known-pos-vs-known-neg.ipynb

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Importance of known positives versus known negatives\n",
      "\n",
      "In this notebook we will show how to compute performance curves (ROC and PR curves to be specific) based on a data set with known positives, known negatives and unlabeled data. We will show how to use our approach starting from known negatives instead of known positives, which is useful of the number of known negatives is much larger.\n",
      "\n",
      "This notebook is intended to enable you to easily change the configuration of experiments, so feel free to make modifications where you see fit to see their effect."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import random\n",
      "import operator as op\n",
      "import optunity.metrics\n",
      "import semisup_metrics as ss\n",
      "import numpy as np\n",
      "from matplotlib import pyplot as plt\n",
      "import pickle\n",
      "import csv\n",
      "import util\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Create or load data set\n",
      "Generate simulated data. Feel free to configure the code below as you please."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# fraction of positives/negatives that are known\n",
      "# known_neg_frac == 0 implies PU learning\n",
      "known_pos_frac = 0.05\n",
      "known_neg_frac = 0.5\n",
      "\n",
      "# if you simulate a smaller data set you can see some effects better\n",
      "# but estimated bounds will be much wider\n",
      "# because the ECDF confidence interval becomes large\n",
      "num_pos = 10000  \n",
      "num_neg = 10000 \n",
      "distid = 2  # can be 1, 2 or 3, these correspond to certain curves in ROC space\n",
      "\n",
      "# generate rankings and label vectors and compute corresponding beta\n",
      "# beta is based on known_pos_frac, known_neg_frac and the number of pos and negs\n",
      "# labels is a list of {True, False, None}, where None indicates unlabeled\n",
      "# true_labels is a list of {True, False}\n",
      "labels, true_labels, decision_values, beta = util.simulate_data(distid, num_pos, num_neg,\n",
      "                                                                known_pos_frac,\n",
      "                                                                known_neg_frac)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Data set characteristics"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Known parameters:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('total number of instances: \\t %d' % len(labels))\n",
      "print('number of known positives: \\t %d' % len(filter(lambda x: x == True, labels)))\n",
      "print('number of known negatives: \\t %d' % len(filter(lambda x: x == False, labels)))\n",
      "print('number of unlabeled instances: \\t %d' % len(filter(lambda x: x == None, labels)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "total number of instances: \t 20000\n",
        "number of known positives: \t 500\n",
