collapsed": false }, "outputs": [], "source": [ "\n", "from pylab import *\n", "from math import atan2" ] }, { "cell_type": "markdown", "id": "8a53bbed", "metadata": {}, "source": [ "# Normal Distributions" ] }, { "cell_type": "markdown", "id": "86e82f36", "metadata": {}, "source": [ "Normal distributions have pdfs of the form:\n", "\n", "$$ p(x) \\propto e^\\frac{-x^2}{2} $$" ] }, { "cell_type": "code", "execution_count": 2, "id": "d8d0e575", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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YGBAUpO6/DZEWQkOBBx8UL24XL4qZL8XF4rXDAXz3Xd3BzJkz4rjLl8XPUbt2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\n/w8egDlzPFI7hwAAAABJRU5ErkJggg==\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# standard Gaussian\n", "xs = linspace(-5.0,5.0)\n", "plot(xs,exp(-xs**2/2))" ] }, { "cell_type": "code", "execution_count": 3, "id": "3e4663f3", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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rr7yiuoyAmDp1Knr1kj8uaWlpqK2tVVxRz7U+TyIiIqLlPAm9GD58OFJSUgAA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\nkBMRhTkGORFRmGOQExGFuf8HDIQ6O1lkX1cAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# shifted and scaled Gaussian\n", "xs = linspace(-5.0,5.0)\n", "plot(xs,exp(-(xs-1.0)**2/(2*0.7**2)))" ] }, { "cell_type": "markdown", "id": "4403f0ef", "metadata": {}, "source": [ "(normalization)\n", "\n", "We want $\\int f(x) dx = 1$ for the pdf, so the whole Gaussian looks like:\n", "\n", "$$ f(x) = \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} e^{ -\\frac{(x-\\mu)^2}{2\\sigma^2} } $$" ] }, { "cell_type": "markdown", "id": "505caaa3", "metadata": {}, "source": [ "# Important Properties" ] }, { "cell_type": "markdown", "id": "08b64603", "metadata": {}, "source": [ "Important properties of normal distribution:\n", "\n", "- all cumulants higher than second order are zero (cumulants are roughly \"excess moments\", higher order moments you wouldn't predict from lower order moments)\n", "- it's essentially the only (absolutely continuous) distribution for which that is true\n", "- it is the maximum entropy distribution for a given mean and variance\n", "- it is the limit distribution for the sum of large numbers of small random variables\n", "- in problems involving Gaussian error models, the least square solution minimizes the error" ] }, { "cell_type": "markdown", "id": "92fb360b", "metadata": {}, "source": [ "# Central Limit Theorem" ] }, { "cell_type": "markdown", "id": "56814ade", "metadata": {}, "source": [ "(central limit theorem)\n", "\n", "The sum of a lot of random variables tends towards a Gaussian distribution (under some conditions)." ] }, { "cell_type": "code", "execution_count": 4, "id": "1ebdad31", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "# central limit theorem\n", "samples = [sum(rand(1000)) for i in range(10000)]\n", "_=hist(samples,bins=100,alpha=0.3)\n", "_=hist(randn(10000)*var(samples)**.5+mean(samples),bins=100,alpha=0.3)" ] }, { "cell_type": "markdown", "id": "5e7e60dc", "metadata": {}, "source": [ "# Proof Sketch of CLT" ] }, { "cell_type": "markdown", "id": "6bdfc5b9", "metadata": {}, "source": [ "(proof sketch of CLT)\n", "\n", "- addition of random variables = convolution of their pdfs\n", "- convolution of pdfs = product of Fourier transforms\n", "- take Fourier transform of pdf $g(x)$, call it $G(t)$ (the *characteristic function*)\n", "- sum of $n$ random variables with pdf $g(x)$ has Fourier transform $G^n(t)$\n", "- take Taylor series and limit" ] }, { "cell_type": "markdown", "id": "55c58eb7", "metadata": {}, "source": [ "(characteristic function)\n", "\n", "The *characteristic function* of a pdf is the inverse Fourier transform of the pdf. Let $X$ be a random variable.\n", "\n", "$$\\varphi_X(t) = E[e^{itX}]$$\n", "\n", "From the Taylor series, you can infer that:\n", "\n", "$$\\varphi_X(0) = 1$$\n", "\n", "$$\\varphi'_X(0) = i E[X]$$\n", "\n", "$$\\varphi''_X(0) = -E[X^2]$$" ] }, { "cell_type": "markdown", "id": "67d5eacf", "metadata": {}, "source": [ "(proof sketch of CLT)\n", "\n", "Assume the mean of the r.v. is zero.