{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "from __future__ import division\n", "import numpy as np\n", "from sklearn.metrics import confusion_matrix\n", "import matplotlib.pyplot as plt\n", "\n", "from utils import draw_in_row\n", "from utils import NormalDistribution\n", "from utils import plot_confusion_matrix\n", "from utils import MixtureGaussians\n", "\n", "plt.rcParams['figure.figsize'] = (10,4)\n", "\n", "np.random.seed(42)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bayes optimal during training and deployment phases\n", "\n", "Imagine a toy example where we have two known classes to classify $y_1$ and $y_2$; lemons and oranges respectively.\n", "And we only get their relative size $x$ with respect to the same common unit $1$.\n", "\n", "- Classes\n", " - $y_1$: lemon\n", " - $y_2$: orange\n", "- Feature\n", " - $x$: relative size to the same unit value\n", " \n", " In this case, we know the real probability distributions for both classes, consequently we do not need to estimate them. Their distributions come from two different Gaussians $N(\\mu_1, \\sigma_1^2)$ and $N(\\mu_2, \\sigma_2^2)$. And they both have different priors $p(y_1)$ and $p(y_2)$ respectively." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "norm_y1 = NormalDistribution(mu=0.9, sigma=0.2)\n", "norm_y2 = NormalDistribution(mu=1.1, sigma=0.3)\n", "\n", "p_y1 = 0.4\n", "p_y2 = 0.6" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets visualize a small sample with both classes." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaoAAABTCAYAAADOZUOTAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvHm0p1dZ5/t59vAOv9+Zqk4NqYwFIZBgQhpQEBURvYI0\nCDiLA43T9Qp2I/ZqW7u1G73X4bp6aSPctrXpK3oREQ04IVMgIEgYEoaQeaxUpapS8xl+v3faw3P/\neE+CSEaIF+9a57tWrVWrVp2z97uHZ/g+32fDNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb\n29jGNraxjW1sYxvb2MY2trGNbWxjG9vYxja2sY1tbGMb29jGNraxjW1sYxvb2MY2trGNbWxjG9vY\nxja2sY1tbGMb29jGNraxjW1sYxvbeCwhX4lBVVUf7v/kDCqBOz75O5j+evbs/18pz30WJQry2E87\n5gSpgbveg73tzcj6AVLZ8pkLfpmn3fhqcv04NO/EhFvJT3st7uIfIBnFYh+T8YM2EA3GOpJYHImQ\noDQC5rEZ46GgJH7lt8/G2C/cmhQhJyHmzK/93Il/shMTtMNki1ohqcVLIqhSBguF+acZdAtJMx1K\ncfp25MCV2MNvRzZO0RcDN5//C1x+28+TJ2dDt4jIKXTnNzJ8669T6RTcY7MgMSeCMVSHPki+8z1w\n5mpszOiu53HDXLnk+OuRha8hqyD9deRn/jb2opciWOSf4D6gStYW0gR1EZsdGUWkQ6jA/H9vOjLK\nkMFpADG4k3cSD3wUe/LP4dQxhif9FHr3uyiGu0h1QjYGzPIetD6H8LzfJ8iEhVYJk0iB/yeZY8wJ\nNcLQnyL5ZRaNg26DeOrD8KFfZLZ+ALPwdIg3sNztgMktaCgZvu43sRf/FFEiaE2RFfMYna2HQ0gR\nMdDFOcl7CnUUAqzfgoYZevs7iUc/iuy+kGrtMDGCNC12R4IBwuNeCBf8BP3SlIWYCLZCVHCSH7Xt\nkgc5zP8sHdXVV/wHVuyvU9QGyNQTzzAkjLWsnYqE6cu4/Nv+AEfx5cyCHDsSJeGql1O3AcknyekI\nuQdNlsMXPIO33PJ3XLbrq/nG09ezPE3E2OPYj8ZNYtXjvuujZFNjbYYv4fD3dNz63l+mPfF/Ml1Q\nplNHTBEjjpAibbfIv3jpcVQckh08xjb7v/zekxniSQoH1hqMMYgZtyerkqMSEsSYiYMwBKXy5/JL\nP/vpx2T8EDvMcJxrr3gS5VJH7cF5GR0kSiGrXPCtJzA2QXI8RnEBqgkNA6EoMO98Oa47ThChMD2x\nXceFJY7svZRffN+1PPc5+/me4YOUHYhdRYeApGXUFTQ/9GFEBmo8gns0MyDRAC1mXqLv/ylMXkfL\nOdJsklul3dzD728U3Nac4vuefSFff8+f4IoJyG7C5pzs9+H3rdJ/8xVUTMguYqR4TOK4G699K7Ob\n/xXFUqRwBhdqsszIaT/+rB/moq/95S9/kIdFBgXFoJrpjaH6yOtJ62+DbCCs4KhJ4TAm3M2v3HQp\nspb598/bQ9H/CbiSdCqCeSaUEbd0B+H5d6NlSREhuPHGKl+qIVRAUVUECwqtQnX175DW/2xrjjtw\npqLtb6EKp7i1fjn/48r38J0Xn8+zdt7FsHgzbpax8ylafyNBjyH7avQ5V1J4gQy9U0rky5jnQyOk\nyGDBhxnFgXcTTt6KufcDqDmB6wuoFghcyM37nk97w9v5Gv1bZMfTIewmxTlaKbrxAXz1L5l/y39i\nuvoUSJ7oIu5R3Yn/nziqmBs+97Yd1NOB6WKB0UBCKUqDqhCGhHWGoc+0c0MfHs9TvusWrDx6662a\n4fidyCd/BdY+SFw9GzvvyEYx9laG0z23nvl+bj29xq6VJZ51QUOhazAEUnMQyhVw58B8k/4nPkAl\n9aP0Icowz1z3tzU7lzMpJ2rv8LUQYiBnQCFGcM7QzQ0b3cU89bs/gNXdX/bODaHhv/z+45kUgisE\n5xRnBOMF2dqdjJIThJCJSQg9dCHTt9APidf+29upq5UvaXzVhJL53F+vMPEN1hqqwmGKTN+NEZ73\nhhgEMDTzQN8+lcte+imCtnhXfVmZREoBc8sbkM9eT+NvYGIzUec4u0BqM1Z28v989gj1/lUOfnKd\nH3xuwS5p0f5GXFDysIpxq+SFFeRb38Kweh6FEUQemSdVzRCV2XufwGJ8CjGexJUb5GEHxgZ0Jpwc\nCv7iBmHHuae57boT/PxLziVt3oqNDXkWscXTUTYQ7Yk/dgcRpbQG+RLuw3349Lt+CJffQr/u2X1W\nwgHihZQjmg3GGXSINFFYZJGzvu4QZnHpSx7voaCaEE2E5PEH34p+9mPI5CC0a+R8hDD0+LSXoDPu\nXt7FR46WLJzr2N3v4atO3sye0oI7xhCEorqYfuk45emCrqqoXvQ39OIoyoRo8SXep0zOeQwqA4Sr\nvoeJRkCgPUPOh8c55lVUznDnwjncMlzMXela9pdPYdfNR3jW2S34OTHOcOwCteRpwvSW+dN+lun+\nFxKTw06/nHnev6KoZiQbsBtonpCJ9B/5GfyJT+GXnkzqO6wA6RSsteSio29O8KHJN/E7b3sbFz71\nXF7yDd/FMz7131jaey6kgtj1uOlp+mEGUSnT5cyeup+FZ/4BgyS8ehAD6h72zv6zd1Qhdtz010tM\npgnvFBGwotjCYEXJojhniEHJGXKyzNfGVPtU9b08+9v+hEfyOUMG269h/uZ7EHeCGCZkNvFyFJFT\n5A5MdS4ZC+ZujBW024+YKfnYXYhPBCJuIZFn52GrZWRxD7z4z0hUGFs/bESrKJ9409OYLH+GhQWL\ncYmhE6YLAgLzdWW6DDkrIoKIEoJAMqxvJPpwPl/1vbdRqcV8CbTgL//2buraUFeGsjCUJTgH1grO\nbJ0pBM1KTEKMSkhK32WGkGk76Bql7TLNPPH6XzvzKGegXPWnF7NU3cXexcyQEsYI3oJxhhQNxiXA\n4JySEoSQCD3kOZzsK772+1oetT3WRMQg8Tj2Xf+BHO9B9G7EehLrWBYhHkb7FTDnQ3UUdA9iGlRu\nR+Z7SHoE+pIQMpW9iFQeZJCLKL/hJ+Gc7wenGKoHPIpj5J3oxcLpQ/irfx4TDwAN0JNij5h7IUTE\nfBWSzgdmaLGJ2HvI4TR0CcShTYkNl4EdQDpSqmle8U6mbidiEyKPPJJVbehPb3DDuy+hmK5RV1BP\nSnIYMAYiijFjxt33irMyUvOa6eaWZCrOv/xqJudeiE0THmUQ/aBIKZA++yaKIx9GwyHEWKI/gWuE\nZDLWzFBzgOGUcnr+b7jiU5/kCU8oSbnl2RdOWTILEE9ADOT+JDKdIGEN3Augu43hO34PVi/+knkZ\n1TQ6qrs+in7mf8dMSoZmE2870DNgpwgluZ8j1vCJuydcf6hg5SJHc6DionPu4pkXLKHNKfJwHBt7\ncpcx1SWICYTlS/C9Er/7rSTnKMR8WcGZah4z0+SouyPMb3wd04O3wCQwpNMUqYa4jjoPsSclx7wX\nDuTLWXvCfnaHu5mXC5y++3OYT9zMs596EVURoL+TwW9S5PPIKWAmO0ndMjG8l/LFx0m7K9ApQo+h\nfkgz/c/eUX3yTw27VkEVvLOoZJzLOGcQk/HeYp1l6AM5QBig72DtDNgCyumzeNLz//6hRgUySS3y\nly9C8gZJMs7eS5zfi3Uduc8YDGCRIqMzyFVCejC1RdcTwdZ4U6As0/YzareXSI9OL0Rf9m5KRkPy\nYAurmvnknzyLpeVPYB1YA95bxGScFWJSnFXECtbKlnFzaFaGPtFsGGadMi0MF317eNTG+lf+616m\nE6grS10bylIpC8FvOSpjMiIjzaAqpKjELAyDMgzQ9Zm2y7Sd0rVK02Tmm/CG3zj5iMZXVa6+4tms\nTj6OLzOaMtaOdJ9ksIVgFMSPe2atoe+2MjAVNk8Zcoakjie95DCFW33E354A6e7GvP8XSO1RbNGi\n/R0ga0guR6pGHWrOgIDMhVCWeBNJ6xm7UsG8h/ZsmuIeilhg7fmIq0BXybufSP+C36X2mQey1uNe\nCqc++V9ZPfQO1EwQeysp3olBkPZ8dOFupCnB99Bbgiq2zJgk0BkyBSZkKApISjcXymKRXJ+H1pn0\nlF/APfE7xqj4EewFmvnwH13CyuLdIAMLi0JZKc0cprXAVs3SiqAi9wdhMWaQsX7ZrCsJ6Lqaxz3t\nrSzvfwFiHPIo61iqimiiMxYznMa+51VYM0A4BroJWpLdEUzcA+l2co5IPBf8KpiEsAP1xxFdQ9lE\nhlX62UGcLck9SLcXO50ieRMNC2RXw7N/kHzRKzDiMKZ4yGxUVUkCNkcG9ZA65P2voFBHbG7Bmh7B\ngFU0RuB2QJBuL8g5MFlEQ0eq5qR8N4U8GTiDzO9gGFqsGgy7iI0ipmdetCwMz2BDBlZe8VbUnwdi\nMMiXVKdXzaQUCVf/J+r1I6RiE3v0avLep6DpOKYFyWtkt4S4Q0i7RuiEofth3nPjnRyaZy55gke1\nYN/Kp7l0z6WYWEPYgNRDmJP0JEO5SJ3Xwb2UbnKUWb3C5AVvxOX6YcvN/6wd1SfeIqzusjiXCYOA\nCks7LMqAdQZnwdiRAsopYUXoO2XohY0ziZhBs7Drsjez70k/8MBjZkgZ4l+9hip9GCQT2zlqb8UK\naA+23GKdxSMpI5WDsADNabQHmTrYDOQStDVYvgYW7oBwFsrjiJO7Sd9zLb4wD0pH3vGJf0t/7HV4\nmxmt4chxL+8EVDBWcB76TqlKIcSMiMFiaJtEHBx975k3PVEzl313SyEeMQ/vsX79DRdS+DnTqaGu\nDZMSilIoC8V7wTtBthwVjIKWlISQYBgyfYC2U/peaeaZpoNmlmlapWs8r//1Iw87h3tv/x+cuumV\n1FXEWgckulbZtdeQUsaIwXolhjGKFxFiEHLM5GTo2kwzE/ogFPWUy150FNz0YceNmuk7xb/reZj2\nNG7HQWj3g14Pw0C2YAIQBHZZOD0h5g3c0hRiC7NMSuMZsoPHOqCEpAExl9PNM8V0L/zL30J3XYhz\nk390uZRBI3FdmFz19LHOVc4hJeAwdBABl0ED6ATMsAuKk2RroMloAKyQW8FHAwsGTRD9gO8uIxaO\n0Bh45QepqMA8eMAEoDHzsbd/MzvqvyenRLUAZeFo20BRjuVQ58eaaVkyChjcuE8xZrwb92boMn1j\naVqLYaCRx/GM77odFUbD/QgxOs4G2oYz7/4hVuQ0DAtg5hh3L9jTY3bSLpCM4GyCukGjR2eKqZ4O\nxbWQE/RKNE+BrsVpB+4oSSMmLpJ1P2pOYcsLSHNBvvoVDE/5V9Te81AmUVVJRIw6huEM+V0vZBIc\n6s6Q8wqwiTUJ8m1oGO4vfqnZieTHQT5DSKdx0w2SZrxOCLHBzVbIaYaxU9Qphiman0BsD2AXltFk\nSHEf6RV/gXcWa+UR1UOHHHDGQlY0dEQx2Pf/FE4job0R50u0GTB1QMkQLXAM6CBB1nOxaTeUO9F0\nkuSmGHcLGIW8hOgm0mzSzE5QLngkBCTsIffLYNfJqmDOxSwuMy9X8S99M5UasjiMUUTNFzncB3NU\n/7RyqkeAD/zROdS1UJSZ2I1Guqx1dFLWUtWKMqasMQWcA8gYmynrzPIq7NjhKEvh0PWvQvMDjZIJ\nAsPG9fhww5i2xTtx5la8ClJ4pIJBhG4uNBpIukrWnUQzJbkaymVYT5ANJhisU7K5hrC5wdAfoutu\no2920Pzta7Che9DvPX3Hb2NNwhXK5rpSlIrzgBqsk7F2gVLVkCRTlEI9EbImygqcT6TUYG2i8nDb\nX04fkQLrwD1/h7MNdQ2TEqa1Mp3AwgSmE2EyUepamdSGaS1MamEygclEmU6UaW2YVMJkYqgqoaoN\nVQllBWVhsHYY1/UhoClz9JOvZFpnrBVmG4qIQdTTtZmcoaw8gsE5wTrBeYsvM1VlKEphsgDTBUtV\nAmnGDW/bQUwPOSqqEas9xbu/FZmfRNmAjUUIn9q6kzVmEEBQa2AAtVOcTNF2Dr1ADSYYfBRsGVBJ\nxMYguhuJxynKJTa7U5j3/huszWgOW6Pfl8uD7eZMrnwJGsNoDttT5O4wORlUDK4FtZ5YG9TVRN0E\nt4BpMsYbbAlmU7FZUR/JMaFthe12kIvDEBaZJ0P6w+8mZTMa7IfA5vG/x8tHqCrBekWAdh5JCeqJ\nIBbQRD0xiDFYC1kjxuj49wioYo3B+YyxkS4IC+VBPnfFMlnDw57L+/YIhUBiCAn9wA8xbY8hOWOq\nexFzENhE5z3GGHANIpugHcQC6QzGRZJ+gjBEcgcYg22uw9qDoIegjegAsIi1AfqL0fYMaUjMP/46\n6vV7x5RbEw94irfExg6PhINUV/4wtTii80gxxRaHif0twE1oSqQIki0yBenXEXcrsTlC4dfQPuO7\ngrDRYBII64QkiAzACsr5aLdKtKcxydLNP0chgn3rU3FxTsKB5gee5z9ANh6TDbmfYWWO/4vn48LN\nMHwcSRV0lugbCJtIvAvR60htA+3GlqBKyf4wOb+brJ/EFe9GzD3IzGCGw2i4C12fMbEgTUCa/cjE\nY5fuRIrzSaxh8gY2rrPEGtU7fooNW0COqA6oPvI86SvqqD78Nz/CrukRykKIQamXFGcyi0slMUE9\nTWhWiqnHFyXWGIaQCVmxW5drMjEgEV8IK36da//8cV80TkYxESYf+HFsyOS4geaN0UBkGJqIKfdR\nlL9FvfJiFsqvwa08CWO+ARfvJa4rktahqMiDgjjIikmJ2A/YPGBsRuaB6ugnaX31gN/70TcJCwuj\ncZcEu/dZnBsdlHMe6wzTBUsIijFjvShnyEHxXjFWqaewuAKTGiaVA0ncdOVzyfmhj+373vdmCidU\n3lFWwqS2VDXUFVSVUhVKXSpVmakqqAulKoSyhLKU0cFVQl3ApNpyUoWhKgVfKFXl+Jmfv/whZqB8\n6i0VSzsEYxWDUk8TkFlYtvcf2hB7nLcYC8ZAzhlvLEqmKMBaWFwWFhaEqlS0Dtz2F46UHswoKykD\nf/2/QQu+Fpw5CnlUd2YSNraQSrRyYDL0zwfjWJ+eg6y8im4oyfMKSeM5bdchNYqJEQmC6AYip/Gp\nZm29pXvLy7hfnqiK5sxcZ+g7XwqxJ+cW9CaQFqMGbTM5ZrAGkRJTPBnC+bgd38NQP484+WoYKnJX\nEAdIQdFg0HUBnSNaYPoZOQ4UTLDdGWxzM4M8uKOKUbn1qm9mx6JirFBVDiNjbc3bgjAok6nHeB2z\nJ2/GM2kN1hl8YUDGWrKxQlbFG6EuldAllBmf/dvLiGH+kOcSRjZEBQqZUfz5szHzTYrKQi7J/VFS\nOEbu18AkiBkxeVQ9Z0uXFTUBtWAoIYB0ChuCeIeEYcwOLLhkYJihcQM7+RjIHFsnulkg/u230+t4\n3vSBXIBkBg3M+4S+64cgbCDDcVz9WegzDGuUZQ9tBpvHgNol9CTIUkHaSFhrwIAtp7Bk8ZYxUDKK\nKwLaZczmESR/BjP9SwqZE+iZFJfSDIcpiv3M//C5hLy5lYk/PKJAXv80w1+/CiOZ2FeonoOrjiFy\nBybdjJoDqEZoHo9d3AQ3JW5uYt2NpHgQ03To0EF3ATIMCAdg8yRmZmBZoASjUyTD0B2GoUbDNfTD\nAkZaCJE+lqR8E8t/9EJ6DFFrxMRH9A3wFXRUmkHPvImFhZK6UhYXJxSFx1eGoeuwBowRVD3tLOLK\nDluMgoqlhRKSwYrDOoMIW9SEUtUHgC+M5ARFXYCZB7kdo4eQAQwZsSXl8R3kPgC/SJ6cRvUE2OcR\nJstg9lOKhVbJswapHblPhE0htuDFoL7EdrsopueRhxpz51+NxvEf4F3/91exuDIBIGfBFECOTBdh\nadmSUsS5MYrxJWAzKYP3gjgz1lfc2JZQllDW4IrEpBKGtQ+ReMBUEoDX/tYKfTfQn/5htH0uORbk\nIEgWREaHWDjBeaEoFO8yvhizvcKBt+CdGetp1iAKVh1GLEZLpjyXuPbduPzN/PHbf/wB55Dna9gq\nYGzCF4aYBW+E5ZUasR1LKxYRqGuLKohTxCjWKmoyvhZiSvgaYgpMFsB5qApBjTLX2YOcMwP05GYN\nlVNjdJ0jDAGTltDCkLUAn5ATho3lF5B2vRhhxlI9oe3eR5ZEnvTkmLA4vAdXelSU7vRxGBpMcyup\nXYN+Rtce4jQKJATBZGHx8AGsW6SL92DTSUgCnSfNM2Z5BRM9iIX5DDGXIMWlzPhTNjf/giGsAQ1m\nFnELgsciRkgmEoZEnB1D+wHitQztnWi/l6O//+MQHzh4STRc88clVR0JKeNsoG8iSE89sfgy4AuL\ntWNm6zwoEWMVMYxBwdYB94XivLKy01FOEs7D0kKBtwbX3obz6w8aRN33ryoBUUhvfTn4vaS8Rgxr\naDiBiZsjHYoB9pETxGGKsEiySjUNqOxDooG+w3cgE4EdCe2V3CihAQmA94R+EzGKdsuI7SCVTJcX\naU+BeedriMljHtAJJEzbMrz3GUi/jA6b4xese9RcS+rW0WRJAjQyZptJSBXQG6zv0diAQprPGU61\noIItgRasGKTuoUio9mMfmwfT3UwwhyjKZZBTOJZp3/trYAwxPbChVx1ZKEmZND+J/exvUqR7UdnA\n2QHkZrRrwM6xGXIDQgB3AJkJhDmmUGgdLgxgCqwooT1E30IKCQoBn2DWoKkA5mAOUMwgDDOsWWV5\nsossEzA1cuYOXOOZN0eYv/376OO9hBi25vrweIz0OY8ef/DvCp71TQbRhIiiKQAZ7xUVIfYwdIai\nDhS1ZRgSZalgSzbXB8o6M/RC30FRwtAlysJgosI/6jeS5MjX/Cpaz5AMdAM5KUY9MXRwboc0nrT0\nYoysQPMxwvG3Yr/qxRCfBnIHmr8Fc+JD4HajnCHPW3wtoNCcWCNMPgobe1kPT2LPFT+H/bmXcB/f\n/fF3fB27pgepqhZjlLKCPICrYRiUohCWVgqGoUMMVDVbMudEVXk2N/pRaBGVMGQmk3E9NI90WWWh\nOfhplvd/9QOutbMFuXwvu86zVH4ZH3+ateOJmXPs2LGDNG1p/EcRDmDNQJaAyNgXFqMj50UMl9K1\nj6NrSmZn1tjYnBOD4hyY6dtZ3neGjXnk7z+W+cHvfOMXjP9Xb9zF+TtPs7DocT6Sc2Zh4sgm0Q8d\nXSv4IjGZCkkzxmecc6OQYxhFFCYJxoNkZWHREYatqBXFq3LXn+3i8pd9MdUkJmHXjiFyDEtHDuuY\nmNEI2W8yFE/Ez24jI8hZ/47l4f3k+gbiBd8EZ3ZR2iPIvXcTd4Bxjr5L5Cxj31yfcQVodHRZWSrm\n9HY/J0/Anpv/hvTkl2AFghXcR16NunVMnoHroRc0Dti6YgiWIhtiVpw/jxwX0T3KdP3bWFh6AnCE\ncM0dNAvKcu/pY6AQi00ju6cWJHmc3cey2aQ3A2ornPvivr5MD6mhqgOuGDUZWKgWwaFkjdRTSxgy\nxgwU5eiwhjYQVUlBqSYjyzupCmIfMHUmtJnlnYbZekYkj1Rhr3z6befw5O9do2T5iw/mlpHSLGBP\nYgsDISAF+HgMaLboZANDRuQIUjp0OmGIp7D22bC2A7Hv49TOJ7Dqnkl36k8pQ0C6CZJ71Iy3cGig\nHAwuC8PsKEW9B/pNsKehnxBiTXXsUxTxFnp3ASVuFHeIErPB5aOkK/89S+0q4m6GXEC4e7zIgVG8\nUjjsvBrpx4We7gQs+4ruvIFqSNjicob+LsSvUixF9MxJch5FFPR5pAtyJjejqMgmZeihYEbQg2g6\nnyGts+PYNSQx+NiPdu4fKTxFEjE4Sj8nXPlqbDoC5RQJjtgapDhGjlv1UGW0iVHHenkAsQYxHjXP\nRfIHSbFDFJxZJsQzYy03C2RFpgU0w7idBnQKPhQwOCh6LBWpaymMJ8WBtVNrnCOnCGfuIEyfhqnz\nON7DyCW+Yo5qM+5F9TAxZpw3GMPWiikpK5OpgEmkaMAkdCt919RjnYC1FAUUhaHZjEynBbMU6FpI\nmxG7/PlLGiyU91xJimtIbBBVcIZBAsXO1xDbNxAkw6F3EHdOqdd2kS//Dly/l/72/wuVxGb3EXYW\nezDNUaQVfGnIvaIRysrgB8v6+jFWVmbMp8+lzgmMI8dEbj/OdJIhG8SAdaP0vCwdzSzjTGRjTamq\nPFID1m5liZYQAlVtyQHKKmMQ2iZR146OvCVhh9mR//mAjqrr1++XoNeTzOJ0jar6bbw346MKApaC\nsvwGFqbfi7AbkUWcXaAfzpDSGUI8SdvdzFD+d0rbsXOqTIZM12eaNjFvMqZU3DBSlsPQUBRj9njv\nHVeyd7pOWQA5YKxBFYYUcWZ09DtWZKzhODOKFQRyTverxpwXiJAVrPU084D3QlGODcopJvw0olm/\nWGkWLfqBnyQVM2TWYNWPvKtEbCfU6RRpz49j8hKkBs0DORa4Oz9O3vuzSHEOuv/TpPkRvBWKZJEY\nySkhzmMIZAKpE/rqBG44RR8eT7jqt+CSF2GjIfgZvjBoN0NiCxrIQchWibnHz3cz1Bei5UHM0JPc\nBnbzXGbFfhbkMAzn4s+7mMnGneQ+4Y2AJkwCMynQHOhCIMVDFNPd2OZT7OYc2vf9FgvP/Rnwn7/m\n91z/R2zc8WrKSrAWrFViEIwYxCa8F2JMFJVQTwDyKE2fgldHdomcdKRqNWFKQZPgvJKSUtaGMIx1\nHuvGPzKqKr4IstUCkXLH/B3fzmKYo8kgehxyRw6KGIPmjK0gpydCf4RswA8ZLQ+iKxeS185nabNB\nuyuouAi1NzKkjn4zUzgoxWN8IJsOskWCkOJpbGnQdDNpfglFtcT6PLH531/JBa9+L6Bb6lfFJGVu\nz6FavwXDKkO/SVHvJjO+kGFShsKS2wFMj13Zh/M/id33R3TT51Cc+mO6vV+LO3UulE/FputgfoY4\nazGOMZMWQz+LlBOHNREGRQ147zBmiisibbOJzlZYp6H63WfCKz+OUf2CpR05GcFKQP/4XFz1dPom\n4/1pjFGcPXZ/BiO5JFrFuzAKeNSgVpEsqK3I6Rq8xpF9WqoJG6cpLDD1aJfGCsh6QJygTjA5I72g\nPqByHEnkhTqeAAAgAElEQVRjCceaGuUsRBc464JMaKD5s3/N0qs+RNISyQ//gsVXjPp79esOkQIY\nOzonMRHrBMFSFI4UFIIlx9EY5TxKY3MWxDlCL/R9oh8SqkpmwJeZpZ3KrVcto6m9f6xEInfraK4Q\nOTN68KS41sHR38XMz8EOSzi7yvTEeZidFyGnbyJuvhl//o/hViesADEcIXUOkoGkZISA0DWGpIFq\nYtBgiM1t6DAeH+2PjDRAhNILgpKHkU4jZYoqUy+CLxPGW/rWEMPIlXdNIiXl1OGEMQoZhl6xVkAS\nhTN4b0CV9WNvfKBl5jde/0QKLxQOCg9lOYomlhYTO1cT+85KnHv+nLPOfg9LO36NpZ2vYXHHj1Mv\n/wDLu36a5V3/mZXdr2fXvvex7+wZu8+KrOzMLC5BPRmzWe8F5xjrF1Z59S/tv3/8d//eCzEax4xI\n7Dh/wBmDk7FIb/zWBcuKMZGsGV+MkuiycvTrY92ucKPE1heOEO5TKUasUQorpPzFGVW0ipEJppsj\nzCF3aAxghFBm8sIp7NpV5GoVWTqALF6Kved1DI//z+TuGPHgHxIPHKFYvITZRhjflPIleaakIZBb\nS7sOGhTTD8znM86e3ED0E7wm1HVMTp9iaA8gWfB2BlkwlQcjVMtPwzRHKIbrobXI8YahuxnX38ti\nuYnMNonpenTjJloZwO9ANKOtoqUnNoHcWEpjKHNNe+Q4m5snOdWsY+58B+o/T6ysr93OgU/9JEJP\nWQlFCdaNZ6MswFcWa6GqCqbTihgMQz/Wn0pvsC4hTlFGMYXGjCaFNAZM3itVnUdBVGkBxQtc8+dn\nPbghsIK4gqXJ4xGmpHQCiXMY