        "number of known negatives: \t 5000\n",
        "number of unlabeled instances: \t 14500\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Unknown parameters:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('number of latent positives: \\t %d' % len(filter(lambda x: x[0] == None and x[1] == True, zip(labels, true_labels))))\n",
      "print('number of latent negatives: \\t %d' % len(filter(lambda x: x[0] == None and x[1] == False, zip(labels, true_labels))))\n",
      "print('beta: \\t %1.4f' % beta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "number of latent positives: \t 9500\n",
        "number of latent negatives: \t 5000\n",
        "beta: \t 0.6552\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Estimate beta\n",
      "\n",
      "As this notebook is intended to show the effect of known positives vs known negatives, we will continue with the true value of beta. Change this parameter to see its effect in the figures later on."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "betahat = beta\n",
      "\n",
      "print('true value of beta\\t%1.4f' % beta)\n",
      "print('point estimate of beta\\t%1.4f' % betahat)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "true value of beta\t0.6552\n",
        "point estimate of beta\t0.6552\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# 1. Compute cumulative rank distribution of known positives\n",
      "\n",
      "We start by computing the rank CDF of known positives, and then determine a confidence interval for it. We will use a standard bootstrap approach."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# sort the labels in descending order of corresponding decision values\n",
      "sort_labels, sort_dv, sort_true_labels = zip(*sorted(zip(labels, decision_values, true_labels),\n",
      "                                                     key=op.itemgetter(1), reverse=True))\n",
      "\n",
      "# ranks of the known positives\n",
      "known_pos_ranks = [idx for idx, lab in enumerate(sort_labels) if lab]\n",
      "\n",
      "# compute rank ECDF of known positives\n",
      "known_pos_ecdf = ss.compute_ecdf_curve(known_pos_ranks)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, we determine a confidence interval on the rank CDF of known positives. We can do this in several ways, our code provides a bootstrap approach and a method based on the Dvoretzky\u2013Kiefer\u2013Wolfowitz (DKW) inequality. Feel free to experiment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ci_width = 0.95      # width of the confidence band on ECDF to be used\n",
      "use_bootstrap = True # use bootstrap to compute confidence band\n",
      "nboot = 2000         # number of bootstrap iterations to use, not used if use_bootstrap = False\n",
      "\n",
      "if use_bootstrap:\n",
      "    pos_cdf_bounds = ss.bootstrap_ecdf_bounds(labels, decision_values, nboot=nboot, ci_width=ci_width)\n",
      "else:\n",