\n", "\n", "Then, the Taylor series expansion of $G(t)$ becomes:\n", "\n", "$$ G(t) = 1 - \\frac{1}{2} t^2 + o(t^3) $$\n", "\n" ] }, { "cell_type": "markdown", "id": "5e2cbbdc", "metadata": {}, "source": [ "(proof of CLT)\n", "\n", "We need to rescale each r.v. by $\\frac{1}{\\sqrt{n}}$ to keep the second order moment constant, then:\n", "\n", "$$ G^n(t) = \\left(1 - \\frac{t^2}{2n} + o(\\frac{t^3}{n^{3/2}})\\right)^n $$\n", "\n", "Compare with:\n", "\n", "$$ e^x = \\lim_{n\\rightarrow\\infty} \\left( 1 + \\frac{x}{n} \\right)^n $$\n", "\n", "Hence:\n", "\n", "$$ G^n(t) \\rightarrow e^{-\\frac{t^2}{2}} $$\n", "\n", "But you already know that that is the Fourier transform of a Gaussian (you can also try to show it)." ] }, { "cell_type": "markdown", "id": "964e8a36", "metadata": {}, "source": [ "# Normal Distributions in Higher Dimensions" ] }, { "cell_type": "markdown", "id": "8c5a93b6", "metadata": {}, "source": [ "(formula and analogy)\n", "\n", "In higher dimensions, normal distributions use vectors and quadratic forms instead of scalars, but they look otherwise the same:\n", "\n", "$$ p(x) = \\frac{1}{\\sqrt{2 \\pi \\sigma^2}} e^{ -\\frac{(x-\\mu)^2}{2\\sigma^2} } $$\n", "\n", "$$ p(x) = \\frac{1}{(2 \\pi)^{k/2} |\\Sigma|^{1/2}} e^{ -\\frac{(x-\\mu)^T\\Sigma^{-1}(x-\\mu)}2} $$\n", "\n", "The division by $\\sigma^2$ has been replaced by a multiplication by $\\Sigma^{-1}$.\n", "\n", "Note that, confusingly, $\\Sigma$ is a matrix of variances and covariances, while $\\sigma$ is a standard deviation (square root of variance)." ] }, { "cell_type": "markdown", "id": "638a0dc0", "metadata": {}, "source": [ "(log domain computations and norms)\n", "\n", "Because the exponential values become very small, we often work with logarithmic values:\n", "\n", "$$\\log p(x) = \\hbox{const} - \\frac{1}{2} (x-\\mu)^T \\Sigma^{-1} (x-\\mu) $$\n", "\n", "But this is just the distance of the vectors $x$ and $\\mu$ in a norm given by $\\Sigma^{-1}$:\n", "\n", "$$\\log p(x) = \\hbox{const} - \\frac{1}{2} || x - \\mu ||^2_{\\Sigma^{-1}}$$\n" ] }, { "cell_type": "markdown", "id": "a6d2c60a", "metadata": {}, "source": [ "# Generating Normal Samples" ] }, { "cell_type": "markdown", "id": "433550f0", "metadata": {}, "source": [ "How do we sample from a normal distribution?\n", "\n", "It's pretty easy to get uniformly distributed samples, but we need to transform that to get Gaussian random variables.\n", "\n", "You can look up the details here: http://en.wikipedia.org/wiki/Marsaglia_polar_method" ] }, { "cell_type": "code", "execution_count": 5, "id": "78660bfc", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "def marsaglia():\n", " while 1:\n", " v1 = 2*rand()-1\n", " v2 = 2*rand()-1\n", " s = v1**2+v2**2\n", " if s<1: break\n", " if s==0.0: return 0.0\n", " return v1*sqrt(-2*log(s)/s)\n", "\n", "example = [marsaglia() for i in range(10000)]\n", "_=hist(example,bins=100)" ] }, { "cell_type": "markdown", "id": "6cf40204", "metadata": {}, "source": [ "# Generating Multidimensional Normal Samples" ] }, { "cell_type": "markdown", "id": "1a6b4aec", "metadata": {}, "source": [ "The simplest multidimensional density is one in which each dimension is just a standard normal random variable.