0ih+cBlTFGheZLO/G3Y8B19uIDuej+kHxJ/Arr4cY76FZvU70d3/\nC3JQKDYyXu4rayXEFpjsiH0kDQkko72n7wus2aCq91NZw0IhtAJRxyBK1ZDsDPfh12AWziJPTuL8\nFNJdGAUTFLwjZ0euz0GjQ6hp0mtxmwcoN6+lX/p+ikMfwy1dwmCuIeZ1GO7FlCU2yGihdGRWyGPg\ngPGkDYPkjPYz8uZxXCrpqpuY6Nk0xTmcRhD9QpoyJJB4lP6zv4EsPx1NpyknFtJxiHdAPAUdWBU0\nRnzaUvgOhuzHhmCzdCkhG9SuknU/Uj6ZMCzgJ49nvrFA6JeJwZKix2zZZe0zOVrIkDcZa299hw4Z\nkwb69k6IDWmzIOWOspjQXPlLDJoIj6DH5isqprAeyB4Rw2xz3KCUMt0sggjWZ1wxPuNTlmMjaMpK\nt5Gwasb6g8LSTos1gvdCWRgWl3quu2KB+1hw1x5F0gQ3HEfS+CKAKIh6eMKPkIeTSDbYONDUNzIc\n+DTmznfhl/81ZmWCDE8nuAHTWUQjEUiDQBoLyLGP2FySm0w4PSdvHsbIcQBMfQ7ksaG2bTP1xGIM\nVPVYjPYGQlBQIaeMKzJKJgUZVX4Odu4x43NGQF0DoqRhVAv6cqzlSX7g1Nk7M0reLZj7eqXs+Hud\nF7wf61FlpUyqzLRWFiawUCtllalqpSyFohjX1zrBGcHa0ViZrd9ntqLzsY3g88Zxef/LqCtL1kxO\n9wkkFGszYhLesNUnJ1iftqTxSg6GnJUYIws7xsuoZuynEhepKhnpSRlf7sgRrnvXi77o+zX10B0i\nxxJj5mOID9BlvL+EvLGbTm9juOmX6D73d4Tbr0DO+WmK9hDZ7cL4RYp9u+juuJmF3cvE3tCv9bjK\nYyxESVuvaNitoAm6Wcmwdoy0dgqhhr/6NqTfSRqGkTWwDh3C+N7OmWuRpWWaMlFuHqaXGWX9L8hL\nZ5GPH0HPfyHm+FX0AZZ6JYYTqBRokvEsm1Gp2HYZ4xPiDU6UWu6inzmaLeVdyKf5zNsvZTIRCj++\nUDm2HyhqBFsarHWIKM1soG07YKTlY0qEMAoYisIibLECW7Sc2WoADmEMKMdOCaUoHM4bVip9QDVu\nYFwv/fTvEsMNDN1RhICGAc1gCpBkyU0kznoWFp+IyJTgfxTCTobVl5HzM8n3XoGZnMMk1kh5BD1f\noXoJsQerBqeQYiIlwRWGcmFsC8mhpUgJrGV9453MQ2JKwh68FhVFRTESEZlSHvoYOR/DhhbyGoTx\nbU6NOtbvqh579CRWIr3cxbT4Udj780h6GkVxIWb/r0I+zEL9MnxxGcxa7NkvZ20AskP6hNh6fO8z\nKtoGxOWtWrIlRqHSNep2jT6fIYbIjk/8Lu19UR5jbcpFZcOdS3XoSmg8hgFSxlS7yZJJ0m8RV4Ko\nQRnGH99RwfTHcNPnkOYHqeQ5FP0Bmp33ovXlsPgykrUUKwmf1qAN5FnYeh3AQAAdEmSwTjGiOAtF\nZVAJONlFl9YJqaM97pkPGww3/T299RT5wVXS9+Er6qhCUIyNpJSxhUFklC37rciiG8aC9H21zRgz\neRBOHEusnR7wBRSl0oUEBnxhaTYzQibEzH01XHPwOsCBUzSM/UuqoK6lv/pNDNpip3toGSjTk7AX\nXEpqLfm6HyHf8KvY7jomCr72oBbRzNBnNjaFZpYxxjCfB5I6cgLbdwwHrwJAjKHe/fVkgboe+1qM\nEcIwNvIa7xD1iI6H0pvxrTbV0XGrQN+NhiBHJetoLKwVlMRkQammys69yj3vrFG+UFQgknFmdCCl\nlfsbi42AMxljFCMZJxHrMtYljE2oAWt0/HOfIxJwhlG1ZwzWypboRfGWUfzgvrA0+h2vfBPZGHzh\n8cUobKkmI82Xk8H4kbokK7M1CL3FGjsayDg657ZRxBnC4EYJuzeEkMjZUE+EolImS8okfJgBRln3\nFszRq9GhwoXxxQdi2qpPQWhuxZnTJDclDxlfd6Pi6+430H/oNynsEvbsZ5DzfvzEkM8ErIFyWhCb\nSOpHI2JxaFRiA2kGaaOj649h1z9DiIBzGN9h9RDEBDEhCax4uOhniOapFMnR1pdhdnwj7u6/wdz4\ne5xsribe/iMwfQLV/heM92AuEAIhC6kDohL6gdkZ6DYHUqeYzrN2uiJWEGSkYH1awBU90xKIo7LN\neWFSebyxoxScwNDDdAligBQNRTXWAp0zgGLFMpk6bPZYKfE24dzYmA1jxt93ipFETInCK176++X6\n/xBWLCa2+Ft+D7NxE66a4Gwca9bKaEhnuxmWM+iAqZ6Fhh5/1rnMVh2heRddez1hdZV08hOk9Y/T\nhwtJ7nvR9v3U1jIMABYbEtZEQpPRqOQI6/NM3yUquZcVtfh2ja45xsk//QmSZoJGSI7cHqbVCbbJ\nQId0A2RBU0IWLZIKiJa02sFZ/we+fBHJBMj3MtuxjAxXMbvuP6L+EnK+G/Hn0U2ntCf/J4u794wl\nDrNMs9bAjkWGIIi3uGI0+nlIECMbeYZxzybpcaa5x135WmrNJOLYspWEvjzJ8jWvJ3Y7mPcnUVuD\n3gbxECYrNgAFpHkmVxkpnoTMBdMNNJtvhNMfYvOsrycs7EOrr2HhQMtQXEvb/jdsvg2XnstggGIB\nHw2aI/MhYcbeccDdv+bzDQibHZICoTmMi7dC62DpLuq0ik56dvz1j9Jkw9hF+OD4ijqqHCzWFhjj\nCCEDW4qvsUtuSw48RvLNPNPPhayZ1d2ACClAs6kQR8lz0oQRTzODe47UHLr1D8aPPHEdasZHTTUy\nZlQJpLfIzgUmpxL97HZC9uRwEHPoGnIRkb4iHlgAGYi90sy6MXNJGeMZswRjGIZM12W6Jm45w4S/\n7Y77v3PfZS9DMsQ4OuWuG7OLYQiUlSGFSEbwXsk5jbSnjBSfJkFIdJsQe4jBMJtlJkuMTyt1easJ\nMJML5TN/vvgFayxbLwqMLxWMNS6R8WfF3Pc0zphpeZPwJuGsbjmx8T0lEd36/6OjERHE6NbfP8+R\ni8iocvvHGz2zW45FMQKC3SpUCyHA0IEmwYqlKBPGJUJgVHFWHqGi3wCPYO2YWZelHxVnzuAcVLVQ\nL/Tc9W6H5snnxz56AxgPjjFIyWO/os0gS+fRmwWKkwOTs56IGXqKxY4YEjFmuo+/inTjGzH5LnzM\nSD9GkO18QNTQdopmIQbL+tpYX+yjMDSZKnXMbvu7sR/F7h6bmwVIo1xdVcEEhg/+PtIfRtZa6v5p\n+PpG+mqdWdGzGAfchsDhG4kHPoBV8JOCnMdnxWLIbGwqRgq8F/p+bAUKg+J8hw9zTBiddm+L8dmj\nrChC6AXING1AzIAxfquHUQi9Z2GxZDK1jCypp20TYRgVf30fGQiEQcf7aw1FmakqYefqhHLr+YGi\nHF8vyVm5584/+aL7L9qitkaqCzHNxeQUIc/u71mKMSN6kso9HZ9AZA2xTydd8x+ZHHwzEifU/y97\nbx5sW3bX933WtIcz3Hvf0O+9fj231C2pGyEhCRCCIhIChUnQSDKQEMDEmJQglRADrhhiYseAkZUq\nDOUYT2VILBJjQI4BY8AgJCwRGSEhNE+tbnX36zfe6ZyzpzX98sc673VLrRYGUxZVyap6dW9V3z57\nn7P32b/1+/6+w+G/RJ/8KuwLvwJ77/+Mqx9GX/555ObbyCcSzVzIY0CJxseC4mjV4KjYWRZUREfF\n8bUjlHycqZ+4aa+illhE+xqqd/492vQgWR+RpkimIwtkrchDJvUaRo04Tbf/w+BPkeyEnHgh88tv\nQC2+iPbMa5GD9xM/+svgLqOWz6K6IJiLh4QhIeuOmYXh4QNcLaQhETpY72cOVwmVNHO5hJn+HZU/\nZn34AR43t5LHNSalQkyxYDiJPPj92O4aMzqYDguVfRoLGTqpMgdeVsh4hnDmLqLKMHsFy3aJzL8V\ne/U3cfn3UIt74fb/ltp/DbNTf51BXg03naba1wRbMQFkjZ0gicYaQw6ZylakIWGldN5hsLidkxh9\nG/A4jb6NSU9Um7OE9/0W2ghBiuTn6dZntVCJJKbJs1llKlMG6DGWQW2M28IVS/fhlCsQ19apYL4r\naGXZ22uRdL3dtEQJ5GS59d5b+Nc/8yYA/K1fgHINWYrDsRhVBjZVwnCVfKpYB+3ub+ge8YzZILVH\n6ow61eP3B4xYbCElcfUIslfMnCaPRdxn9PU2VyO2pndPDAfPnnttEQu67SNdq0KmaDTdKhRIDCFK\ngTurutxXKWrGtRC9JUXNNICrYLlTbI2SUNocKVorxKNFE9KTOgqlbuiBlS5fPIXcsF5SbJk/ZKBo\nVEDdcKfY8i3K70ohSj9pMF6KzSepy7fd4JNXjBOSMt5nFIq+S4Ux6MpOPEewjcZPglKGqb/uSA1+\nyIQ4oLSm24SinFVxKyYVJJcCmAPcdLNFB8V7fn7JdTxErr0fRURisWiSUMSlRIXd/wSmWmGcgvBR\nkqvpHrHoW78Cc9/dVGGBVgo2hxwPwhADvo+oqAg5Ixo6H+n7qcxssinw89KwPjyiOtrH0sHyFChN\njoV8QwaJoCJUz/oa1OHDhUW4+3+weSxRY1mcfYDGD5AsBoWECRYLgg9MQ2Lr1IWtFMedxxhHzqCy\nRnRBIS4/+jF2tjOMmoxkS05lNhVjxlqDpsCW4zQy9oLKwu5JzdBPrI4DdWNxVSE7GVXMabUG8Rll\nPf3oyUmjxICC4+Me5wyLHUc7L/B1Dorxg9//lO+/okUNB0j/OMw8Nl4u120Lz1oMce8uOHwnsgfj\nY/+C9NjfYJp20A+Cq+9D3f09uOkyfPhfwSO/iH7k18rc+MEP4diFUaEXLeI1TgosmVJmigkfBOcM\n/eBxraYylpn+ON1hS776CDoJqMB06W2IatBhgZIjjNVls2MdWmmkFcJxQF/WzFYZqj9A73+YPLwL\ndeq/J/XvI3zsn8Hd9+PufS1s9qk/9oeYszW+jhjtgAqaGq0LghIzVJWlqTRNVbwuV/uZNMG1C4+w\nYMOJs7czfPDXyLZAthmo0gaVvhF2ekQ1oDPCdTG+Ai0YZ0i9h1tejrv0cWwNiYdg9qPk9M+Znf5a\nWL4A7J0IIym9DbP+XepHf4m8+nn8FGnO/BChVmStqCqLlszqOBElMW6KK4czjuBB60i4sofvP4Ej\nMlz997hwAt9Y7Om7cIePIIqyg3ya9VktVM9++fvQWuOqTIqKfrMlS6CoKoOQGLoyj0EJWhlysLSz\nQjnvusDhvgcxTBvD+kqkO4KmdXTTw9z7vIJ9ujufg0wdwnmoFCpmCLngtAHiWrDHCpZw4rymtTBb\nw3S1J4+C8o4YE2GEOAm7O4ZhgDFnkgg6WoaJYkOSM4cHI7E9+cQbdYmQoe/KhQhBiAn8lLfMKqgq\nRwogqWIaFXXl6FeRZmbARurGMJvXJK/xvSZ5xXxRyAsqO1bHlmGAD30wc+nt337j0CJClvLgFymE\nDERtWVv6hrgxiyKJLkNh2eaBbQuOUCCuvLVZkO1/S6it7c11/4XtjfYpLijD3kuxTlNVEFNhM02j\nwo+aMAW0UuSQWZ6Evovl5bxBKcOsbdCi2KwSxgpCjVYVVWtpFqC2MzIllkuPBsZJo/TwxJjs3P2I\nqUDqAk0YVQZlDkIlmF6h6i9Hnf0GUtUyj5H+Q2+mWl1EPfeLCdeE5BU7zqA9pTNylhwr4lRYgMYU\nq6DVqpz76DPNfI8pBbxqyZtV8RHMBTHIAtppxIEc/wLKBmTvZayjYnnifriU8A//JsfVxPpaIHaK\n6CEe9EgsThDXjoX1SkECEyHnAGLoukSMmlo5zp89/8Q3XGu++NWPgSr2R/OFQ2VVnPnHhKSyeYoZ\n+k0qgnbRxCERpohzpfsdelCmCLLns4qxg2mMpFweptZUxBjwPtC0iqqBk2fBuH3e+8Yl8UkIjwDx\n7a9H0gyReZnfpbg15S2eeWl6CGnPoupTNGd2yTunaU6/hHTvC5DpDzg6+HWGR99I9MdsPvJ/k64k\n9N452qUBtyRNis21kSkl+nUiek0OmeQTMrkbMyCZFOkw0I0LUtXA+kGUskwCZlIkv0PMK7TxW8a8\nQnxEugQ3fSnu5iXmxMsJM4tcOCCOgn73L5LSO7Dxduov+UvoK28l7d1OGtdw63/OeFhRxUwygqIn\nbTxaoHEFJejHSNbFIaRylqrRuEYzX8Dg13TXPs4n3vqTKFkT0WgRePN3g3sXweyjq548HKJ8QWZS\nKAjAMCaCBfPI70N3iX5wGP21pPyzKL1HOroKj72FNF5lPPo3hOVXQf15qOf/PbT5aqo7bkNf+gHq\n4IqJtMvkZNlpy1ii1qCUI7mw1YEKqnmYjDCla8xOPZO8+jWuXbrA5foWxn/7vxHJlJ33p1+f1UJV\n3XQ3MSZigBiKCWuKMAwJP5UZjXVll+2nQAqJEAIpaKZRqFzpsoY+cryfCbE4KRweDjzyPs3zP//r\nAPAsoHIY6yE6xBamnAK0MlSNRUhk55ApE8NYBqlWQAu6VXgRTOsYYiSlhHNAVIhWYBOLmUHydu5i\nFTuf9xduvE8RodYO52AYhLa2pUgqxdAVE9z1KqDRbI49RltUTrQzyzSUbi3nTD9MHFwNgMKPiaEX\nqkqTTWC2CDz2SMMdL7iTQZ5gPGYpdNMsbAsWJCnD7ZwzOW/nXxlyssSoSUmTs0ayIuXiXp62hS7f\n+Ke2/onl95xUea30ZCpFWS/