      "    pos_cdf_bounds = ss.dkw_bounds(labels, decision_values, ci_width=ci_width)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For reference, we will also compute the rank ECDF of latent positives. In practical applications this is impossible, as the latent positives are by definition not known."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "latent_positives = map(lambda x, y: x == True and y == None, true_labels, labels)\n",
      "sort_lps, _ = zip(*sorted(zip(latent_positives, decision_values),\n",
      "                          key=op.itemgetter(1), reverse=True))\n",
      "latent_pos_ranks = [idx for idx, lab in enumerate(sort_lps) if lab]\n",
      "latent_pos_ecdf = ss.compute_ecdf_curve(latent_pos_ranks)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the rank CDFs of known and latent positives. It may occur that the rank CDF of latent positives is not within the confidence interval of known positives, in which case the corresponding bounds on performance will not be strict."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# convenience plot functions\n",
      "def plot_proxy(color, alpha):\n",
      "    p = plt.Rectangle((0, 0), 0, 0, color=color, alpha=alpha)\n",
      "    ax = plt.gca()\n",
      "    ax.add_patch(p)\n",
      "    return p\n",
      "\n",
      "def fix_plot_shape(fig):\n",
      "    ax = fig.add_subplot(111, aspect='equal')\n",
      "    axes = fig.gca()\n",
      "    axes.set_xlim([0,1])\n",
      "    axes.set_ylim([0,1])\n",
      "\n",
      "xs = list(range(len(labels)))\n",
      "plt.figure(1)\n",
      "plt.fill_between(xs, list(map(pos_cdf_bounds.lower, xs)), list(map(pos_cdf_bounds.upper, xs)), \n",
      "                 color='blue', alpha=0.4)\n",
      "plt.plot(*zip(*known_pos_ecdf), color='black', linestyle='dashed', linewidth=2)\n",
      "plt.plot(*zip(*latent_pos_ecdf), color='black', linewidth=2)\n",
      "plot_proxy('blue', 0.4)\n",
      "plt.xlabel('rank')\n",
      "plt.ylabel('TPR')\n",
      "plt.legend(['known positives', 'latent positives', 'expected region'], loc=4)\n",
      "plt.title('Rank CDF')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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y3nuZt3TWRVU6nVr+W1BQWYlWp4OJE9VudFCBIjBQdnyLpiNTVaJVSEtTG/Yu\nXlQji9RU9du7j0/9v7Hr9XpOnFjH99//kWvXEjEzs0DTTNHrdVy7lsC1awkAuLp6k5OT0qDSH1WV\nlqopJ02r7KObG4wcWXnkqqWlbNwTrYOMOESzcfgwbNqkzpcoLFSHJrVvf+Pf2OPjQ1m5ch7x8WcA\n8PYexPz5X7Nnz/sAtG/vR4cO3enSZQht2rjedL+ys9VUmZeXylGYm8OIEdCxo5zNLZo3maqSwHHX\n0jT47jt1JKuLiwoWDVFaWsLPP7/O9u1vo2mlODl15L77FjFixFOYNsL8UFoaXL2q+tSzJwwbJslt\n0bJI4JDAcVcqLoYvv4Tz59V52A1NIIeF7WLVqicrNu+NGvUsDz/8DlZWjbPGNTZWLZcdMkRVpnW9\n+YGKEE1OchzirlJYqHZPf/89REZC374Nm/bJykpg/frfc/LkdxXPtW3ry5Qpi24raJSWqkR8drZK\ndhcVqWKD/v63fEsh7loy4hB3VEQEhISoI1qTk9UKpC5dbpzH0Ov1HDz4Od9//0eKinIrnn/oof8x\nbtzvax3T2lCFhWqvRXGxylm0b6/KlnTuLNNSouWTqSoJHC3a999DWJiqz6TTqdpMdnYNW6qalnaF\nr79+ikuX9gFgbm6JTlfCwoXrGDBgxi31JzKychmtn59aHeXjU//eECFaGpmqEi1WTg4cO6aWr7q4\nqFVTDfXLL8tZt+4liovzadOmLXPmfEqHDgGcOfPTLQcNvV59vfSSKrtubV0ZRIQQNyaBQxjdxo0q\nf3Azexyys1P44os5XLq0F4CBA2cya9ZH2Nu3A8DDo2eD76XXq/fPz1dTU9evq+kxT08JGELcCgkc\nwmjS09X+h3PnGpZkLirK4+jRbzh/fivnzm1Br9dhbm7FnDmfMXz4/Aa9p6apOlZZWWpkY2qqTtZz\ncQF3d3VWh58ftGsnQUOIWyWBQxhFbCwsW6ZWJ9nZ3XiZbVraFZYunUF8/KmK58zMLJgz59MGB42s\nrMqNekOGqADRoYO6Zm8vtaKEaCwSOIRRnD6tpoa6d29Y+0OHvqwWNHr3nsqCBauxsbG/4WtLS9Xo\nJisL7rsPxo6VkuVCGJMEDtGoSkpg1y4VOBp63veZMz+xb9+HADg7d+LRR5fQq9fkG76utFTt7s7M\nVMtoH3xQHY4kU1BCGJcEDtGorl6FnTtVPsHZ2XCb0lIdZmbmlJQUsmHDHwkJ+RiAAQNmMG/eCiwt\nbW/4Ppph1P/UAAAgAElEQVSmlvd6eMDUqepgJCHEnSGBQzSa1FRYs0YlpGsGDZ2umLi4U4SEfEJK\nyiUWLPiGZctmEh9/GjMzCx588G3Gjn25QRv5iorgwgW1Se/xx2WjnhB3WksZ1MsGwBbg55/V2Rm9\ne1cvH5KaGsnixaO5di2p7BkTrKzsKCrKpW1bH55++lu8vQc1+H1CQ9V7zJ8vG/aEqI+xNgAa+4iZ\niUA4cBn4cx1tgoHTwHkgxMj9EUaSnKwKFRoqNR4S8inXriVhY+OEt/dgAIqKcunf/yH+9rdTDQoa\nxcVqL0ZUlFpKO3WqBA0hmooxp6rMgI+Be4FE4DiwCbhYpY0T8AkwAUgAGphOFc1BTAzs26cCRWSk\n2i/h51e9TXp6NIcPrwCgS5fBhIXtAGDq1H8yadJrDSp/HhOjNu55eKh9GMHBKocihGgaxpyqGgos\nQo06AP5S9t//VGnzG6AD8H83uJdMVTUzmgYffqhGAJ6eKnjYG1g5q9friYjYz+rVT5OWFoWFhTVP\nPLGCQYNm1nv/7GxITFSHJjk6qmW2/frJiikhbkZLrFXlAcRXeZwADK7RpitgAewD7IEPgK+N2CfR\nCHJz4ZNP1Ca/Xr3qL4ceG3uC5ctncf16Ko6O7vzmNxvrnJrKyYHoaJVYNzdXI4vBg9Xjus4YF0Lc\necYMHA0ZIlgA/YGxgC1wGDiCyomIZqioCE6eVKXI+/SpewSgaRr793/G+vWvoNMV4es7nKeeWoOL\nS2eD7dPSICMDpk1TS2tNTORYViGaK2MGjkSgU5XHnVCjjqrigXSgoOzrANAHA4Hj9ddfr/g+ODiY\n4ODgRu2saJhly9T0lKur4aBRUJDDmTM/ER6+myNH1OBx1KhnmTnzA8zNDWezY2NV8vuRR1SpECHE\nrQkJCSEkJMTo72PMGWNz4BJqNJEEHANmUz053h2VQJ8AWAFHgZlAWI17SY6jGdDp4B//UPWf6iqN\n/umn0wgN3QSApaUtc+d+waBBs+q8Z0KCmpaaMQO6dWvY+RxCiIZpiTkOHfA8sAO1wuoLVNB4puz6\nUtRS3e3AWUAPLKN20BDNxPr1apNfp06Gr3/zzW8qgoatrQt/+EMIHh69qrUpKlK7y8u/t7CABQvU\naikhRMvQUtaoyIijiWVkqFVUDg6GV08dP/4ty5fPBsDBwY0//ekQ7dpVHsBRWKjOxbh0SZ0vPnCg\net7J6ebO6RBCNJwcHSuBo8lER8OqVWo1Vdeu1a9pmsZPP73G9u3/BsDa2p7//e9qtXpTJSWV5c7N\nzOCJJ6BNmzv5EwjROrXEqSrRwmVnww8/qGKC1ta1g4Zer2fDhj+wZ897mJiYomkaM2a8W6tIYXS0\nyou8+OId7LwQwmgkcIhqIiNhyxa1p6K4WE1RdetW+xCkkpIiVqx4ghMn1mFmZsHChd/h7NwJL68B\n1doVF6vNgpMm3cEfQghhVBI4RIUdO2DbNjW6KD+P21AivKSkiOXLZ3HmzE9YW9uzcOF6evSYUKtd\ncrLan9GzJ/TocQd+ACHEHSE5jlZOr4dNm9RpfefOqfIeLi51tz916nvWrn2enJyr2No68cor++jU\nqW+tdqmpKrdx333g49PwQ52EEI1HchzCKH75BXbvVgUE27Y1vGKqXGjoJpYufRgAU1MzXnhhu8Gg\nAWq0cd99EBRkjF4LIZqSBI5WqqREndS3f786dtXVtf72Fy/uYdkyVZjQwsKGP//5V4NBQ69XxQkd\nHFSdKSHE3UcCRyuTl6cS32vWQESEKoPu6Fj/a8LCdvLppw9QUlIIwCOPvF/vSMPWFiZPvnEwEkK0\nTBI4WpFDh1TyW6dTG/L6979xmfJLl/bx8cdTKC0tAcDbezAjRjxpsG1mplpFFRysCiAKIe5OUhmo\nlcjNhb17VV0oHx8IDLxx0Lh8+SCffDKV0tISRo16BmfnTkyb9k9MTQ2XrU1PV0UK77nHCD+AEKLZ\nuJURhwnwCLCukfsijESngy+/VAUF+/e/cXu9vpTo6GN89NEkioryCAp6lNmzP2Hy5GScnT0NviYm\nRu0Kl2W3Qtz96gscbVAFCX1R54EvAaYBbwKRSOBo9kpK1NTRvn1qY1/v3vWPMvR6Pd9++zyJieeJ\njz9dETTmz1+JqalZraBx7ZoKGM7OKhk+dWrto2OFEHef+gLHKiAHdbjSeGAeUAjMAc4YvWfitn36\nqRpl5Oaq6rN1lUIvt3LlfI4cWYUaVGoEBc3hiSe+NDg1VVqq7j1lCkycKOXQhWhN6gscfkDvsu+X\nA8mAF+rAJdGMaRqsXauWxd4oYJSW6jhyZBXnz2/l1Knvy+9A7973M3/+KoNBo6RE1a/y8lKrp4QQ\nrUt9gaO0xveJSNBoEY4cgcOHoUuXG48yDh36gm++ebbac4GB43n66XUGg0Z2tjoBsFs3dY6GEKL1\nqW9dTSmQX+WxDZWBQwMcjNUpA6TkSAOlp8Py5aqEiKfhPHYtoaGbWLXqSXJz0/H1Hc7LL+/C0tLG\nYNvz52