{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": false, "input": [ "# some preliminary stuff\n", "%pylab inline\n", "# import scipy.stats for the pdf of the Gaussian\n", "import scipy.stats\n", "# seed for the synthetic data\n", "random.seed(615)\n", "def get_synth_data(N, beta):\n", " \"\"\"N : int, how many points\n", " beta : float, precision parameter for the target variable\"\"\"\n", " X_N = uniform(-1,1, N)\n", " X_N = column_stack((ones(N), X_N))\n", " # for this example the true function is f(x,a) = a_0 + a_1*x\n", " # where a_0 = -.3 and a_1 = .5 are the parameters that we\n", " # are going to estimate\n", " a = array([-.3, .5])\n", " t = dot(X_N, a)\n", " return X_N, t + normal(loc=0.0, scale=sqrt(1./beta), size=N)\n", "# for this example we assume that we know beta,\n", "# the precision parameter for the gaussian noise of the target variable\n", "beta_ = 25.0\n", "# for this example we assume that we know alpha,\n", "# the precision parameter for the prior of w\n", "alpha = 2.0\n", "N = 20\n", "# {X_n,t_n} n=1,..,N dataset \n", "X_N, t_N = get_synth_data(N, beta_)\n", "# graphics stuff\n", "x = linspace(-1, 1, 70)\n", "y = linspace(-1, 1, 70)" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot the prior on w\n", "w0, w1 = np.meshgrid(x, y)\n", "m_0 = [0, 0]\n", "S_0 = 1/alpha * eye(2)\n", "Z = bivariate_normal(w0, w1, sigmax=S_0[0,0], sigmay=S_0[1,1], mux=m_0[0], muy=m_0[1], sigmaxy=S_0[0,1])\n", "title(\"Prior on w\")\n", "xlabel(\"w0\"); ylabel(\"w1\")\n", "extent = (-1,1,-1,1)\n", "imshow(Z, extent=extent, origin='lower')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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a68XbNfk8YieJ69TmtVyuGnSIylFHKZZz5KA3LsZybA9jhwgck4FTplLx9MVU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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot some sample lines sampled from the prior on w\n", "random.seed(1234)\n", "N_lines = 6\n", "W = multivariate_normal(m_0, S_0, N)\n", "for w in W:\n", " plot(x, w[0] + w[1]*x)\n", "ylim(-1,1)\n", "title(\"Some sample lines, w sampled from the prior on w\")\n", "xlabel('x'); ylabel('y')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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9PWtYWPSBmVlX8PleMDJqAk4hU45YHI3g4I/h6roFVlZDgawsYMsWYPNmoHdv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\nO3dy1e0Cc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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot one point from the data set\n", "n = 1\n", "X_n = X_N[range(n),:]\n", "t_n = t_N[range(n)]\n", "xlim(-1,1); ylim(-1,1)\n", "scatter(X_n[:,1], t_n)\n", "title(\"First point in the data set\")\n", "xlabel('x'); ylabel('y')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot the likelihood of the first point in the dataset\n", "def likelihood(t_, x, w, beta):\n", " \"\"\"t_ : float, target point\n", " x : array, location\n", " w : array, weight\n", " beta : float, precision parameter of the target variable\n", " Calculate the probability that the true function f(a,x)\n", " take the value t_ at the location x, given that a=w and\n", " beta is the precision parameter of the gaussian noise.\n", " \"\"\"\n", " return scipy.stats.norm.pdf(t_,loc=dot(w,x), scale=sqrt(1./beta))\n", "Z = zeros((len(y), len(x)))\n", "for i, w1 in enumerate(y):\n", " for j, w0 in enumerate(x):\n", " Z[i, j] = likelihood(t_n[-1], X_n[-1,:], array([w0, w1]), beta_)\n", "extent = (-1,1,-1,1)\n", "imshow(Z, extent=extent, origin='lower')\n", "plot(-0.3, 0.5, 'w+', markeredgewidth=2, markersize=12)\n", "title(\"Likelihood of the first point in the data set, white cross = true value\")\n", "xlabel(\"w0\"); ylabel(\"w1\")\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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URnwI7TnASV9CnkGS5h6RB+nlY5TyJSajWEIey8xLYgK8gE6DB9XKwEg+xknl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\nM4aZei+n2mhw7XdPwrkieQou5y0Kv17LOeXVz2tFX1uCuib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IuCZovbfOeJxuGMeBMQ2k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\neGVc6vqefPJJ3vCGN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"text": [ "" ] } ], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot the posterior after one point has been observed\n", "n = 1\n", "X_n = X_N[range(n),:]\n", "t_n = t_N[range(n)]\n", "phi = X_n\n", "S_n = inv(alpha*eye(2) + beta_ * dot(phi.T, phi))\n", "m_n = beta_ * dot(S_n, dot(phi.T, t_n))\n", "w0, w1 = meshgrid(x, y)\n", "Z = bivariate_normal(w0, w1, sigmax=sqrt(S_n[0,0]), sigmay=sqrt(S_n[1,1]), mux=m_n[0], muy=m_n[1], sigmaxy=S_n[0,1])\n", "title(\"Posterior on w after one point\")\n", "xlabel(\"w0\"); ylabel(\"w1\")\n", "extent = (-1,1,-1,1)\n", "imshow(Z, extent=extent, origin='lower')\n", "plot(-0.3, 0.5, 'w+', markeredgewidth=2, markersize=12)\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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dYuDJbQp8psopcnd+KrEwuTI58LTreW9Db2Kx46GGpzyeNC0ZgMgvNW5pYSW0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"text": [ "" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot some lines with the parameters sampled\n", "# from the posterior after one point\n", "random.seed(1234)\n", "N_points = 1\n", "N_lines = 6\n", "W = multivariate_normal(m_n, S_n, N_lines)\n", "xlim(-1,1); ylim(-1,1)\n", "for w in W:\n", " plot(x, w[0] + w[1]*x)\n", "for x_i, t_i in zip(X_N[range(N_points),1], t_N[range(N_points)]):\n", " plot(x_i, t_i, 'o', mfc='none', markeredgewidth=2, markeredgecolor='b', markersize=9)\n", "title(\"Some sampled lines, w of the lines sampled from the posterior, blue circle = point already observed\")\n", "xlabel('x'); ylabel('y')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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QQMjDLxljrQ8HNWYpDmrMKjYtNtXVQHq64aFV/SCXlwd06GD+0GpYGODiYpu2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\nUTs7v0RiHMji4rSz9rehzpV2hf6/vTuPi+o89Ab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"text": [ "" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot first two points from the data set\n", "n = 2\n", "X_n = X_N[range(n),:]\n", "t_n = t_N[range(n)]\n", "xlim(-1,1); ylim(-1,1)\n", "scatter(X_n[:,1], t_n)\n", "title(\"First two points in the data set\")\n", "xlabel('x'); ylabel('y')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot the likelihood of the second point in the dataset\n", "Z = zeros((len(y), len(x)))\n", "for i, w1 in enumerate(y):\n", " for j, w0 in enumerate(x):\n", " Z[i, j] = likelihood(t_n[-1], X_n[-1,:], array([w0, w1]), beta_)\n", "extent = (-1,1,-1,1)\n", "imshow(Z, extent=extent, origin='lower')\n", "plot(-0.3, 0.5, 'w+', markeredgewidth=2, markersize=12)\n", "title(\"Likelihood of the second point in the data set, white cross = true value\")\n", "xlabel(\"w0\"); ylabel(\"w1\")\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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BhpWjOcnR7yQYNOOMaxFEzZgnNncE1wF6DrlNJUpFZjp1rxfFWczn4fZGovQJ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"text": [ "" ] } ], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot the posterior after two points has been observed\n", "n = 2\n", "X_n = X_N[range(n),:]\n", "t_n = t_N[range(n)]\n", "phi = X_n\n", "S_n = inv(alpha*eye(2) + beta_ * dot(phi.T, phi))\n", "m_n = beta_ * dot(S_n, dot(phi.T, t_n))\n", "w0, w1 = meshgrid(x, y)\n", "Z = bivariate_normal(w0, w1, sigmax=sqrt(S_n[0,0]), sigmay=sqrt(S_n[1,1]), mux=m_n[0], muy=m_n[1], sigmaxy=S_n[0,1])\n", "title(\"Posterior on w after two points\")\n", "xlabel(\"w0\"); ylabel(\"w1\")\n", "extent = (-1,1,-1,1)\n", "imshow(Z, extent=extent, origin='lower')\n", "plot(-0.3, 0.5, 'w+', markeredgewidth=2, markersize=12)\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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RPw1PZIKv8juCDycBb6g748f4ztALf1qM8q9szB0OageoHRr2MFQEKjDUcu0y\nJLm0/3nOS1bZIU2RhF1GmX7rl2lRxiZPptb6lbeyJNIFTLOM7ge3Q6EyJnpYxONfdm0+jjjpjBTp\nCO1Ey8Sj1Oh/EKeeeiqbNm0ik8nw8MMPc+GFF/LSSy812Hp16Hmfn9oNFfMY/R7G2onQT4byiiHR\nGU9rUc/+T4hl7XAwtmv4M/Bn0LvBHQQ9AG7B70rjeMtpGamhRB5UEVQJDO1iWC52EhyrQIfKUUgk\nKJBigE766WKf6iJjdZGigG2WIK2opg3ctDUU8URXujDwOhTiN7E3LGKJdA4PG/10cLRMPDNmzGDT\npk2115s2bWLmzJl123R2dtaen3POOXzkIx9h9+7dTJw4MeaIZxymnB4qGtXhQPwNEieeyE2mlC8e\nhk/Lk9J+XY+m448DTJmwjckTtnFUZisz2cy/8Y8A/Lz4NqaVtjGttJ3k1grWFgd7J7ADTzzbwd0D\nlUEoD0K16A0Yd11PPHYCEgnv0SiDUQXDwVuQ1BehabkkzDKZdL5uKEYHOTIqT9oskKYICROdsHCS\nulZpHTv1qqPAabTeTvT7C/flEQ6ePur/qT9xQEdpmXgWLlzI+vXr2bhxI9OnT+fee+/lnnvuqdtm\n+/btTJkyBaUU69atQ2vdQDrtTiPpjPZfOa5fT+SGM/BGesfOfKohozFSDpZdJmUUyZCng8HaGToq\neTL5IulcGWuPg7Fbw049TDzlHBRyUCoOrdvnAmkT0r4QrAqooAhmDeXDSLok0iUyE0w6SdDBIFkG\nyZIjY+RJqwIpo4hj2ziJBCoVuo7wShe2f63a8NfkGk0+cd+90A60TDyWZbFq1SrOPvtsHMfhAx/4\nAPPnz+c73/HqHC6//HL++7//m29/+9tYlkUmk+EHP/hBq7J7iIgrRjW6IeJkFbOwld/IEztLRsqF\nlIuRqmLbFZK+eDIM9ePJVPKkCmUS/VWMfa5Xn7Mb9K6hVNkDxQLk8pAv148Lr/oOUH7DGn4QpkL9\niVSHS2JChUylQFnb3qAK5eUjrQqkVZEkJSp2inLCgYRuIB0/uX7lcqx0oi1YIpx2pKX9eM455xzO\nOeecuvcuv/zy2vMrrriCK664otnZahFx/XiiEU/MzRXTyo4FKuFiJB1POokyCatEUpX8UebF2lkT\n1TJmsQo5PVSB3A/OgFe8quQgX4R9Zeh3vbrjcN1yWXup4kK2DNkC2P4xgpYwI6exCg7JUoV02evN\nnDT8RKmC95AxAAAgAElEQVQ2yVhRVTFNx5vbOdxlKa7LTsM6sLiirNBuSM/lljOacBq9Du1uMKxT\ns7K1N1dysuKLp0zCKMeIp4JVclBBj+FAPP1QGvSKVwMF2OvAXtf7ONyaXgbKrjdbqS6DXfAGkpsd\n1Pr+KF88qqTJVEqkdYmUVSLhiyeQj60qGKbbWDo1+aiQfOI6DEoFc7sj4mkLRqsDatQzN/RWpHOz\nsjVGwsFKeBGPbXg3esIfZf4ISznG2URntYxRcoaGKviTsruDUMp5xav+IuwDdlMvHo1X11PxH60K\nZAp+97yg308OjLzGKDpYZQenUiapyiTNck04QbKMKqbpoiwdL506p8R9T1KfM14Q8YwbGtxUcaUN\nA5SpUYZGmS6G4WIaLiaOP1eg99zAwdAuytH1yw9XwXXAcaCi/aiGoTHhYfEEn5Xwtq064Fb9aXMq\noKIzlTpguNprbg+NclfhmQNHDVhEMuMdEc+4osGNFlcH7cvHMDzxGMqtCSecDNdFVXX9bKIVTxyO\nWz/zTZCCERMaTzhB3W9ZQ9UFpwquLx0Vmq1UVb1Wr2CAqYHGG8EVyIda/8CRXRItUgnjDRHPuCGu\nxYbh0olEPIbhyScqHNOfot1w4yMe7Xjiqer6aKdCfcRjE1q52K2PeFQVdCCf0NSmyiUU8QQC0t56\nXUqPIdqJXrjIZ7wh4hk3NBhVHZ3f3E9aq6HF9lxvOgpXDRVuvEcTN+iEGKlHUYY3DCxoqY9bwTgQ\nTy0ZYJreuFUVmb1C+/U12gTXUKG8hJOX50bX5CX/+nX0A2E8IeIZVzS42eJuUBe0q9Cut9ieGxRs\nlC8cP+ZxlYkOiydojjf8folq+CSr4Ygn3FnaVt4agoYNKjGUgp21Da4FrulNjxEq8Hn5036BK7xI\nREP5iHTGMyKeccMI0gkeQzeq1n6k4ypc18A1jLooI7jptWGgTTUkHV9Ayl+FJiqdoB9fWDy1TsaG\nt2qyYYMRmpFVB9KxwbUUjqFw1FAe3Ih80DHyqXuMM5MwnhDxjCvCKyXo+rfDa1IF9TRVA6dqUq1a\nVE2LivJm/SuHGrErZhnHNoYGlfq9jc0M2DlIp6Di+PU3LhhufcTTqYZShw3JFBj+qHgyXtIZRTVl\n4CQMSlbCmwTM8Br2vXzYVLFxtInrGOhwS1i401CQYqOe0ZLQToh4xgWRMlQ04omu8FsBXVE4FQMq\nnnjKKkFJe4vU1JJKkbFKuCkTnQUVzFjYCWYOkgVQBa8ymDIYFUhFxWP4yYRsClIZMPxj0OU9ullF\nNW1RStjk7RQFw1t/q+ivXVH2BVR1bdyq4fVGDGqyYwWkffHElcViQyREQO2FiGfcMEr9TjTaqSjc\nioGuWFSqNhXDpmwlCPoKB/KpWHmclDfzHx26JgwzB8k82Hl/8CdgOl5QNCziMaHTAjsJdiAeXzp0\ngu4wqKQtiokEBStNQaUo1ASYrEU+FdfCdUx00G4flk54nIaOXvhY5SO0CyKelhDcBCr0OiyU6H/n\nEYoPmqEbM0hl0GUFJQNdMnHKFhUjQdFO1RbdC1LRzlNO21Q7DcwJYHRr1IBGFcHyBaC0Vz+jDEha\nfoClvaqYrO2nBBgTQHWD6sFbsdRPbpdBOW1TSKQZNLx1t/JkKJCmqNMU3RRFnaJSSeCUTHRJee3z\nJeqb+WtRjwYdnn91WDks5jsV2gkRT0sJJiEPGqeD/85uzPPo69AhomvclfEmSC8aUAC3YFMxkxST\nqdpKn4N0MKA6ydp5OrMpSoaNna9i5V3Mgt+p0D+VYUMiBzoDdnGopKOBZBISSTCSoCaC8tdlZwow\nGZgEbrdBOZskZ3kL/Xnrk3Z4i/85WfLVLPlqhlIhSbVooQvKW18rkE85dH2O9icDiq573KjCWcTT\njoh4WsJYopmRBBRKwfK/0e7FJdBFA/IKt2hRSSYouulh4ulMDJA3khSTNhQ0FMAoud68Ov4pDBvs\nQa/C2S16wYb259UyU14y0ngLBk5kmHicHoNSJslgSDw5suR0lryTJVfOkC9nqBaTuAULouKJdG70\n+gqEw7xoxCOtXe2OiKdlRItVowkoRkTa9eamqeJVyAbyKeEtjlfAE0/BopxOUnTS5HSWQdVBP110\nMkCnNcCg1U+ONHqCgmIZq+KgNKA0SoFKgtWBN5C0EMlK0BKWxita9QITQU9RuL0Gbo+i1Jkkn8gw\nYHWxjwn1UU81Q7GcppRP4eZtKBhDi/kF8gnX97jh2vRorXOjeh0RULsh4mkKwR9+uGgFw7v6x8km\nWo8RGVTlmt5sXGVzaK3xIt4yM/6Ic6fDoJxJkKtmSLhddKhBsipHVuW8ybj8qt5KcgB3Qg4DB9ty\nMG0XI6FRndQmcadA/X0dnuw9qNeZCJWJFsWeJIVMkr2JbnZaE9mtJrKHHvbQzR662acnkK9kqeST\nMGDCgAGDCvJquHyqoa9xWFNeOMUVTyX6aTdEPE0l/MffaHxRI/mEU1g8GqpWvXiCm9YXj5szKHcl\nyFeyWG6FfqNrmHSSlNBJA2OCSyJVRCVdSBiolIvq0t6x/DWz6u7lYDWINN767D2ge6DSaTGYzdCf\n6WRXYiK7DC/txpPPXrrZRxf5apZyIYnuNz3p5NTQYn7RiMcNR4KjSadR8VRoB0Q8TSMc9jcaVR29\nSeJurnDdRnlo/tGy9iqUSwytOe6vzOnmDMqFBG5FoxyHLDlvnmNVrJuIy0i62MkSaXIYKRcSDkYK\nVKc7dLwS9fdwaGULPQHoVuhuKKUSDCay7LYnsMOcyE4msgtPPHvpYa/upt+dQL6coVJI+BGPqs3h\nUxfxlPFGq9aa0RtFg3ERT1wLodBqRDxtQXAzKeL/W4frNEJFLV31Bj9V/ZspJtohA+xTuB0WTlZT\nttLkUh30p4okkmVsKlhUMXBrQymqWHRYeVKZMim3jJ30100vORgV18+WN42FkzBwbS9VsxbVjEU1\nabPP7mSnMZFdaiI76OXPTGEHk9mpJ7GnMpH+Sje5chel/gzVfbY301gwXWpQrKtFPtrrPu061M8O\nFJnoJ1Y64e84rv5MIqFWIOJpOdEbIdy8Hv1vHprcJkiOf8O5DBW1QvU7pEFnDJyst0he2U6R7+yg\n36xgJIeGaCp0TToVLDqtQbKZAhkrTypbwq5WsKtlLNdB6WDiLqia3nCMqmFRTCQp2imKiRT7zAns\nNnrYrSayk152MJkdTGKX28ue8kT6i90M5rqo9ttU+230PjW0EukgQ9IpAKVAPOGmu7GMqxjpe5bi\nVysR8bScqHQaNaWHI57IVIGu9nYNillJhsSTAp1W6IyFmzYhYZA3K6i0i4OqSQfwpWNTwSZv99Np\nDdCZTpIhR1IXSWFiU67NnwPUxlqVVcJrIlfeiln7VDe76WEPPeyil51M8sSjJ7G3MpH+fA+5gS7o\nV+h91Ec8QXGrJh53aHaxuo49UfGEW7fGEvW4h+QXFPYfEU/bEa4LilYuRyOfMt54cX/mrarh1fPk\njaEVRcMrjCYUrmV4vZjNLBiQsKsYtkbbigreANISSQbpoEMN0qkGyJCvDbRIUAlNVUptnzIJv39Q\nlhwd7GMCe/3Wqz3uRHY7E9n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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot some lines with the parameters sampled\n", "# from the posterior after two points\n", "random.seed(1234)\n", "N_points = 2\n", "N_lines = 6\n", "W = multivariate_normal(m_n, S_n, N_lines)\n", "xlim(-1,1); ylim(-1,1)\n", "for w in W:\n", " plot(x, w[0] + w[1]*x)\n", "for x_i, t_i in zip(X_N[range(N_points),1], t_N[range(N_points)]):\n", " plot(x_i, t_i, 'o', mfc='none', markeredgewidth=2, markeredgecolor='b', markersize=9)\n", "title(\"Some sampled lines, w of the lines sampled from the posterior, blue circled = points already observed\")\n", "xlabel('x'); ylabel('y')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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ERHsXocPgc2lafD4Zu3fxNCnM5EQiEbhaMcZY83DsZKbELXiMMcYYYx0MJ3iM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\noouUIuXxmGAw/A16fQV8Pkdge5OEhL6hHppo/MyPL89/CV2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"text": [ "" ] } ], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot all the data set\n", "n = N\n", "X_n = X_N[range(n),:]\n", "t_n = t_N[range(n)]\n", "xlim(-1,1); ylim(-1,1)\n", "scatter(X_n[:,1], t_n)\n", "title(\"data set\")\n", "xlabel('x'); ylabel('y')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot the likelihood of the last point in the dataset\n", "Z = zeros((len(y), len(x)))\n", "for i, w1 in enumerate(y):\n", " for j, w0 in enumerate(x):\n", " Z[i, j] = likelihood(t_n[-1], X_n[-1,:], array([w0, w1]), beta_)\n", "extent = (-1,1,-1,1)\n", "imshow(Z, extent=extent, origin='lower')\n", "plot(-0.3, 0.5, 'w+', markeredgewidth=2, markersize=12)\n", "title(\"Likelihood of the last point in the data set, white cross = true value\")\n", "xlabel(\"w0\"); ylabel(\"w1\")\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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RKmRwiAXf1xB6ChJbBOnylISqoqNCui6hhEQIQCYjo4yIyhHSqLoRSzpVtxs0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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot the posterior after all the points in the data set has been observed\n", "n = N\n", "X_n = X_N[range(n),:]\n", "t_n = t_N[range(n)]\n", "phi = X_n\n", "S_n = inv(alpha*eye(2) + beta_ * dot(phi.T, phi))\n", "m_n = beta_ * dot(S_n, dot(phi.T, t_n))\n", "w0, w1 = meshgrid(x, y)\n", "Z = bivariate_normal(w0, w1, sigmax=sqrt(S_n[0,0]), sigmay=sqrt(S_n[1,1]), mux=m_n[0], muy=m_n[1], sigmaxy=S_n[0,1])\n", "title(\"Posterior on w after all the points\")\n", "xlabel(\"w0\"); ylabel(\"w1\")\n", "extent = (-1,1,-1,1)\n", "imshow(Z, extent=extent, origin='lower')\n", "plot(-0.3, 0.5, 'w+', markeredgewidth=2, markersize=12)\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "# plot some lines with the parameters sampled\n", "# from the posterior after all the points has been observed\n", "random.seed(1234)\n", "N_points = N\n", "N_lines = 6\n", "W = multivariate_normal(m_n, S_n, N_lines)\n", "xlim(-1,1); ylim(-1,1)\n", "for w in W:\n", " plot(x, w[0] + w[1]*x)\n", "for x_i, t_i in zip(X_N[range(N_points),1], t_N[range(N_points)]):\n", " plot(x_i, t_i, 'o', mfc='none', markeredgewidth=2, markeredgecolor='b', markersize=9)\n", "title(\"Some sampled lines, w of the lines sampled from the posterior, blue circled = data set\")\n", "xlabel('x'); ylabel('y')\n", "show()" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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f6T1kt4KDDMYYY+2qe3fp30OHGk4TRUClqnnfXG3HDz+0bJtGY2nrdpLdFhxk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\nW2OxYgUQ7uJMjFVvhe6YDtrDT7Rttjx0LHgytW2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