5+l8n5UzwGkWZdzStAh23WqgCMXWrTFVpQgA7g+yFo4MOH4sjR/Cg\nKRuGMMDYlx2ytRXjUOIWfu93Ix+5eBfX2z67+2wIAyILxBaoR1KZdbqsUUkjR/8W+cgbqbtD5HZh\nJolwbU33gV/HOY1Y2XasGm2FfsxMacIYSzRF6wIKaxXTJFu9W4dd3ITVBnEWkQZTnUbXFpNLR5In\nyFETgpAv/S7Lwxa/ejuyNOg0sewmFpUjGWjmNVnKsTKKuimWVko78rbwQ/FujEEYp0A/HpLNEzCo\nmZ1Bm0JYSjltEYzirykI2hRvRyVFy1i3QlLbeaTSWAdtW+xSBM3hVSFN4IeCetRVTVVrmnn5LPyQ\naRqL0dAuMoaBd/zcM7h+hySZkGtvJStD9CvwY6FJAzlk8pixBxG1vAz2Fg4PBtyZzyH430It7qM6\n+63s3fxdGP0w9tp7qM6NmBMJc/ki0iXS1QvFPzKWuJruEFLOdEMsuWsm020iIQQ2U6IbPGHcEKcr\nrD76KwgZlwK2BruIGHsFUkAlQdKWvl6Buvhm+sfWdKs3UdVfC7OJql4SbzlPPH4P4/G/Iu3/Dmn1\nOHzoO9C6x7/7d2jWA/3GolOF0xZtDSEUopYkTRwMRCEOtjCkxTBsAnSK1REYySzGy+S4g82gQo88\n9ibYHBNXkEdB6w0pCqqtyljCKtqpxp39Xugegd0vYLZskHSVLDehx11cfg7dzV+DyZepeBVN/xDp\n8LdR4VeRnc9Fdu8mXc24URgPAna9QOcEGMIqIRVICqQe+iMhD674Qa5gZhNq/QmoapZyQLt/he6h\n/6sUInn6OdVntVBpBeu+PCSnsQxhJSuq2tJ3BYrqN5qxy+RgCF7wY4G6jFH4EIgp0neKnDSuVtRz\ny9lzFc+8Uzh117cAUMuS2NxMDgZlnoMMurQFVhFyKlYwDuimYqGyxcddZVFGE7zHGsM4BmY1iFYE\nBZPSpCSMCEZt4ymcZhJBVU8YpRqtCQuDUpocK4Yhbmc710kBZR4Uo5CT4MdEFpjGjJCYeosQqWvF\nidOmQDwU0kEMBZLJovjYxyaOjh7h6vEX3jh2zkWblFLZrCYpMSkpQ0xlY1CMZw0hKmIq7yMkIWVN\nSgWGSLkM2LdcAHLhJZBy2Ynnbad1PZrkyUthsBTm4sGBQuJW/4VGYek2scxyRBHGTF0ZxrUpLC1r\naNuaFKGelxws7wMxZOqmRKCgE7bOeJ943hfVnDhxEdQEgL/pZlS7IOcaTekKlSi0M8R1JncBpYpD\nQ/YZdahRLhGBxaJmHDOGzJgzrp2z6QVDiSWJPjAMGVUp+r7E0yCCVZp+iMQz50kIhtJ55zSHGEtS\nh1KYukKNmcppJCZC7Khy3hJdIBynbfJz2VV7EaIqMx+rMznC0HmSFF/Ifoog3Cj2h/uXCemJEAtv\nAjEUNl7w5coI0LaOti3wclNZ/JRpastmrTDGkdJWApI0Q58JI0x9MaKtXEUKmrpV+DAR04QPW1ha\nmVIMJ6GpLdom9pYfJ+ciEDXK4LTHqoRFgclFc5WLk4SuFLI0DIcW7MSJk69BrQfipMkXf5Xwgb/N\n9Lt/heraGYJpEV+R0g6bVCApSRplwTQliHm+W+QvgmIzFKhqPq/oN2yFrtcFsMfM1gORTO4+CkMA\nBSolkgfZFqrsE1oUZhOp7JzWzojrt6LtrYTh97H6Hurbvp/q1NdA9wFUdxXi55MOP4K9e4IWZqcS\naTPgp8Q0FuPjcZNIKePa8hxwVdmMj0PAzRSmcty8q+kPH6TxN6GSImkQOy+UdN1Sm10UhyhVdHB+\nNWJchRZFaAzmyj/D35EJ9hwMp8nufZjVQ+As3XKJG/4xcvSrhMfewNSew8xfxrXhAsr8Bkfv+XeY\ncw2+Cri2JuaOGAWcwSoYR4pRuCoSvhjLfVnXmtW+ECdQcWLZXKLrH2Fv9wU005psn17W+9ktVLQ8\n75WPEzNodBmqeVgfJ+q27KCVLl1DSpmqNlSVwgdFiImhh+gr6rpEpQ8+sT6KrI4Seze/GGXKnCiq\nDPYMMbdkOYuY0pHFUbBKkUNCMiir0M4SgwZbXhPAtZYpJbKBqDR9At+AQ6ibilml6QMEyZjZLdxx\nx4vY2E9+p/WhI6WM5ERTWRDNel1IA9fdqMch0zSOyhVYrK4rRLbCX19mVsErlCpFzY+ZwyuK/UcV\nm33N579Eo5Rhz77lxpFzLq+dstoWK0WMTxSdlDUx6RKMmDRT1PioSEkToiLEUuDijaRftUVnMjkV\np4KcZPta2+j6T90ZKUP0FdYUp3bJiqETgi/dx2xu8D5jXdmIZF/O208lONJPE3Wj8X15CPtJSMEw\nbCB5w3icOb6mMNrSj8JjjweQGgCzuA8Rg24rkNtR2V3nyKNbjapBElRWs9mU39WgqJUmpwndWBAL\nWZPzWOZFWWFdBU6hE1hRaAtWObS2jFNmp16yc/8344hglthaoesZIjs0lnIOOiEWJCVsbXFKlVnW\nkEnrSEpCRZHtxWGicfPywFeKEDTHY0Jtz8FtPWidscSYmSK07Q7xSfdhlfN2JpmoKrbaJ7Ml+ZTu\nNsWAdUVEPd8phJ+UcpGGDELTaubzmrZx7JzyKJ0JoTxktdY4p2jnQjvTVE0CBBHL8WHET471uiLG\nUqiUTLA+KF1/NUfidn6YywxVJtCScNPdyCcexPvfIF59B2mClD0mTNQ7dzKoNWkccT5ijg9wGiaf\nMYviESrKopXQzhUxlzReaw3WaKYpYa1CK4XShWh0ePUKcTjEAubKIyStyf2A5EK/Vih0KhtGnCbs\n7WDnHensBOFW9GJBtgGpP0j3tr9KfOhnsY9GRjrs3c9lOE50xxpmlqnbQvJV0QlqAVsX6GzycHic\nOTgI1LVlmmB1EIkhsukyfjMw38l0DSQ8alojB1fI4QQpJ5Q+LsiNMVQ1iA+l07zzL0JYYfZPkx79\nRTq5BJ94J+n4Mr57iOq9/wCzuRc5822Y+7+E6ujtyLnnc+LoFrjwYZZna/yRwYWMnmssimpRMR16\nUirQpXNgrUVVjpgFyZp2Zoumy5YN9Gbt6K4+RN91yOUPoZ/GBg0+i84U15dpzqA5DfqQYa2YzRXG\nGsaNR9uyo+77TGVrkniyCLaOdCuF1orNOrBYNIUZ1wvHY+JF3/wglb3jxjEskL/oezn+N69iOQpW\nFqAOioBYyXVDDJTWxCnQLCzJR1zjGLzHj8WUM45C1AqTgV7IZAavMNKgZCSazMHRZe780r9MI/Un\nqfFv+bI/4JG3PoeYhOMjwVWZdqYLoUCDNQ5xRUM1Dlv3iSajrSbnCNlwfJCZLSiEhaw5vJqK6HaZ\niUGok+Lh35vxsr/7SzeO+8Pfd5n/9e/fTAiCD5oQMyEovNsSrMbXo8wOx4cZ50oeT/Fmy8XTTSVi\n8JQsedEAACAASURBVPjg2dlZME4X2e9ej3GZEEuBittCFmOBCf/B6w6ecp1TM1Epi9F6+1AsDhXj\nmEoelTWQHU3rESwxTWgM1jjCmEg5Y6wiBU1VFTPe9WH5DDeHjlkjTJL58B9lbrnvWcV9gqIXoj1F\nXh8whVNo9RDa1iXJ1Nhyd4gnCyx2NHhhtbWGqifLNEVyKn53ccv4nEQxpISYikwgBKGpNUOXSCqz\nOPNMnAuMs9PorJAHfgH5p8+jkTlK3Y3od5ct5yToBGIFFXIx7w4JawwbEVpnCam4lU+jIsaOrEpE\nVG4UvlEQHX7y1G2ZWW6OE2pmWLa7zJaWlkAJXAdRwjQWI2LJGltFRIpDffARow2mLjEvfhJkzJha\nIVojJiNOkKAYfCDE0lUmE2mXsD6E02csm2OPrcBVqdwXk+boKLJc1rztzRP3vejFXHzXf8cdL/4Z\nJqmpzRJlHXko71NS2YkrXeQqWYPhI6ioqATk7Jex87E3lcp8recgfpyT5xbs3/xczEPvQYei85pZ\ng6wi/VCKZRdh2C9iZGtLRImrCmrR97Cz4whJaNCcve1upphQePzFD6Bci2NG6lXRnwVB1wrtgT5j\n7TGcuwv3iYdB3g0XHVVyTOGjtLsNcusLmHYfxV28CA/+c5bLBBugnlNbx7C/QkdQzuGcRzlNNwV8\npHhaSsUweKrKbpmyAa0MRkHrIkckqqwJ7/gJXFtjWGPiZcrQm0IFNQV2l1pwH/tpciXo8ZkYOxHm\n7yQv7sVwL9N0iba5BKfupxsvUvkLsH4Y+aNvRz3UwgnDVAvzLtJnh7OC+MRmHam2ujcVC9O4oENx\nq7+E/UuexdIxDZFpyhgZ2TvVErGkS+9E3fyCp60Tn/VCpY3h/ldf4P2/1NI0muAFfETb8lDzUyzQ\nnETSmKlnhrFLNK0iJ8N8GYhh4niTqc/9RV78sn+IVp+c2SloplPnmbtbyOGYTddQqwqjEyYnqA1p\nApQmSkKGSK5gGD1NUyNMDB3giqeg0oo4CfUSZiTGOOGqEzgBU7fYV/wAn+oZ0566BVtpZCoPB72l\ntVunAUtMZTdycBV292C5sHgfiUP5abWhmQvLXc3xAShlaJsSb5LThK0VlVc893MDmk+mqPuQ8V7T\nbzR6+h+5cHyNtm256847MXt/hbZW3HRbES9fdzLJ6Bvsy7jtskYvBAR/UNNOf5VLH32EofeF9rv8\nBYLvyU/j2XVwIJw9GQiTwrmKbDxGFK66XjwTlUsFDl55mhaMzqQ0EqOCZFAmFlGjUyAWa6Bbe+pl\nYPICSfOiFxpIH+aGe7lS5HtfgjnoSFZw4RyEiyW5NkZstiirURGwiilk5jsObQLTAM2yIeeJg2vC\nJJ62KYQQZ4sPoV3A1FUkmXB1gdm77Nl75n+GSwrtMjkHkr2V1XCBJu3gBlBWQ5XJCnRU5Zs4CIXj\noqltRTAeDSSpSHhMDeu14KxGJWit0K89ZqGIg6bSCTeDoA0nzpxn8V1vKV3K9lseRePq0vUqHVmv\nYWc3FoKDUsQUCT04ByKZnBSNqgnjSD0zBRqtHV3naVuL70F0xOmaxTLifShWZp3HVcWFpd3RKG3p\nOs+d98DGvZ13vGOXO14MlbFgbkGF/ULFEVDOoGJCUkYZi4kZtCYMCvu4Ic9+C9qMOboDf+LDnBwD\n43HPqfwJMC2XeuHcCUhrzxSKT+QwlWTv5Qy0dUyxCJiDL4zHnBPDEEpcjAG//whnbnsJgRp1+/Mx\nj/92kThkjeRUbI9SKt8VU3hZ1cWHSGuLOfM3kb23YD72JtqdBVzesDn+f5gDB8/4HNqHPorpoN6r\niQf7qFDswWzl2PQTXUeZlwssZ6bMU4lIhtUmsrdTkbMha0tQhstXYTeDkTX28kcBV+LmxwEqs73Y\nBW5XUiz6DAL3/AA8/FO4VcQd1wyXPkx10yGzU19M5A9Rv/9rLBaCnN5wfOqV7MX341/65cj7/yHz\nMy+H/reZ2UIu01mzs0goV5N9IEchkotdnAPBMA2RxULhh8SJEzOOj0aCz4R+hOU+6uK7MC94qjfl\njTrxmYrIf6qllONZr/Ach2eRySgtTFNk7ENRzmeIOTJNijBBymVeJUiZqQg4V3P/S59apKCUjDZb\neMXfoWoFt7yFkGfk6MhqiZ9SscBPgaggGg0JvIcpTIXRZ4r1kWxZiao29F7Re8O0akgoYnMefdcr\ny4P1Kc/rObl6BSEUISNkJGvWq1zw6b5EjtRt6S7GId1g51kDmIR1hvWRInjFNAW6YWK9mpiCsFkJ\nOSte8uoLWPXJF/wv/Zdv4uDRb0HG7ySYH+f8nf+Ym+/8KVT7fQQKAWCcFKNXjJNi8Kq890mYvGL0\nMEyZaYDgFXY2sNb/C4tbf4bFrW+gOf0GmvQA/ZVv4Kdfd/XTXuMv+XZh3CxoG8PYe/quiEP7TRGU\ntk1VIucT7O5pdvfc1pgWJFi0i0Sv8TGAOA72EzFHFJaULVZrmpli1ijueMUbbxxXVEbd+51Qe2Cf\nqG9jvd7eFAJJlW5NDIgU0smwTmzWkFNkHEZiMrRL2J0X5nQ1K3EXWoRpELT1TAE23pJ3nsmO2mH5\nTT+LtqaIuXUN972GneY0WR/j61OMYxFwixFEb4MiG4sxmnHwJAmFmGPKRqSZW5R27C40ymZEZxoj\nNBUYFNolooIgLVLdyaWHHkXv7mypz2U5XTPwbKytivlxZZlGQIptV91o6lrjnKVpDO3MIExorRj7\n4ozup0TTaHIoBAwjLShPCCXG4nDfs1y64gqhNWmCafL4oWL3jEGM48xtxZNSEDh1D+IqtHOImZFC\nmeopisWPKNlCgQHsVRiAETzvJx4Hgtc4LfjDY1KaWDAR+7EwkAqSijOKkzuFwCQI2laI0iQU45iY\nzwrE3jYGLYZmZ06aWwxCrm5G28i0GQCFMmobu1b8NxGN6SH2YHYSbH4I9fBb6HKCu78ROa3gNDDA\nqUffD6fnTDtADXEURp/RWnF8HKjmFbu7ht1lyYwLoYSK9l0mBGgaxabzZU6YPE0VOXv+BClZjDqB\n9x8n+y3ptlJbqINSqBJgDMqXe394y0/SH2VyA6kZyHedY1KO2FxADmvifV9AOHMazD00l36XdO0h\n9MV/hB4UPPJmhhHiDCRlaCxjB2M/QTIMfSYm6AeNVg4/JWJSeK/JZNa9Z+gjYYAQDW4KPPTut/E0\n5jrAn5NCBeB2NC985XsZ5XlMxdUEpUtek1KanAoLqeg/Cu7tfXnYT1F47qs7lH5qkbqxtEV276O7\n95swao6TuxmnXfpNhGQYRQhRU5lyM08B7BJEatIIMQhihboSEoKqDYozTLKH2ztD5yeG5QnO/Rc/\ngbOf/mN9xst/GaUsooTkDTmy3dkrjLL4SREDHB7kco9lARPQtmh04lRu3mkAxCHZ0m0006ipFs/l\nnq9dwd7ppxz37E33Y3bfQKd+mill+gmmqQw9/VgKlJ9gGDP9KIyj0I8wTIphUoxjYZUNXhimxDRl\nxkGeiKf3mSvT/4lavPGpb3q7FJkxXX9oui0hRmOMIUyKfhMJAWbNHKUVq+OAD7HMl2wkR1to1Nmy\nWXuUKDarzGYTQTIhaTbHhpETnDzzJCslUXgqhlRzjBCcgLMkfwKrd1FZ8AJDKtCebR12VkSRUUDX\nGp8AW+jkSity0HhJZGMwumxi2spidGZOx9F8wJpVeWBsXTf05/5XeJ2R+gRTdwZMi49VgWUqiBrW\nfWTwGVUrsi0EihA1qlH4LHRTxlOcybMo1t6gbU0OdXHb5iwqR+w0Mv/y7yOr8JRQzS/8mt8j54Cm\niLCdNYxDodevj3NhhSbPep0YhuI12fcljTV6g9alPSsz1YTWmRgUSiqCLzPN9VExkz7a1+xfyGz2\nFTEFPvThTIyBMzvvAiATiS94bWHidQmJ54uJbUUR9KeSvUUSbG2K+1RjEQGrhLoG6zLGWKraIlmx\n2LGsNopujFy+BrNli3NSUIkafIikEMi5eOvZyqDwWEuRoGSFP+rQz/wKtFa482eLndl8F1M/o8Tt\nKMqM02jEZ0yrsbViWkthcU4T8wrSe/93YgfNJY2aG3K0zNYDM28YrxY9mqI8W2pryH0q5KqoMU2J\n99Gm6BSNKb6L7VwxWwg+CleuZi5dWJEsxQWkmtBuInZ9KfKpfPNIUhCDKCgLSRTxLkWTTiE+IUmY\nV+dIdoN97GGkuh23+X3kE4+gfENjLHLTV2ODoG65i6F2SAXjFVUIXzkgJaybbhO2SKPG1lKc/muL\nsUJd1/QdbFaeduGwbS4ktLDm9KKl+wy+tH9uChUAVnP/A7/P/a/0jO3X4qfE5gjGQYjeMXSqxM8f\nZYYhkrqKbnLc98q45S89/RJA60z1ed8N6Qh25og7T9SnmawmxQqfM5uhvI5xkEZFjhpVFZaWFUjo\nguVXFus6arsmNqdpq2dwz/f8C0xlME8Df2kM9319KGw7SQVeCYrkYdN7UixOC+280GmHjSJ6gw9l\nBpSiQsSw2Cupqz4IUTLPfs3EM7/yj9BPoiJ/6vqh773EOAjDUCjy/agYBin/RhiGUpSmUTFOmmkQ\nhm3B6kahGzP9kBmGws6cPPhRGKdcil4Pf//vXHva4yvgBd9yhWGMiIooMUhSCKUoF08rzcFBj58U\nYTJINqAzWTToMv86PggYW9JNm9aglGO1UkzNV3Lva67x/Fc9trX72R5XKSod0a/5BU6fuAdjdiGf\nZGDFMA14BQTQIeN9oB8D/bCN71CKmEqqMkC/KoJaXRpuMA6f5+h8O4NdIovzaHc3d/8P/54oT8Cv\nWmvEOMzL/yatvpnkWkJyGM7j005xy/DQGIXRhpQLGUAZhXKFlTlNEVdHVHKFaWYVEoSoK4KZyPEc\nV/orjItb2ezsceaVP4jOT70fctMgYggho3DEANaqG5/VOJTC0zTFRzMGS9MUCy2RzNhPxGAY+hJB\n46dIvynRNCkJy0VVkIJDQUmBIpt5kXosjLB6SHPPF76hnEt2pLP3oBbnaeo5mRMkf5J8/TtoQTWa\nkHJJVI5CXIVi1yOUPLWqsC+LDCMTBmFnR6MVnDmtSqenNSjFEDXKOgZVHFnipNBGoTRFF5c0dRXx\nPTR3fTVRBI/D1A5BkWMR1Mt1nBJQ1pAniul0a5GUS6L7rMUohVtW6Dbjc2LsA90wkEJCNWXGaWeK\nrA3RFDsnvRXkh0GKTZaCpISUMnVTpAQ5GnSGqtacrJY0eKwzsF5Bttj5Hortpl3ZG8GR5NL5yaCo\nr7XIyUsYqdGPgz98LyFq4u5XYC98kHR1oDqhGf17Gdb7hId/AzkEe+1RjCSMrVkshGxA6wpXVWXj\nXYFrIeRCjNpsoOuLBGmaAtYVUL4wmstmaXVwQDTT1gjq068/X4WKEvWMsTzvFb/Ifa/quO+bJo6P\nYQzXKb6O2ljc+R/hnr9wic/5+lURCurPPG5TgMPglEX+6z8giqWZ7yBVg5dTKHcTKS+LJVLaIckM\n21rGnFEs8RG8hoAj5B3GzR5OPYuhPUXarDjxI3+Irc5iSlV72vPQBu561X5xtlJFq5RTIVMghm5T\n2I4pb2MvUulmbFUo3SXDx+BDwlXCfV/5EAbzFEr4p1s/8D2XGIZMP0DXC12v2Aww9IpuEPpesRmh\n64RuUHS90Hey/VvZ/k1mGMuNNkzCNBRpwU/92KeH/J70znHK8qxXr4rFTwUxZNJUvPKyFCamc6ZE\nd6SESHGwME4Tg7B3omFnr+zilI5kMlMO3PR5P8dzXv5GDMstQeJTr32Fqi3jV74O6sxysUea5uQq\nUynIylC15f+rrGa2U4Svsj3HaVPgl2pRnLinmEhBk6Slaio6RtrF7diTz2b2nX8LXXfYT7keTgvx\nzBdzdP524mlDXd1LP+iiY+otkVKMRcoQupkpuimz7hNhTMWPTyoiAZFESJn2ZEblk0g+i1lWNLN7\nOH32hZz8/veQtlldn7pMrOkO05YwUyBHaxqODoumSmHIOTMNZQBujMZQ0a8y3UqIsbAUjTH4MbJa\nF+PiEBMxZHJqWR1HFKawZ5Vg6mIP9oxnwt3nFXpWxPBKJeoYMYDIWcR6tD1dZmrOkTLomIvuTJfm\n0LQK1ViMK9KR4yMhKoUfMxjBNJowCdYqRBv6zcQgGa/hiIy3Jd4mJhCbt+44iozHzJYEPWd3V5hM\n+TvLHtnsojToeoFSd0J8ErQuUkgmVpAQMUbTOkU46CFl4vGEHrcELAdzCziLBiqnMMxpGo2maBz7\nHo5HIWlFHBI6CbUpBBOJZTwQY2bTwal2j4uVIdKjpgFUC01VBlEyL5l2EhFVJCxCxs0UYjKuPsYc\nGcgT+p4XYJfPY1fOgTmCtsbYxHQcqfch7JxEtzNkuURsjZkEnTx5stgEm/VEngLZGKA0FEMnGClZ\neZqMVoZpjPipiObX60TMGZUSZ8/cAptA9efVQukzrxpUg1aJF39Hz3Nfs+K+Bzqe8w0HPOMbDrj7\nC78PxQKltsytP8EyOiPf8euY6tkovSDH80R1gmR2Qd0N7KDMkpBmzBYn8SiwNVnmJPYw9RLdzgm2\nhlNfxl2vez+1Tv9BxQINC73L/Q8Exs220zMFGtHaUNelze87qKqanDKVM0SvQSW0LYws7wOPbyrM\n8iyfZiD2aZdS8M0P/Cpdn9j0pXvs+8y6EzY9bDqh2wibTlhvf276TN8LXZ/p+8w4Fv+2fhDGHoZR\n+LEf/Mhnqs2ftKxe8jnf7Fn1xUpda800loJUu0LDH8dABvxkiiFv1GiTCjzoNUY7jCtC5aNBc9Mz\nvw6tnn4QK4BSmXZxE/r2L+Hy4oVQPwOt72QzPIcsjhDOUnIhyrxCVLH+yalCt7BYOtotDKO0prYz\nUAsqe4q67rm2uoB50QO4m5/HaE6iPjW6QCmMTux9xQ+y9+h7ybVGmhbszQTbgoHEnKwqYlZbETXM\nmhaRhqwSIXqcgKjiq4YGqS+yu9hlmBLzhTD7tp/klMo02n76DZPT3P91jxc4MyeMUqzXHctlhcKg\ndNFpaaPJyTBNkRALJDhbFOd1yYowJWyl2NkFtCHFwsrsuwGlYYqRqlZoqyArrFHM2xpbyY3TsirT\nWUHOvQS7Y3H6JCmdQ4W9worMoFxVZn1xex2zAh8J03XtXYmZqRaW0SuG0RNMJuqSoq1mJSkAJdQa\nJAt77YwhC1pp+qHMCXXdUDcz1O4u6WV/DTFCFIMVTTq+QlwHJM7B7iEqFcsfo8GUHzKBqg1IYeBi\nIISii2KnwktxEAkjIAnfweZ4IseJlGFzDLY1uAXk1oKZkWqgsoxZUTeGKIUVPGWhWSoe6w5oXvpS\nmlyDEbLaJYVAjBMxrrcohaCMIU/bnyI4McROCAuBuITVu1BdhXQfoL/460xV8W+0u4JKCxYHR7hp\nTXIB6Xp0bYiT4KciaVgsaoYo2CrT1hW78wI5SC4b7+LSX1CJ2awixMhibvG+iMwPjy6So0V/hriP\n/8DHy5/tkk81g/tPf3wAVI4kZTj88VuZL28mLo4Yrwoxbkrqph7RMmMcI7aeEHcbrd/n8eS5em3G\nF73+nVDtUun6T3UeWeD4PW/m2kdfCc2G4Eu+k1Il7n0cc4nXqGZAceUQEbLJrC/AC//yiOJPfuyc\nI6//6dto6hJrf50+akyJ8FBKkSj6qCRSGFKxYOnBC6NXTEM5vx/9a4/ibPMnPofEinf93An2lgbJ\nEdGFXLG7V6FN5nA/snviOjafsa5ApEoL41Qc3V2tufXLA+ZPsN9KOaI//lbib30/uqpIUTFuHkFl\nh/cXsBZyXpCCx1YDU2+ozYzNeISrICeFSnejl440LWnyx1n7wK3f8yvoM1+AVPVn3rBkwZOJP/MA\nTh9w9dIjzBqHkURlDMf9QyXQMp/B+yv4SRfLMGkhRZKayPkU0VeIVcyb+/Cy5jDtc+6H38NJUUXh\n+hlW6DIP/nZLbWDoE1VTMY2BdiHknJkthPUKTp5yhElTzxLDJhbfvqQJIeN72D1tSuyK0WhV4GJJ\nDZuNp+sCTsPOSRjWBaYOUbjvW+SJO1ZAVIBxg3/Tt1IfePJ0CNMFJF5BG4VIQlRx/c5bobSIQltD\nGhKiDRIjSm0toK7bfglFj2c0/VQSnUUKq70fQYyiMYphLALmE7fsEb3jQ0dX+dKfli1ndMteO7yA\n+dcP4I99SWCe3owzgXFMNDODSCb1BU6cBmgchcjhanI3EZIDFUipzD1nlUVXBc4/OkzFGslohkHI\nRvA6o5ImrTLLvRbfB7ohYnXpBPugyOxx73NfhPvu3yyu8PEY90vfBf5KqZz+Ct5/iMqZUvTZCuq9\n4BaOsQ80dQ1JSF1AsmAXcJzAZsfcJsJqgUwr3EkNRztMPtDMOoLWTKsiJJasCFHQxhFEsZgZVMpc\n3p9wTeEahIFtEKwr8J+B42MwFTSNZn72Fo7DLif++ntZPs2X5/+ThQoomU8Il7zifOrJekb+sTsY\ndoTjIdEaRcoJoUYwdNnS+omPH3g+/6ceRyWhMplsMvZPUSyeWAkIZOl51xvOoVqFTZ6rlxRnby44\nvWwNJRtT46PlOQ88CnZO6ST/9JfwR37qHLUrsIxzZXhvzDasTZVgyLTVRqUo+FDCKn1Q+BFe/8NX\n/iPeN0QJrN73dq59+OugXpUdlYoYY8kxkzM4pwnBoUwkxVgShGMmRMPnvjqgPzXR949ZIhEVLHzk\nI0zv+GZyXBL7EaMHQpro11douR2xF8mMGL1gHHtS3KAMxNzS2FvR2rM+7thpNrR/6wgGYVZJ+fZ9\nxhOAqAIhCu0bX8fhpX9JnAzWRNrGM8VA3Hhs3iOYR5EUQDcQe8aYMSoR0wmsrdF2CX3F4ea9POvv\nrkC36BSfyNz6DCv7yAd/xWGMYRoS7cyUIk3CVZra1gx+oGkc/RBwFpx1JAk4V4yE65mlW3nGYZu3\n1lmWe5EUHDEUCrjSFj9mPverB0JbDG6f+CwSogwTa9QvfBX1sIefjvHd41R6H6s7tCsGvKEveWdJ\nFDlA5Rz9JpC8MD9liV6YxpJQrHXxJezHTPIaNzPkFBCvcNYypIBzlr4rf2/MHldXRyxPnsJvRp7x\n4wfo2m7n3oqY18Rffi1y9QPouAPxnTg00a+o5pacIzkqdCjdYg5lo1e5iqHz2EpjyRytYTk3TDHh\nKuhWxbS3Gwos161hPgOPZmdWMcWRfqyhn2jmGpMN+0eBnZvOEv2M5fO/iOZb/wkmKSQ7qrf+KFz9\nHZgyYX2Iqz5U6OlYSEXaoZwjDWXOp6To4/IA5sSC/uqG2bxkbJHLPC9MIxI11cmKdDiSksXNI+MG\nQGF0RYgTjXMcrwOVc+V6kUtGmhGstcQ+4yXTVIbgE84VE+VIIM2XrGeOZ/xPV5gp+/8Xqj92Zcjq\niBR3ME6jCYVRporrt5EalQYwsxufXLmV/yzWBJJI6jL7734b1z7wWsg9Mi8iuvmd/4TbXvgqtFII\nbhum8Wcjg/sbP3G6JLhqhTJyAzISthlYSYq9UlDEKPztH/yPK1CfvBIQkTzx4G++lK57L4TINCoW\nS411mpwLbKDQBBQ33fGjnHzef4PTM/6kn4FIeX+KxJQ1q3/6Cmp9gB9BHUWYH5A2PUo7ovSoWNPU\nC7rpKkZbJM5IZkMVd1g959u4/Rt/jEqNoK5vVv74u+H67Z8QzPphhn/0MmhO4GNPdMdIrLCjQvRA\niLa4LlQtWXWI1BiruDBl5mnO/P9t795i7szq+45/1+k57L3fo/36MAwzjIcAGQZNHUqTEKga0kag\ngtKkaSikrUiVREppqXJRpQeKaDpq09JeVCJJUVWilqAIRTRXGdES5YSECG0ISYcyEDKGGeOxx/Z7\n2vs5rWMv1vbYgZlhcEhEYH184wtLfvy+fp+111r//+//fT/HxvnXMY951M1zfQYbHWYYeOShE3gC\nbavxzuVPwA6amcDaxMZmxTjYnB6y3uGPLubK1hgxxgCJbhVpWsU0CKx3eZZaktz3eodovjxW68u/\nJ0vi+3+Czj9M1WtM2CcxouQh3o+50VsJgg/rhvfcjB18LioIIaKVxAWNkOtmdSTO5rttlRSe3Ken\nDFgP2HxHqM0ecachdSd5/js/DJy45VIkL47ifT+KjJ9nGkdECGj9f3ArQbVwhCmXwauYP9ilmJMu\nQkiEKeGdZLaRKxilgm5IgELIgBQVwXtsyKnmfvJUBsYOOpdPO4g59sw7gTALZHMKOTvL6X/6EWoz\nAhUjEv3kH8Kv/QgCh4pLWO2DuQLCEAeH1Iro87DKXG0XUTJP5aXW+G5CS8E05jFIlc4BzslLppiI\n0dO2mq7LPYhbO4qD67C729AddViX455CyCk2N/alANEFhDKs58bgfWI+n7EMIzHO2P7+f8Lsu/45\nRpiyUH39y9l+65oyxC1jUZNQ68Xpme9ivhY+9Bvv4GOfeM/6ZZB7s77j5T/GX/+eB/9U/948ItQT\n4gH9xUcZLv8KT37xYZQOtE0innotd73sJ9FqYl0nzu0v1Hkmk48Rw8TKJaaffwV1usJxmKF6h6oD\nIUgSde6zMgvM1HF9UOj7X8ddf/vfUjGDpEnqxryvr+YJIh4YQmCGw+1f4ui9r2be1hxOnmpMCDWS\nmK/Hwgi62NLaFVcnzfN+8F0059/AQqk8aDMoxFf5EIlI/8Tv8Ye/+d20tUMaRwoRpQyTt1Q6l5u3\nM4kdNaqyOJfY3KzWi23gRvOLNoAQWJsbhbtV4PFrd/BX//7nULr9Cs8RcoXnR/4RXHiMo2tPUFdX\nEOmYWs+xtkeIQ/wIpLQ+cpIkcsyWNvmI2MVIsBohc7GInxJNo/AhV7tWdSKgSdJB2sSPFU5FGrHD\nvD1HesNb2HngzUTWs9jI4bs+Tci4j/3A38N1PTOxwi8lUjyCUQ2YnjRGZJ3wY24fIEqGlaNtNW70\nBCmQIjH0gmaWg4hTysUrPgVkMriQjzCncR16K8GYlohFRM3kBNEIVJpz5bjjFT93hShbZNK5RuSr\naAAAEJ1JREFU7y4azK/+rZwk4Tz4CvzvkYJfT2FOCClyItgQkUCyoCpD8oHoE6pWJJvA5RgzUsJ6\nQaUSLuagAVMDSZKiYnIOoyVh8ow2J6UPYy6A6m2kESCTxMYIQWAUWAdEyeRD/syvGu5++wXGnTmt\n3CwLVfH1L+HIH/G+dKGWkMc+8jUPVEkQoyWoimsPP4T6v79EPDygWx6w8dLXwPwu2rv+IrMXvAyE\nRCIheYTUuepLiNv+QboRSJyfI7/4r//Bewmf/F8srz7B4tQe1d3fidy4m637vpcw20SkvLsUt+7q\nb2NrH/BIBH6wfPYDO7SnLHbMx61R5NBboRPzeQ6J1iYP27SjoK4VCE/yhpgcppKEdRq/HRPToHnZ\nGy0Qnuq9+gpfCYZVJH3ojcjuGnI4wNpDZGgI7ou0amK0kbrKd2RK5WKeaiYZh4iZa1aHgUblhvzR\nBZTMwcuVTrgkCLHChkQr7+FwOmAxn6GMxqsFx23Lubd+hGQSbVJf1n/mcOgPvJkULuCPtojucyjR\n47iODOuZb25dbRjyGHvnJAny8+l892y0wKeUczFd/nM3hh87C1ILQhAgIlLs4MQBJmpckAi5w0o4\nzqh70T/+76nOvJKqWifbANpbwkN/h+nxz9C2Ae8UMn6B5CdiGqkanU8nYiKO5F4tJ/L1FRBzkjDJ\nRVSSecTJehQSIiFNDiIMY2SaHDEKVCWwfUBW4GJOWJnQ6FRh3YjwkbrSTIOj0vkOz5jcFyjMLmom\naP0Zdv7VwwQ9oVVTFqqiKJ7OVSbX8OkPnKFaTNQqx1qZSsB6knDd5gUgxIhzicoopEooIZjGQFyH\nShsjmAbJva/vkZjn9IZ56sDST3kn8L5Xsc8rYPn7VHqJHa7RNktit4ueX2JYgbfQNhsI1RFCJAYF\nCEQwBDHibA557Yc8ny4hOVhNbLYvJvl9RGvxacbl6SxSXuf8T38cK3aobnwI+tK7zwiDGDH/9c3Y\nvZr6ykX8cJnlcp+tzRYpEtP0BDopXAoYmRjXg04FitHmZA+lYVjlsn3vc1HQuFTUbe41CgKUaEgq\nEZhQ8iT9qke0LZU7walTL2L/1a+hOf82dJVo0PmJ40SSNdP7fgDDZ4jHe5iZAH8R5GMQYOxt7o+T\nEgYPRpHG3PYSI5hK5gnQHmyfqOc1dppIHqRRVI3Kaf0h30kqJRmmmCv8hGDZ5SnDkyJP97XrZLAB\nZrN84+etgKQIwrN39tt47OgC9WJk418csCc14hmOBb6Oy9OLovizsUdtFjzww4d8y2t+n3hs8CFg\nbe6NSikxDZGxj0x9wkjJ4UEkOMVyGYjk3i+XEkdHkXte5whCP+ePwTcCPNA11Ab/lo9zgo9SzTRK\nblJtncHHc1h5DY9AxG10q4liwRATCE0yEaFrJq9xKWHaCisVeiYZpUOKBbpaEJue0LaIrkL2O8z0\nNb71wQvYuINmvZN6ugIdGZG+wr/pvTRuk85C5E505fDSEuwBKhpcgFlt8j1fm69kkgpoCcIYui7v\nooejfIOjZIWZhzxKZz3LTc3HPJ4lGQ6OJ2Zbe8zaO+k3Fnz0wm8h7/9JWpWYxdx/lZ/PQEqoN/1n\n+ng/ZrYBdUMyQHcCP1kanSsUx8nnTE4v1+NmcgL62Ee8Twx9QjYK1yVMBUkLpApY5+kmhdSCJ5+E\nySX2j0E2Cus1Ugq2ZoaFFMyEJKUGqwWqrkkqYWRCiYiLDqUTl4+fZNANz3/jb7ETNS7YZ/w/Uhaq\noigAgRAGs/kivuWHr/PSH+j44sF2nkQtcibg1SuSlCTTJDA6YW0gBkU6rnBjy+bZd/KC77uY08lv\n87BGiApRJfixTzBfHJG2K8aVRpoWzDmWq13kbCMnTYTLOWZKRqRscF5Bu4QI42iJIQAaF+D6sM/J\nk3uk1DOMkmr2Er5A4CU//Qg1Yj2E9Vleh0miVKBpNpHf/jZm+hpSdqT6XiInGOMLsdKASkzjHQQJ\nnc1xRWkdBhsmyaxpiaGi3YF20eK8pRbrcnoJWilCUohwL21zls25ZJoi+6tL+BN38lfevc+eTNQy\n9x3dPHS+UTF7CpMOOZ5dJQ0T0W4SKwmpzc3CjtxPphMIn8MSogYNVSOJEeYLcpN5s668VYpgBSIm\n5rNAInH6jlw0sTXnqeo9U+WBnSokCJEYRoLNI19WK8UU8vzB+bbC7N7B2Y2aF9pLiHu/DaUl5lkq\nZsvRX1EUT2MiD2kLTAdX+MQHv5X5ZsjzxKyEypD8yLj1vZz/a3msTFrH9uRhGM8S3PZsEgThUekQ\nP53k8d9+K/c8/v8Y3RExSpZHTyKFRAoLoSHEi0iRqKp7SGHChYCploz2GCUlqyEhk0GKXYLeQE4r\nZvqYE//yUZI8hRgPGcUWdcNzathPKZBiQn7mPVz+8H/kzO63M3WfoYtQuyPG7vPU84g73ICqR6VT\nBHWATg5PgLSBCAGhenzSedcy00zjRKU3IRn6KaIXM/y0QTvuI8IeV9qecw8+ShVysMDTLaoJcGmk\n+txvwO+8h+gCzl7HDReplUeLIxA9Qoscut0nqhqClfmuzCeUyHO2gk0s+8iJ05rgBNPockC2zgEF\nQx9zX5QLHB9E5tsVAk93nIs02tYwuNwG0HU+BwdFaOpdLu3vs3fHGYbVSP/yV/PS7/8gqjb57lWW\nPqqiKJ6zPGGblCdei2RJSZPEkItPRIUSAqJFyCZHeTyVDvInO6i52UIQc4Zfd4nVz/9l7MmTpN5T\n9UcEfUCQ24j+mEgFYiSlFj/2aDPDxSVKwOQTi62aa71jO52k23sl5370v9ApRRurr6qk/+YDBvqk\naB/9Hxx+6EGEqJDUNGaiO95nsgcsmjnB7zPZCW0CUURkaHB+QIsF0Q0EEWjrhn6YULLGkhvKK30W\nL65xZTXjXHOGq3sv4a5/8AsYYXI5+bN83WKMiKgY//vraP1BnkYeLEpeJPQjSipSmpD0iJxXm2O7\noszNvz6ipXxqzIv3UFUi78ZCJOYUZkJ0+EmjK0/wksiNCkLB5AQi5mgs61owAxJDzS7L4QqprUj6\nNGLRcPfbPotarBAs8nehNPwWRfHV+9If1XjL7yU3Owm/9q+SBHlXF3oSFf7Cx1l98G8gZ/cRxSUY\nLtKNOyxmPs+xE7M8ldm0TE4zr+DAjYjxNJM74NQ/+ygLswlVgwiOKlcE3NaDedHjg0Zeu87hQ9/B\ndjhLv7QYoxj7Q0KckEkgoiTFDqUnpN7GjQNIgfUWySFBaESKTN5QizOEZKnbHbrlJWRfUf3Nn+HM\nq/4ufpoQul3Pr/tKj+dxF/8n9td/ERdHGnEFrl9ByH2COkK4xKzZpF8NNFVCptxbFUnElAs/lNS5\nGjB6hFA5zmte0U0DdgSSQOqEH6CqFcsu0BiNJ8ehCQlS14x2QodFHgFSeZr2DGKrYt49H/3K18Nr\nf4pFSNxonyoLVVEUfy5571FKQUykcJ2lOQn/+m6W9nFmW3uo9fgYS83h/ueRosIyZ5y9kPNvfwjS\nglFqTIoIYRAi4ISgSvK23oAp5T48QUKIgEejP/JOwqd+BU/PFbnD1sWriBOXsNUW7mpEqZokliRa\novXs7pxm1V/FxwlCYHQLenfAstnhVLPL9cOal//MJ1mmkU3fgLnxAeE57FZjXuS/8J9exAm1IIya\ndmERvme53Gd3Z4H3S5bLI9oKtAQXcsFH8Hk3VVWGfnLEkIO0qzo3HHfLXMl4o2JxdSDY3k3EoDg6\nCmycbLCdAu2JYgLmOBsxSTExUnGOU6dexO9eeZj733WBjWHE1ppq3cJQFqqiKP7cunEcaEnU62bt\n0U0k7Zkxg+SwUWOkQpLyiBRyjxspAnJ9BxVJ6WYP2p/MuiGYhAl5Ejk/+z087i6wNb2YuHOV6ugR\nDsIe82bM87vUBnbo0bVmchVSV0SVuHogOdM8weGnel783y7TOcN8uyUOirq59Vj1uT3XlATVuE/3\n/lcxr+6BcR/bSyb/aap6CzdcY1Z3uDFPD6iNZJo8JInWeaCjUTlBIkhJCAkCyAR5AGVEaoMLDm8F\ntUmMFmRlkMYzdDNacY6lPSSoEVk1qLAgzRsuP/lH3P9v9lm0TzCps7RRPlVpWRaqoiiKPyU3dn0p\nJfA3d33H0+M0G9uY1ObUidjipn2maaAbE15s8eIfegfyO99KnRJT8FRSAnnBtTLd1s4vl25Eqv0D\n5C+9lmtmj109sL9/naaamPolC3UHY/wDFApde4ZV7o3CG5KI1FUkEOiXAiETTT3DT5EoR2LI1X6V\nhlUH7cxgXaIyNYPoMO6lpPAk8+1trh5cI9XbsHghx4ef5vw7PkVqNhEeok7ISFmoiqIo/izZBFXK\nuaGEbaLIKe9G5JRyQcRLRYqWKBVVqhFpIIk2l5vf8la+rSzRBFaAiZExdvDp96M+9gs4L+n7gPIw\nX0i66Xep7DmkeoxpnDPb7OinkZoW7y02RBKJRi8IweUcQ+GxU2Te1gzDRGVgcjlpwgiBMTWhmnDd\nearKslpdp92QHKwcZ03F7o+/j9WZ+0FvspAVQYG65R9ZFqqiKIpvIimtF8UoEI99mPBrDxKGFUMa\naduaOFom9wQaAbEluhWq6YjTHOcD2uQ8x6mXCJWT54PvAYNPHiyIymEt6GYDJkmqPMQXkOJlYmxp\nF3tM9jHCuMmJf/zLzHf/AnEdkP50JfZloSqKovhmkyAKx+QUVfos3S/ez/LyD7LZfoEgeuZzw3J5\nDTt1bM62sBHSdIhUnuVwTF0n4tRQ146x2yDpQ5LPEUpNtUHXr2jaBZ2bmAZL3Z5C+ZOk9hI9LeNy\nRrh2kQfec40Y5lhhaVSeNPDHci7XnmmhKskURVEU35BuVgqacICo7kL/yIqDM59lY7OhndUMvaeu\nt5A0dIPD+4bR5/EytahRUaHNCVI4xWxRoeVpZottkLAKS4SBw35FdNBUZ0lO5niroWFnPOb0X3oL\n9777mDHUDGIJ9mb6xLMmgXyJsqMqiqL4BnajYjI3pjlA4f/oVzn+5Z8gveAuNi4dcnXWsnn9SfwJ\nB2OkG2FDbuGCRcgBH8HIimHoaJuWhMu9YNGyHCt2TnvC2HA0blPVFfsHifve/tvYjT020wTy1nik\nZxk5X3ZURVEU33zEegyNEJCExgnPePYN7PzDT7J7ZUa3MNw5O8k4D8ReUMV7OaXP4kJACJBijlSG\nEBKLtqGfPJEFdbPBoXoeG5vnYTXDiwc4fXwJmge47999kq6p2USQhCElQV5ubm/JKTuqoiiKbwKJ\ndT+Zj1yMgudVI27SxBrsh36W5qPv4vrGdbQ6xWqsaf1I3Uis6xGyZZocVVMRk2IInn40bDLRmDt5\nxD3Bq3/qY1yfnWE3WKIWCCmRCZzQPHPc7B9XiimKoigKAEIISKUQKc+79iIikkJ7ePR/v5vqY/8B\n/+hjaC0INqL0nJ5A3G2RYpfuju/i/JveTmiej9AGmRIRDckjpSafNkYiYv3ruSkLVVEURXHTLdOp\np3XiBxGmFEnSYkRFdAmBA90wjJa2qsBHtBQ5aFeJPH07BYRQtzR+3V4CyDMtVEVRFEVRFEVRFEVR\nFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVR\nFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEVRFEXxDeP/A4ZYrbd1a4nSAAAAAElFTkSu\nQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_samples = 10\n", "\n", "x = np.hstack((norm_y1.sample(int(p_y1*n_samples)), norm_y2.sample(int(p_y2*n_samples))))\n", "y = np.hstack((['lemon']*int(p_y1*n_samples), ['orange']*int(p_y2*n_samples)))\n", "\n", "draw_in_row(y, x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And lets see their respective probability density function." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEACAYAAABiTXicAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQgghhBBCCCGEEMnh/wHkBCWVZj/PxgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_lin = np.linspace(x.min()-3*x.std(), x.max()+3*x.std(), 100)\n", "\n", "p_x_g_y1 = norm_y1.pdf(x_lin)\n", "p_x_g_y2 = norm_y2.pdf(x_lin)\n", "\n", "plt.plot(x_lin, p_x_g_y1, color='yellowgreen', label='$p(x|y_1)$', linewidth=3)\n", "plt.plot(x_lin, p_x_g_y2, color='orange', label='$p(x|y_2)$', linewidth=3)\n", "plt.ylabel('Class densities')\n", "plt.xlim([x_lin[0], x_lin[-1]])\n", "plt.legend()\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Posterior probabilities (Bayes' rule)\n", "\n", "Now, with their densities and their prior probabilities we can use Baye's rule to compute their posterior probabilities.\n", "\n", "$$\n", " p(Y=y_i|X=x) = \\frac{p(Y=y_i,X=x)}{p(X=x)} = \\frac{p(X=x|Y=y_i)*p(Y=y_i)}{p(X=x)}\n", "$$\n", "\n", "If we assume that these are the only classes we can compute $p(X=x)$ with:\n", "\n", "$$\n", " p(X=x) = \\sum_{i \\in \\{1,\\dots , k} p(X=x,Y=y_i) = \\sum_{i \\in \\{1,\\dots , k} p(X=x|Y=y_i)p(Y=y_i)\n", "$$\n", "\n", "Then, we can visualize what are these probabilities given the feature $x$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAk8AAAEACAYAAACqIZJKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p_x = p_x_g_y1*p_y1 + p_x_g_y2*p_y2\n", "\n", "p_y1_g_x = (p_x_g_y1*p_y1)/p_x\n", "p_y2_g_x = (p_x_g_y2*p_y2)/p_x\n", "\n", "plt.plot(x_lin, p_y1_g_x, color='yellowgreen', label='$p(y_1|x)$', linewidth=3)\n", "plt.plot(x_lin, p_y2_g_x, color='orange', label='$p(y_2|x)$', linewidth=3)\n", "plt.legend()\n", "plt.xlim([x_lin[0], x_lin[-1]])\n", "plt.grid(True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Error for a larger sample\n", "\n", "The posterior probabilities are the optimal bayes in this case. This means that if we know the real distributions for both classes, then for a given sample, predicting these posterior probabilities minimize the log-loss error and the accuracy.\n", "\n", "Then, we can test the error that is not possible to reduce because of the variance of the distributions.\n", "\n", "We can create a larger sample from the same distributions:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaoAAAAnCAYAAABe1gxEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nsizL+v/G/wHVkRdnsya8sgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_samples = 100\n", "\n", "x = np.hstack((norm_y1.sample(int(p_y1*n_samples)), norm_y2.sample(int(p_y2*n_samples))))\n", "y = np.hstack((['lemon']*int(p_y1*n_samples), ['orange']*int(p_y2*n_samples)))\n", "\n", "draw_in_row(y, x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "And then, we can see compare with the predictions from the Bayes optimal." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/usr/lib/pymodules/python2.7/matplotlib/collections.py:548: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n", " if self._edgecolors == 'face':\n" ] }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAEyCAYAAADNzKrKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\niIiI1Jv/D899ANacHbJWAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q_x_g_y1 = norm_y1.pdf(x)\n", "q_x_g_y2 = norm_y2.pdf(x)\n", "q_x = q_x_g_y1*p_y1 + q_x_g_y2*p_y2\n", "\n", "q_y1_g_x = q_x_g_y1*p_y1/q_x\n", "q_y2_g_x = q_x_g_y2*p_y2/q_x\n", "\n", "q_y_g_x = np.vstack((q_y1_g_x, q_y2_g_x))\n", "labels = np.array(['lemon', 'orange'])\n", "y_pred = labels[q_y_g_x.argmax(axis=0)]\n", "\n", "cm = confusion_matrix(y, y_pred, labels=labels)\n", "plot_confusion_matrix(cm, labels=labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is not possible to reduce this error as it comes from an intrinsic ambiguity.\n", "\n", "## Deployment time\n", "\n", "However, how can we be sure that during deployment the only objects that will need to be classified\n", "will come from these two classes? We will refer to these known classes as the _foreground_. If for the training of any given model the classes that do not belong to the _foreground_ are removed manually or are not available, then during deployment we should ensure that only the _foreground_ classes apear. If that can not be ensured, the performance of the optimal bayes will not be optimal anymore.\n", "\n", "In this example, lets assume that there are two new classes that were not considered before.\n", "We can see a small sample and their respective probability density functions.\n", "\n", "- Classes\n", " - $y_1$: lemon\n", " - $y_2$: orange\n", " - $y_3$: strawberry\n", " - $y_4$: apple" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaoAAABdCAYAAAD0byLjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEv/f8H8BypiVQuZGgPIAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "norm_y3 = NormalDistribution(mu=0.3, sigma=0.1)\n", "norm_y4 = NormalDistribution(mu=1.2, sigma=0.25)\n", "\n", "p_y3 = 0.4\n", "p_y4 = 0.6\n", "\n", "n_samples = 10\n", "\n", "x = np.hstack((norm_y3.sample(int(p_y3*n_samples)), norm_y4.sample(int(p_y4*n_samples))))\n", "y = np.hstack((['strawberry']*int(p_y3*n_samples), ['apple']*int(p_y4*n_samples)))\n", "\n", "draw_in_row(y, x)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-5.5511151231257827e-17, 1.95)" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEACAYAAABiTXicAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nJJb/B/PNXgXP4LCDAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_min = np.min([norm_y3.mu-3*norm_y3.sigma, norm_y4.mu-3*norm_y4.sigma])\n", "x_max = np.max([norm_y3.mu+3*norm_y3.sigma, norm_y4.mu+3*norm_y4.sigma])\n", "\n", "x_lin = np.linspace(x_min, x_max, 100)\n", "\n", "p_x_g_y3 = norm_y3.pdf(x_lin)\n", "p_x_g_y4 = norm_y4.pdf(x_lin)\n", "\n", "\n", "plt.plot(x_lin, p_x_g_y3, '--', color='red', label='$p(x|y_3)$', linewidth=3)\n", "plt.plot(x_lin, p_x_g_y4, '-.', color='red', label='$p(x|y_4)$', linewidth=3)\n", "\n", "plt.ylabel('Class densities')\n", "plt.grid(True)\n", "plt.legend()\n", "plt.xlim([x_lin[0], x_lin[-1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because we are not interested in their specific class but we want to consider them as a _background_ class, we will\n", "merge both classes in a mixure of gaussians.\n", "Now we can visualize a sample with both _foreground_ and _background_ classes and their corresponding probability density functions.