HUKLV6qqH3F0I0jaYoOWJ4zaVo1i5eVGXM+xren1dLSUkh27b9m9zcdDw9e/P885vrDBp5\neWqz4IMPSk5DiNasvn/+NsDvUGeCP4NsFmz2NE1t8vPwUEtja8rNTSc+vnJdg05XzPLlc4iOPoKL\nS2deeGEbtrZOdd4/IgICAiRoCNHa1fcRsBIYgFqKOxlYfEd6JG7ZiROQlKQOTaopLe0Kb701kM2b\n/wmovRorVszjzJkfsbFx5Le//Rknp44G76tpEB+viiA+8IAxfwIhREtQ3ygiAOhV9v1y4LjxuyNu\nhaapgHHwoKoTZci3375ARkYsrq7eAKxb9xLHj6/FysqOl1/ejadnb4OvKy2FM2fUbvNx4+q+vxCi\n9agvcOjq+F40I5oG69er0UZhoZpKqun48XWcP78VMzMLFiz4hvXrf09IyCeYm1vx/PNb8fYeWK19\nUZHabZ6drepPBQTACy8Ynv4SQrQ+9WXb9UBelceyqqqZKS6GY8fgp5/Azc1wldu9ez9i/frfodeX\nMmPGu2RlJbB797uYmVnw5JNrGDDg4Wrt4+NV4Cg/AXDAABg69MZ1rYQQzU9TrKoKBfo19huKxhMS\nAj//rHIadZVGLy7OR68vZezY31FcnF8RNH7zm0307DmxWtuEBJX4XrAAunc3fv+FEC1TfZHoNM0n\ncMiIo4qCAnXM66ZNqkaUU90LocjMjCMrK5ErV35lw4Y/YGJiwoIF3xAUNLuiTWKiGmWUlMDs2TBw\nYN33E0K0HE0x4mgHvFLHm2rAu43dGXFjWVnw+eequKC7e/1BA8DFpTMREfvZsOEPADz++Be1goal\npSpQaGtrOEcihBBV3WgDYD0nUIumsHQppKRAvwaOBc+e3cyKFfMAmDHjPYYPnw+opHpcnBppTJig\nchlCCNEQ9QWOq8A/7lRHxI2lpamVTt261XU9iuPHv6VNm3aMGrWQ+PhQli+fhabpmTTpr9x778sV\nbSMj1Wjl4YcbHoSEEAJkN3iLER4O332nalDVtXN7y5Y3OHx4JUFBjxIYOJ6PP76v4kyNadP+haap\nkUZ6upqWeuYZtalPCCFuRn2B49471gtRr5IS2LNH5TcCAw23iYs7zeHDKwEYOnQun3xyP9euJeLn\nN5K5c5djYmLCpUuVG/jGjpWgIYS4NS1ldX6rXFWl16tzwk+cUPsr/P3BxqZmGz1ffTWX48fXoml6\nevSYhKWlDadP/4C7ewB//vNhbGwciY9XG/hefvnGCXUhxN2hKVZViSZ05gzs2KH2VrRrB716GZ6i\nKizMoaAgG03TM3jwYzg6urNz5/+wsXHkued+wsbGkcxMNcU1c6YEDSHE7ZMRRzOkafDf/6pchJeX\nWi5bn5ycFMLD92BhYcOSJQ9iYmLCb3+7mQ4dJlNQoI6OnTABJk26M/0XQjQPMuJoJdLS4LPP4OpV\n6NOnYaU+HBzccHLy5IMPxgMwffp/6NZtMjExKli4uMjKKSFE45HA0cwkJqoRQl0HMen1ekxrzFld\nvRrOJ5/cj05XxKhRzzBw4B+Jj4fOneGee+T8DCFE45KPlGbmwAFVmdaQ5OSLvPfeWCIiDlQ8d/16\nGp98MpXCwhz69p3OzJmfEBNjwvjx8OKLEjSEEI1PPlaakV9/hcuXwdfX8PUzZ34iIiKEJUsepLg4\nH52umCVLHiI19TKenn2YP38VV66Y4eurzgUXQghjMHbgmAiEA5eBP9fTbhDqzI8HjdyfZu30abC3\nBwuL2teOH/+W7dv/A8BDD/0XCwsbVqyYR2TkQZycPHjxxW1YWbWhtBSmTTN8DyGEaAzGDBxmqPPK\nJwKBwGzUqYKG2r0NbKflrPJqdGlpKiHu5lb7WnFxPitXzqewMIeuXUcxZMhcfvzxVY4fX4u1tT2/\n/e3PODq6k5ICrq7Qteud778QovUwZuAIAiKBGKAE+BaYZqDdC8AGIM2IfWnWMjLggw/UDvGaG/wA\nIiN/oaSkkLZtu/D734cQGrqRHTvextTUjIUL19OuXT/S01ViffBgyWsIIYzLmB8xHkB8lccJZc/V\nbDMN+KzscevZrFHFmjWQl6fO9TYkIGAcfftOZ968lSQlna+odvvQQ+/Qo8cEkpPVuRwTJsCQIXeu\n30KI1smYy3EbEgTeB/5S1taEVjhVlZYGycn1Ty+ZmJjw3HM/kJOTwttvD6WoKJdBg2YzZsxLhIWB\nnR1Mnw4eNcOyEEIYgTEDRyLQqcrjTqhRR1UDUFNYAG2BSahprU01b/b6669XfB8cHExwcHDj9bSJ\n5OXB11/D9etgXvZ/4uzZzXh69sbFpXO1tiUlRXz22XTS06Px8hrI3LlfEBpqgq8vPPqoOtRJCNG6\nhYSEEBISYvT3MeZv+ObAJWAskAQcQyXIL9bR/ivgZ+AHA9fuypIjixdDbKw6X6N8FdRbbw2iR4+J\n3HPPCzg4tAdA0zRWr17IL78sx9nZkxdeOIFe74alJbz0kpqmEkKImoxVcsSYOQ4d8DywAwgD1qGC\nxjNlX61aRAQkJamjWsuDRlzcKWJjT7B9+7+xsLCuaHvw4DJ++WU5FhbWzJ79A7m5bnTvDuPGSdAQ\nQtx5xi45sq3sq6qldbSdb+S+NBslJarqraapUucAen0pX375GACjRj2HjY2KCLGxJ1m37gUAHn98\nOXZ2g5g8GUaPblgdKyGEaGxSq+oOi4+HFSvUEbBVS5zHxZ0mOfkiDg5uPPDAm4Cqert06UPodMWM\nGvUsPXs+Sk6OBA0hRNOSFf93UGEhbN2qyqX7+0OHDpXXdu9+F4DAwAnY2DhQWqpj2bJZZGTE0qXL\nYO655z0uX1b5EAkaQoimJIHjDtE0VS49NNTwfo2xY1+iffuu3Hff3wH48ce/EBERgoNDB5577keu\nX7fmvvvUslshhGhKLeV31xa/quqjj+DiRejdu+6d3eUl048dW8MXXzyKqak5c+bsxcFhJG5u8