\n", "\n" ] }, { "cell_type": "code", "execution_count": 40, "id": "ce78e1a7", "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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FgwBHtu9raQGora2JT61YFDqmpSWcj8mk1E9/ijklk5LK0ahxdG2OH0u1eL205W5KyZwT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\n/XmMCoOF0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deUz+dTKysr6qtf/ar613/91/A7HEiEUCfpTjzcvn374d8vvvii9pWvfCVt\nY3n99de1jo4ObXZ2Nm1j0EtfX592+fLlAz9vIBDQGhsbteHhYc3v96c18aBpmjY8PJwRiYednR3t\nD//wD7W/+Iu/SPdQtNnZWW1xcVHTNE3b2NjQnnzySe3nP/95mkelaf39/drv/d7vRd3mwJVcQ0ND\nWpXcl770Je3kyZNad3e39uyzz2rT09NpG0tzc7NWW1ur9fT0aD09Pdqf/umfpmUc//mf/6lVV1dr\nOTk5mtfr1T7/+c8f+Bhee+01rbW1VWtqatIuXrx44OenfPnLX9YqKiq0rKwsrbq6WnvppZfSNpZ3\n331Xs1gsWnd398Nn5PXXX0/LWK5du6b19vZq3d3dWldXl/aDH/wgLeMwSn9//57Z1ZQjA5tiiimm\npFNMZGBTTDHlSIup5EwxxZQjLaaSM8UUU460mErOFFNMOdJiKjlTTDHlSIup5EwxxZQjLf8fl1hQ\nXCCd2isAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ps = randn(10000,2)\n", "xlim((-4,4))\n", "ylim((-4,4))\n", "figsize(5,5)\n", "plot(ps[:,0],ps[:,1],'.',alpha=0.1)" ] }, { "cell_type": "markdown", "id": "eb9f826a", "metadata": {}, "source": [ "When the variances differ, we get distributions that are elongated along one dimension or another.\n", "\n" ] }, { "cell_type": "code", "execution_count": 41, "id": "9b77c7ab", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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h1RAgSyWl/umf8PlrrwFA9E1ptLTk29v4nPWfBMVAoJ4DbnERGtHODkDD7QYY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\nhFSIXagUL6Sy0ptI6PXserIwHG/+3efj/Bi4T60Wjs/HIZ/fH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}, "metadata": {}, "output_type": "display_data" } ], "source": [ "sps = randn(10000,2)\n", "sps[:,1] *= 2.0\n", "xlim((-4,4))\n", "ylim((-4,4))\n", "plot(sps[:,0],sps[:,1],'.',alpha=0.1)\n", "figsize(5,5)" ] }, { "cell_type": "markdown", "id": "5f0fc148", "metadata": {}, "source": [ "The most general normal density combines rotation and elongation.\n", "\n" ] }, { "cell_type": "code", "execution_count": 42, "id": "3165c724", "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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GIgC1rS3M78TE4RdZPI7fCwvCqtzVVXofzV5y1GY3N8s/VychTZBrilLqcNXz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\nywklOFk/uKCuXsX3rMzEgsRLS6KpxmJYUCwOPTkpVcFyOSx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xiHb3ve/BQxgKSeoVPY2L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9ffL1iDzycP7OZNLCw2kn/4IRaQ1yuoCJk8YjEs5kuXJLKyt4cxundP+pyErgwO4v+rqzCAW1sY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\n6duNRtNzUjC4GIUI+aVt23h7ehIaskOhEHPbbN/BTIYj6W96M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/Tb3/6WotFo0dYRCoXo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\ngZELECDAfY3AyAUIEOC+xv8DbekJB8hWKFoAAAAASUVORK5CYII=\n" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "R = array( [[cos(0.7),-sin(0.7)],[sin(0.7),cos(0.7)]] )\n", "rps = dot(sps,R)\n", "xlim((-4,4))\n", "ylim((-4,4))\n", "plot(rps[:,0],rps[:,1],'.',alpha=0.1)\n", "figsize(5,5)" ] }, { "cell_type": "markdown", "id": "3cedf997", "metadata": {}, "source": [ "(coordinate transformation)\n", "\n", "Let's start with a normal density with arbitrary covariance matrix $\\Sigma$:\n", "\n", "$$ f(x) \\propto \\exp(\\frac{1}{2}x^T\\Sigma^{-1}x) $$\n", "\n", "Now let's decompose the $\\Sigma^{-1}$ matrix into an orthogonal matrix and the eigenvalues:\n", "\n", "$$ \\Sigma^{-1} = R^T \\Lambda R $$\n", "\n", "With that, we can represent the normal density as:\n", "\n", "$$ f(x) \\propto \\exp(\\frac{1}{2}(x^T R^T \\Lambda^{1/2} ~ \\Lambda^{1/2} R x) $$\n", "\n", "And that means that our normal density is related to the standard density by a coordinate transformation:\n", "\n", "$$ x \\rightarrow \\Lambda^{1/2} R x $$\n" ] }, { "cell_type": "markdown", "id": "4c2d8629", "metadata": {}, "source": [ "(recovering rotation and scale)\n", "\n", "Let's try to recover the rotation and scale from these samples. Note that these values are close to the parameters we set above (the `pi+` is needed because the direction of the eigenvector is arbitrary up to reflection).\n", "\n" ] }, { "cell_type": "code", "execution_count": 39, "id": "8ee4d886", "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "eigenvalues [ 1.02305825 3.9323627 ]\n", "angle 0.705607128771\n" ] } ], "source": [ "M = dot(rps.T,rps)/len(rps)\n", "ls,vs = eig(M)\n", "print \"eigenvalues\",ls\n", "print \"angle\",pi+atan2(vs[0,1],vs[0,0])" ] } ], "metadata": {}, "nbformat": 4, "nbformat_minor": 5 }