\n", "\n", "- Classes\n", " - $y_f$: _foreground_\n", " - $y_1$: lemon\n", " - $y_2$: orange\n", " - $y_b$: _background_\n", " - $y_3$: strawberry\n", " - $y_4$: apple" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAa0AAABHCAYAAAC0/hhnAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nkNTs7JI3AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "norm_yb = MixtureGaussians([norm_y3, norm_y4], [p_y3, p_y4])\n", "\n", "p_y3 = 0.4\n", "p_y4 = 0.6\n", "p_yb = 0.3\n", "p_yf = 1-p_yb\n", "\n", "n_samples = 20\n", "\n", "x = np.hstack((norm_y1.sample(int(p_yf*p_y1*n_samples)), norm_y2.sample(int(p_yf*p_y2*n_samples)),\n", " norm_y3.sample(int(p_yb*p_y3*n_samples)), norm_y4.sample(int(p_yb*p_y4*n_samples))\n", " ))\n", "\n", "y = np.hstack((['lemon']*int(p_yf*p_y1*n_samples), ['orange']*int(p_yf*p_y2*n_samples),\n", " ['strawberry']*int(p_yb*p_y3*n_samples), ['apple']*int(p_yb*p_y4*n_samples)))\n", "\n", "draw_in_row(y, x)\n", "\n", "y[np.logical_and(y != 'lemon', y != 'orange')] = 'other'" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-0.89779211006006121, 2.8629863743796746)" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAl4AAAEACAYAAABiTXicAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nCIIgCIIgCHrz/wH6ArNAv/T3wQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x_lin = np.linspace(x.min()-3*x.std(), x.max()+3*x.std(), 100)\n", "\n", "p_x_g_yb = norm_yb.pdf(x_lin)\n", "\n", "p_x_g_y1 = norm_y1.pdf(x_lin)\n", "p_x_g_y2 = norm_y2.pdf(x_lin)\n", "\n", "plt.plot(x_lin, p_x_g_y1, color='yellowgreen', label='$p(x|y_1)$', linewidth=3)\n", "plt.plot(x_lin, p_x_g_y2, color='orange', label='$p(x|y_2)$', linewidth=3)\n", "\n", "plt.plot(x_lin, p_x_g_yb, color='red', label='$p(x|y_b)$', linewidth=3)\n", "plt.ylabel('Class densities')\n", "plt.grid(True)\n", "plt.legend()\n", "plt.xlim([x_lin[0], x_lin[-1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Error during deployment\n", "\n", "If we keep the previous optimal bayes solution we can see what would be the error when this _background_ appears. Lets generate a larger sample and measure its performance." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAaoAAAApCAYAAABk3G00AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlmVZlmX9xfhfUTZ0w2gxwK8AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n_samples = 100\n", "\n", "x = np.hstack((norm_y1.sample(int(p_yf*p_y1*n_samples)), norm_y2.sample(int(p_yf*p_y2*n_samples)),\n", " norm_y3.sample(int(p_yb*p_y3*n_samples)), norm_y4.sample(int(p_yb*p_y4*n_samples))\n", " ))\n", "\n", "y = np.hstack((['lemon']*int(p_yf*p_y1*n_samples), ['orange']*int(p_yf*p_y2*n_samples),\n", " ['strawberry']*int(p_yb*p_y3*n_samples), ['apple']*int(p_yb*p_y4*n_samples)))\n", "\n", "draw_in_row(y, x)\n", "\n", "y[np.logical_and(y != 'lemon', y != 'orange')] = 'other'" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWkAAAE3CAYAAABo/7DJAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q_x_g_y1 = norm_y1.pdf(x)\n", "q_x_g_y2 = norm_y2.pdf(x)\n", "q_x = q_x_g_y1*p_y1 + q_x_g_y2*p_y2\n", "\n", "q_y1_g_x = q_x_g_y1*p_y1/q_x\n", "q_y2_g_x = q_x_g_y2*p_y2/q_x\n", "\n", "q_y_g_x = np.vstack((q_y1_g_x, q_y2_g_x))\n", "labels = np.array(['lemon', 'orange', 'other'])\n", "y_pred = labels[q_y_g_x.argmax(axis=0)]\n", "\n", "cm = confusion_matrix(y, y_pred, labels=labels)\n", "plot_confusion_matrix(cm, labels=labels)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see in the confusion matrix, it was impossible to predict as other classes. But in this case, this error is not intrinsic from the variance of the known classes, its reason is partially because we were not considering the possibility of getting new classes during deployment time.\n", "\n", "What would happend if we consider the existense of the _background_ as a known class? Then we can compute the Optimal bayes considering the k+1 classes, where $\\{1,\\dots ,k\\}$ are the _foreground_ classes and $\\{k+1\\}$ are all the unknown classes joint into the _background_ class.\n", "\n", "### Posterior probabilities considering the real background\n", "\n", "Now we consider the background class as the mixture of all possible classes that are not known\n", "during the training. In this case, we merge the strawberries and the apples in the same\n", "bag and we call it background.\n", "\n", "$$\n", " P(Y_b|x) = \\frac{P(x|y_b)*P(y_b)}{P(x)}\n", "$$\n", "\n", "$$\n", " P(Y_l|x) = \\frac{P(x|y_l)*P(y_l)*P(y_f)}{P(x)}\n", "$$\n", "\n", "where now we add the _background_ class\n", "\n", "$$\n", " p(x) = p(x,b) + p(x,f) = p(x|y_b)*P(y_b) + \\sum_kp(x|y_k)p(y_k)\n", "$$" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(-0.89779211006006121, 2.8629863743796746)" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAk8AAAEACAYAAACqIZJKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nFAqFQqFQKBQKhULRV/x/nGuCO5HQ0vMAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p_x = (p_x_g_y1*p_y1 + p_x_g_y2*p_y2)*p_yf + p_x_g_yb*p_yb\n", "\n", "p_y1_g_x = p_x_g_y1*p_y1*p_yf/p_x\n", "p_y2_g_x = p_x_g_y2*p_y2*p_yf/p_x\n", "p_yb_g_x = p_x_g_yb*p_yb/p_x\n", "\n", "plt.plot(x_lin, p_y1_g_x, color='yellowgreen', label='$p(y1|x)$', linewidth=3)\n", "plt.plot(x_lin, p_y2_g_x, color='orange', label='$p(y2|x)$', linewidth=3)\n", "plt.plot(x_lin, p_yb_g_x, color='red', label='$p(yb|x)$', linewidth=3)\n", "plt.ylim([0,1])\n", "plt.grid(True)\n", "plt.legend()\n", "plt.xlim([x_lin[0], x_lin[-1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These posterior probabilities are now the optimal to minimize the log-loss and accuracy errors.\n", "\n", "## Error on test set considering the real background\n", "\n", "We can now evaluate the previous generated samples with the new posterior probabilities that allow the model to predict the _background_ class." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWQAAAEyCAYAAADNzKrKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "q_x_g_y1 = norm_y1.pdf(x)\n", "q_x_g_y2 = norm_y2.pdf(x)\n", "q_x_g_yb = norm_yb.pdf(x)\n", "q_x = (q_x_g_y1*p_y1 + q_x_g_y2*p_y2)*(1-p_yb) + q_x_g_yb*p_yb\n", "\n", "q_y1_g_x = q_x_g_y1*p_y1*p_yf/q_x\n", "q_y2o_g_x = q_x_g_y2*p_y2*p_yf/q_x\n", "q_yb_g_x = q_x_g_yb*p_yb/q_x\n", "\n", "q_y_g_x = np.vstack((q_y1_g_x, q_y2_g_x, q_yb_g_x))\n", "labels = np.array(['lemon', 'orange', 'other'])\n", "y_pred = labels[q_y_g_x.argmax(axis=0)]\n", "\n", "cm = confusion_matrix(y, y_pred, labels=labels)\n", "plot_confusion_matrix(cm, labels=labels)" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "We see that the error should be decreased as we are considering the new scenario with _background_ classes.\n", "\n", "## How to estimate the background during training?\n", "\n", "The previous example is just a theoretical justification that the background needs to be considered. However, how do we estimate a possible background distribution without having the samples?\n", "This is explained in the next tutorials." ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }