{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "%pylab inline" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "How to determine the weights?\n", "\n", "Simple approach: Squared error\n", "\n", "\\begin{equation}\n", "E(\\mathbf{w}) = \\frac{1}{2} \\sum_{n=1}^{N} || \\mathbf{y}(\\mathbf{x}_n, \\mathbf{w}) - \\mathbf{t}_n || ^2\n", "\\end{equation}\n", "\n", "Where $\\mathbf{x}_n$ are the training samples and $\\mathbf{t}_n$ are the desired targets" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But first...the \"probabilistic interpretation\"\n", "\n", "Assume t real-valued and Gaussian distributed, with mean given by network output\n", "\n", "\\begin{equation}\n", "p(t|\\mathbf{x}, \\mathbf{w}) = N(t|y(\\mathbf{x},\\mathbf{w}), \\sigma^2)\n", "\\end{equation}\n", "\n", "Then the likelihood function over many observations is\n", "\n", "\\begin{equation}\n", "p(T|X,\\mathbf{w},\\sigma^2) = \\prod_{n=1}^N p(t_n|\\mathbf{x}_n, \\mathbf{w}, \\sigma^2)\n", "\\end{equation}\n", "\n", "With negative log\n", "\n", "\\begin{equation}\n", "\\frac{1}{2\\sigma^2} \\sum_{n=1}^N (y(\\mathbf{x}_n,\\mathbf{w})-t_n)^2 + \\frac{N}{2}\\log(\\sigma^2) + \\frac{N}{2} \\log(2\\pi)\n", "\\end{equation}\n", "\n", "Using a max likelihood approach, finding $\\mathbf{w}$ is equivalent to minimising the squared error" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#..." ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Local Quadratic Approximation (5.2.2)" ] }, { "cell_type": "code", "collapsed": false, "input": [ "# Say our error function looks like" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 48 }, { "cell_type": "code", "collapsed": false, "input": [ "ls = linspace(-1,1,100)\n", "\n", "w1, w2 = meshgrid(ls, ls)\n", "\n", "def E(w1, w2):\n", " return w1**2 + w2**4 + w1*w2 #+ 0.5*w2" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 305 }, { "cell_type": "code", "collapsed": false, "input": [ "imshow(E(w1, w2), origin='bottom')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 307, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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5nNa0kYFW973pp17WvkrZmlPQEAFY3uAtQG0BWcuDahtFgKJCs1Oa1YdTzl95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"text": [ "" ] } ], "prompt_number": 307 }, { "cell_type": "code", "collapsed": false, "input": [ "# Gradients\n", "def E_w1(w1, w2):\n", " return 2*w1 + w2\n", "\n", "def E_w2(w1, w2):\n", " return 4*w2 + w1# + 0.5\n", "\n", "def grad(w1, w2):\n", " return array([E_w1(w1,w2), E_w2(w1,w2)])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 308 }, { "cell_type": "code", "collapsed": false, "input": [ "contour(ls, ls, E_w1(w1, w2), 40)\n", "figure()\n", "contour(ls, ls, E_w2(w1, w2), 40)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 309, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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b9PnY5u/X8n4bfT7yfH+s+3xs5P0+z+s15fO5/9fAlBH8PY7J9zvX+AEd77fV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\n7x/2Kn//cL5/O/PizPOArhb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g7yHIMocQRhDihEBhdUVYD0EUIbiu0Mz7FHJmf0HuxD9ojaAL5+yGvvgfuyFc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\nghz3YFrRHHq7jGTzEKhPKvM8hK9dC9x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"text": [ "" ] } ], "prompt_number": 309 }, { "cell_type": "code", "collapsed": false, "input": [ "# Hessian\n", "E_w1_w1 = lambda w1,w2: 2\n", "E_w1_w2 = lambda w1,w2: 1\n", "E_w2_w1 = lambda w1,w2: 1\n", "E_w2_w2 = lambda w1,w2: 4\n", "\n", "H = array([[2,1],[1,4]])\n", "H" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 310, "text": [ "array([[2, 1],\n", " [1, 4]])" ] } ], "prompt_number": 310 }, { "cell_type": "code", "collapsed": false, "input": [ "# Consider point w0\n", "\n", "w0 = array([0, -0.8])\n", "\n", "E(*w0)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 311, "text": [ "0.40960000000000008" ] } ], "prompt_number": 311 }, { "cell_type": "code", "collapsed": false, "input": [ "# Taylor expansion around w0\n", "\n", "@vectorize\n", "def E_approx(w1, w2):\n", " w = array([w1, w2])\n", " return E(*w0) + dot((w-w0), grad(*w0)).T# + 0.5 * dot(w-w0, dot(H, w-w0))\n", " \n", "print E_approx(*(w0 + .1))" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "0.0096\n" ] } ], "prompt_number": 312 }, { "cell_type": "code", "collapsed": false, "input": [ "rangex = ls#linspace(w0[0]-.5, w0[0]+.5,100)\n", "rangey = ls#linspace(w0[1]-.5, w0[1]+.5,100)\n", "\n", "rx, ry = meshgrid(rangex, rangey)\n", "\n", "contour(rx, ry, E_approx(rx, ry), 20, colors='r')\n", "contour(rx, ry, E(rx, ry), 20, colors='b')\n", "scatter(*w0)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 313, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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FxPFHRmK/jRvxXfTrZ5rMJML42roVxjcyEsZ7yBDDuDszchirV4OpN28OFv7ZZ4bv4uZN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+3UKVTtf/5ZXSNmXBw+Zo0aVmazWsD161AKdeki38EtCTHoi0w/w2XzSSEP7pr/KFd5O4R3fLqG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\n+DD59fPzSUTlq/aeHpqU9u+nd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