Nxz\n6jRAIYRoCDnIqQU7eBCio6FHj/rLgZiampKYeJ6vv34agAkTPmDcuJH06KGmtuzt71CHhRCiHhI4\njKykBEJCVCL8RhVr8/Iy+fTTaRQX5xMYOJdPP30Ob+870UshhGg4yXEYkU4Hy5erpbft21e/lpQU\nxtWr4ZRPwel0xSxbNpP09Cu4u/fn//5vCd7eLWUmUQjRmkjgMKK9e1UyvFev2lNUK1fOY9GiAA4f\nXgnAd9/9josXd2Nj055XX/2JmTMNlMkVQohmQKaqjKSwEM6eVedrWFpWPq9pGqGhG4mJOY6pqTkD\nBz7CsWNr2b//U8zMLJk1axNTp3aq+8ZCCNHEZMRhJBcuqGNga05Rfffd7/jsM7Wmtnv3MaSmRrJ6\ntUqGjxz5PrNmDcbL6073VgghGk5GHI2stBQOHIAjR1QdqaoJ8f37l7B37weYmVkwefLfGDr0Cd57\nbyxFRXn06/cYvXs/S2Bg0/VdCCEaQgJHIzt8GDZuBGfn2hv9hgx5nJycFJydPRk+fAGffTadtLQo\nPDz6Mnbs54wda2Lw6FghhGhOJHA0soMH1UjD0PkYVlZ23H//IgC2bn2T0NCN2No6ERz8PX362DBx\n4h3urBBC3ALJcTSis2dVHaobjRrOnt3Mpk1/x8TEhMceW423tw+PPnpn+iiEELdLAkcjKSyETZug\nTZv6N/pdvXqJ5ctno2kaEyb8k9LS+/DxkcKFQoiWQwJHIygpgY8/VmeHVz33OybmOBcv7ql4XFiY\ny5IlD1JUlMuAAY/g4/MaI0bAzJlN0GkhhLhFEjgaQV6eChq9elU+V1CQw8cfT+GjjyYRFXW47PjX\np0lODsPdPYDRo7/A19eExx8HO7um67sQQtwsCRyNICpKlU2vujv8hx/+xPXrqbRt2wUvrwHs3/8Z\nx49/i5VVG+bO/Z7c3DYEBVWeACiEEC2FrKq6TSUlEBZWPUcREbGf06d/AOCRR94nMfEc69f/DoD7\n71+OmVkAgwaparlCGOLi4kJWVlZTd0O0EM7OzmRmZt6x95PAcZvWroWjR6moYrt79/sVQcLJqSNe\nXgP5z3+GoNMVM3z4c3TuPJOJE2HkyKbrs2j+srKyaOln0Ig7x+QOr66RwHEbNm2CY8fUWRk2ZTUJ\n+/d/CGvrNmRmxjF69G9ZuXIB6elX8PTsR8+e7zJwoAQNIUTLJoHjFpWWwrlz0LFjZdAAcHHpxIgR\nTwGwffvbnDu3GVtbZ4KDf2DAAGtmzWqiDgshRCOR5Pgt0OthwwZISQFXV8NtLl0KYePG1wC4995V\n9OzpzYIFsl9DCNHySeC4BefPq0KGXl6GA0FmZhxLlz6EXl/KmDF/oUePKTz2mKygEkLcHSRw3KSS\nEti2TR0Fa+gMcJ2umM8/n0leXiY9e04iIOBf9OpVfWOgEC2dt7c3e/bsuXHDu9Q333zDhAkT6rx+\n8OBBunfvfgd7dGdJ4LhJhw6pzX5Vz8x47717+etfu3D58kF+/PFVoqOP4OzcieDgr2nf3owRI5qu\nv0IYg4mJyR1fydOcPProo+zYsaPisampKVeuXKl4PHLkSMLDw5uia3eEJMdvQk4O7NtXPa+RlhZF\nePiesu+vsHv3u5iamvPww+twdXVl5kzoJAf6CXHXa03Lp2XEcROuXoWsrMrqt1lZibzzzmgAPDx6\ns27dCwBMm/YOMJRevaBbtybqrBB3yMWLF/Hx8WHdunWAmsZavHgxffr0wcnJiVmzZlFUVFTRftmy\nZXTt2hVXV1emTZtGcnIyAIsWLeLFF18EoKSkBDs7O/70pz8BUFBQgLW1NdeuXSMmJgZTU1NWrVqF\nl5cX7dq146233qqzf/PmzePZZ59l/PjxODg4EBwcTFxcXMX1X3/9lUGDBuHk5ERQUBCHDx+uuLZi\nxQp8fX1xcHDAx8eHNWvWVDw/smxd/ahRowDo06cP9vb2rF+/npCQEDqV/cb49ttvM2PGjGp9euml\nl3jppZcAyM7O5sknn6Rjx454enry97//Hb1eD0BkZCSjR4/GycmJdu3aMUuWZd4UraldvKhp332n\naX/4g6YtXapp772XpTk5eWiA5u0dpLm799AArXfvGdrLL+u1lSs1LSGhqXstWqqG/J0HDH41tP3t\n8Pb21vbs2aOdPHlS69y5s7Zly5Zq1wYPHqwlJydrmZmZWkBAgLZkyRJN0zRtz549Wtu2bbXTp09r\nRUVF2gsvvKCNGjVK0zRN27t3r9arVy9N0zTt0KFDmq+vrzZ48OCK1/Xt21fTNE2Ljo7WTExMtIUL\nF2qFhYVaaGioZmVlpV28eNFgX5944gnN3t5eO3jwoFZUVKS99NJL2ogRIzRN07SMjAzNyclJW716\ntVZaWqqtXbtWc3Z21jIzM7Xc3FzNwcFBi4iI0DRN065evapduHBB0zRN++qrryruoWmaZmJiokVF\nRVU83rdvn+bp6alpmqbFxMRotra22vXr1zVN0zSdTqe5u7trR48e1TRN0x544AHt2Wef1fLz87XU\n1FQtKChIW7p0qaZpmjZr1iztrbfe0jRN04qKirRDhw4Z/Bnr+v9Z9v+60cmIowEuX4bly+HkycrR\nRkzMcXJz02nfvisuLp1JTr5A+/Z+DBq0nBEjTJg7VxLi4u62f/9+pk2bxtdff83kyZOrXXvxxRfp\n0KEDzs7O3H///Zw5cwZQSeUnn3ySvn37Ymlpyb///W8OHz5MXFwcQ4YM4fLly2RmZnLw4EGefPJJ\nEhMTycvLY//+/YwePbraeyxatAgrKyt69+5Nnz59CA0NrbOvU6ZMYcSIEVhaWvLmm29y+PBhEhIS\n2LJlC926dePRRx/F1NSUWbNm0b17dzZt2oSJiQmmpqacO3eOgoIC3NzcCLyFs529vLzo378/P/74\nIwB79+7F1taWoKAgUlJS2LZtG++99x42Nja0a9eOl19+mW+//RYAS0tLYmJiSExMxNLSkmHDht30\n+xuDBI4bKC2FLVvU3g0fH3W6H0Bg4DjeeSeVIUPmcurUBqys7Jg37wfatXNg7Nim7bNoHTRNM/jV\n0Pa3+95Lly5l+PDhFVM1VXXo0KHiexsbG/Ly8gBITk7Gq8rKEjs7O1xdXUlMTMTGxoaBAweyf/9+\nDhw4wOjRoxk2bBiHDh2qeFzXe9ja2la8R00mJiZ4enpWe08XFxeSkpJITk6mc+fO1dp7eXmRlJSE\nra0t69atY8mSJXTs2JEpU6Zw6dKlm/hTqjRnzhzWrl0LwJo1a3i07OS22NhYSkpKcHd3x9nZGWdn\nZ5599lnS0tIA+O9//4umaQQFBdGzZ0+++uqrW3r/xiaB4waOH1cjjq5da19LS4ti69Z/ATBnzudk\nZfXCx0ct1RXibmZiYsLSpUuJjY3llVdeafDrOnbsSExMTMXjvLw8MjIy8Cgbno8ePZo9e/Zw+vRp\nBg0axOjRo9m+fTvHjh0zGKAaQtM04uPjKx7n5uaSmZmJh4cHHTt2JDY2tlr72NjYiv6MHz+enTt3\ncvXqVbp3787TTz99S314+OGHCQkJITExkZ9++ok5c+YA0KlTJ6ysrMjIyCArK4usrCyys7M5d+4c\nAG5ubnz++eckJiaydOlSfvOb31RbvdVUJHDUIzy88gzxmpv38vKyWLr0YXS6IkaOfAYrqzkEBMDc\nuU3TVyHuNHt7e7Zv386BAwd49dVX621bPsKZPXs2X331FaGhoRQVFfHXv/6VIUOGVPzWP3r0aFat\nWkWPHj2wsLAgODiY5cuX4+Pjg2tdZRpqvIchW7du5dChQxQXF/P3v/+doUOH4uHhwaRJk4iIiGDt\n2rXodDrWrVtHeHg4U6ZMITU1lY0bN5KXl4eFhQV2dnaY1bGL183NjaioqDrfv127dgQHBzNv3jx8\nfHzoVrZqxt3dnfHjx/PKK69w/fp19Ho9UVFRHDhwAID169eTkJAAgJOTU8X0WVNr+h40Uzk5sHo1\nXLsGNUayaJrGypXzSE+/QufO/Zky5X3c3WH2bLCyapr+CtEUHB0d2bVrF9u2bWPRokUG21Td8zF2\n7FjeeOMNHnroITp27Eh0dHTFfD7A0KFDKSwsrBhdBAQEYGNjU2u0YWgPSV37SkxMTJgzZw7/+Mc/\ncHV15fTp06xevRoAV1dXNm/ezOLFi2nbti3vvPMOmzdvxsXFBb1ez3vvvYeHhweurq4cPHiQzz77\nrNbPBPD666/zxBNP4OzszIYNGwzuc5kzZw579uypGG2UW7VqFcXFxQQGBuLi4sKMGTO4evUqACdO\nnGDIkCHY29szbdo0PvzwQ7zLS3E3oZayg0e73TnZm5GaCl99pZbfBgRUPv/jj3+lf/+HuHRpH99/\n/0dsbZ147bXT5OZ606UL3OIoVohaTExMWtW+AGOaP38+np6evPHGG03dFaOp6+9LWfBq9M952QBY\nQ0oKfPABFBdX34NRUlJEaOhGdu9+F71eB8C8eStxdvYmNhZJiAvRTEkAbnx3YqpqIhAOXAb+bOD6\no0AocBY4BPS+A32qU2qqWkHl7195FOylSyH86U8dSE4OQ6crQq8vZfz4P9K791TOnFEBpneT9loI\nUZfWXh7FGIz9p2kGXALuBRKB48Bs4GKVNkOBMCAbFWReB4bUuM8dmaoqKoJPP4WEhMrRRmlpCf/8\nZ2+uXg3H0tKW4uJ8/PxG8sore4mKMqdDB3j2WWjTxujdE62ITFWJm3Gnp6qMPeIIAiKBGKAE+BaY\nVqPNYVTQADgKeNJEIiPV0ltf38rnzpz5iatXw7GxcaK4OJ82bdry1FNrAXP0enjkEQkaQojWxdiB\nwwOIr/I4oey5ujwJbDVqj+qRlKRWRZlXyfwMGDCD++77O4WF1wGYP/9rHB09OHsWPD1rr7gSQoi7\nnbGT4zcz1r4HWAAMN3Tx9ddfr/g+ODiY4ODg2+lXNSUlcOkSnD0LtrbVr+XkpPLLL8vRtFImTvwL\nPXtOJD5ejUqefLLRuiCEELctJCSEkJAQo7+PsXMcQ1A5i4llj18F9MDbNdr1Bn4oaxdp4D5GzXFc\nugSffKKmnDp1qtzsp9fr+eijSYSF7cTPbwSvvLKP4mJzoqJU0OjTx2hdEq2c5DjEzbjbchwngK6A\nN2AJzAQ21WjTGRU0HsNw0DCq9HT46Sc1ReXtDUlJoRw5ojYHbd/+H8LCdmJn58pTT61FpzMnMhKC\ngiRoCCFaL2MHDh3wPLADtXJqHWpF1TNlXwD/BzgDnwGngWNG7lM1u3bBlSvg56cer1//Ctu3v8X5\n89vYtOnvACxY8DXOzp5cu6amqMrqkwnRarW2o2Nb+1GxNbWUxc1GmaoqLYV//xssLMDZGeLjz/Dm\nm/3RNA17ezeuX09h4sRXmT79LdLTIT4eJkyABx5o9K4IUU1zn6rq0qULX3zxBWPGjLlhW1NTUyIj\nI/Hx8bnt9w0JCeHxxx+vVrSwKTTmz9QY7rapqmbt4EG1Z8PRUT3euPFvaJqGg4MKGv7+o5k27Q0y\nMgc2rFcAABNoSURBVKCwEKZPV9NUQoib05yD4K26G3+mhmq1gUPTVMn09u3VDnFN04iOPgpATk4K\nbdq05ckn1wBmREXBoEEwfjx07Ni0/RaiuTl27BhDhw7F2dmZjh078sILL1BSUgIYPlYVYPPmzfTt\n2xdnZ2eGDx9eUUYc6j56Ni8vj0mTJpGUlIS9vT0ODg4VxQCrkqNiRTmDxyLejqNHNe3llzXto4/U\nUbDvvpupWVraVhyr+cIL27SlSzXtlVc07Z13NK2wsNG7IESdbvR3HgNHxt7K160qPzpW0zTt5MmT\n2tGjR7XS0lItJiZGCwgI0N5///2KtjWPVT116pTWvn177dixY5per9dWrlypeXt7a8XFxRX3ruvo\n2ZCQkIojWevSGo6Kramu/5fI0bGNp7AQDh8Ga2uwtFTP6XRFFUPP8v0aYWFqX8eDD0q5dCHq0r9/\nf4KCgjA1NcXLy4uFCxeyf//+Ott//vnnPPPMMwwaNAgTExPmzp2LlZUVR44cqWhT19GzWgOnh+So\nWONqlYFj/351SFP5tJNeX8qXXz5GSUkB/v6jmTr1DeLi1El+f/oTdOnStP0VoiatjmNjb/arMURE\nRDBlyhTc3d1xdHTktddeIyMjo872sbGxLF68uOKoVGdnZxISEkhKSqpoU/Po2dzc3Ab3R46KNb5W\nFTjy8tThTNu3g5dX5Shi27a3CA/fg719e+bPX0tcnDmaBjNngr190/ZZiObuueeeIzAwkMjISLKz\ns3nzzTcr5uwN6dy5M6+99lrFUalZWVnk5uYyc+bMG75XQ6rcanJUrNG1qsCxejWEhKj6Ui4u6rlL\nl0L4+efXMTExYcGC1WRmuuPqCk89Vf0QJyGEYbm5udjb22Nra0t4eHjFKXnlah6r+vTTT7NkyRKO\nHTuGpmnk5eWxZcuWBo0q3NzcyMjIICcnp952clSscTW/HhlJZCRERECvXmBnBwUFOezc+Q5Llz6M\npumZOPFVvLzGUVoK99wj01NCNNQ777zDmjVrcHBwYOHChcyaNaveY1UHDBjAsmXLeP7553FxcaFr\n166sWrWq3qNfy691796d2bNn4+Pjg4uLi8FVVXJUrPG1mg2AP/0E+/ZBjx7q8TffPMeBA0sA6NZt\nDC+9tIOkJHPat4fnnwc590U0pea+AbA5aw1HxdYkGwCNQNNUIUM3N/U4Ly+LAweWAmBv346nnlqL\nmZk5169D164SNIRoySTgGt9df+b4nj0QGwvJydC9u6p4u2TJg6jlzSY8++wPmJu3JypKLc1tJhUE\nhBC3SI6KNb6W8qd7S1NVsbGwZInai2Fnp8qmf/75I5w8qXavjhnzItOnf0BoKAwcCFOmgMf/t3fv\nQVHXewPH3y6ghJIgt9BEQDt58hLqlOQtTyOFOHYUL+ENzRE1L2Vij6J5yWng6DzPeMmebFI5ZPVw\ntJOXh4xI53Eq4iAqF00JUZE5QAoy4iUQduH547ssu7QgJsuyy+c1w+xvf/vb33798nO//L6Xz6e5\nNFNCtBHpqhIPo627quz6juPIEbXYr36gW6ut5upVFXy3X79RTJ++nZwcFSJ91ixJASuEEC1ht2Mc\nNTXw66+m+cO/+moN5eXXcHN7kiVL1EpRZ2eIiJBGQwghWspuG478fLhzpyGkSFbWEU6c2IZG48ii\nRQfp2tWdwkIVTr0+Oq4QQogHs9uG49o1tTJcp9NSWnqFv/99LgCTJ8cRGBhMbS3cuqUi3jo5Wbmw\nQghhQ+xyjKO6Gs6dg/v3LxITM45u3TyprKwgKGgSISHRgLoj8feHoCDrllUIIWyNXd5xpKdDXl4d\nX389n4qKYoqKcvDw6ENk5D6gE7duqePCwxu6soQQHdfYsWPZu3dvm3xWWFgY+/fvb5PPshS7u+PI\nyFCZ/e7f/4mrV1WYZo3GkQULEtFo3MnOBi8vFVZE1mwIW7JjB9y4Ybnze3uDPteQTSkoKCAwMBCt\nVvuH4zq15dqPY8eOtcnnWJJdNRy1tSrybWUlXLr0iWH/5MlxBAQEc/YsDBumZlE9/rgVCyrEH3Dj\nhorqbCmNgsbanLZa96LT6ZoMfthR2FVXVU0N3L0LTzxxl4wMlfKxb9+RjBu3kuvXVVTcmTOl0RDi\nURUXFzNlyhS8vb0JDAzkgw8+AKC8vJzevXuTlJQEqMi5/fr1MwQZfFBa19zcXEJCQvDw8KB///6G\nVLMAlZWVREdH4+/vj5ubG2PGjKGqqsqQytXNzQ1XV1fS01UK6H379hkCCYaGhpp8znfffUf//v1x\nc3Nj+fLlzeYn2bRpE1OnTmXOnDl0796dhISEZtO/1tbWEh0djZeXF4GBgezatQuNRmN43bhbrK6u\njvfffx9/f398fHyYO3euIfJvQUEBGo2GTz/9lD59+uDl5UVsbOwj/uZah101HElJUFFRR0LC6+h0\nNWg0jixd+r9oNBoKC9VCP1mvIcSjqa2tZeLEiQwZMoTi4mJOnDjB9u3bSUlJoUePHuzbt4+oqChK\nS0t5++23GTp0KLNnzza8/4svvmDDhg2UlZURFBRkSHJ07949QkJCmD17NqWlpSQmJrJkyRIuXrwI\nwKpVq8jMzCQtLY3y8nK2bt2KRqPhhx9+AFQu7zt37jB8+HCOHDlCXFwchw4doqysjNGjRzNjxgwA\nysrKmDJlCrGxsdy8eZO+ffuSmprabFfV0aNHmTZtGhUVFcycOZN58+bRuXNnLl++TGZmJikpKezZ\nswdQGQ6Tk5PJzs7m7NmzHD582OTcxt1i8fHxJCQkcPLkSa5cucLdu3dZtmyZyWenpqaSl5fHiRMn\n2Lx5M7m5uY/6K3xkdtNwXL4MmZlQXh7P2bNf4uT0GG+++Q1lZe5cvqxWj4eEWLuUQti+jIwMysrK\nePfdd3F0dCQgIIAFCxYY0p+GhIQwbdo0XnrpJZKTk/n4449N3t9UWtekpCQCAgKYO3cuGo2GoKAg\nwsPDOXjwILW1tcTHx7Njxw58fX3RaDQEBwfTuXNns3cKu3fvJiYmhqeffhqNRkNMTAxZWVkUFhZy\n7NgxBg4cSHh4OA4ODqxYscIk46A5I0aM4NVXXwVUA9Vc+tcDBw6wYsUKevbsiZubGzExMU3ezXz+\n+eeGu6iuXbsSFxdHYmKiSSKsjRs30qVLFwYPHsyzzz5LdnZ2y39ZFmIXYxx1dZCaCleu5HD48FIA\nZs36CB+fcfz2G8yYoQbEJW+4EI/u2rVrFBcX4+7ubtin0+kMXUagkjXt2rWLdevWmRzXXFrXa9eu\nkZ6ebnK8VqslMjKSmzdvUlVVRV/jUBAPKONbb71FdHS0yf6ioiJKSkpMygAqM19zjI83Tv9ar7a2\n1pCStqSkxOR8jT/LWElJCX2MBq78/PzQarVcv37dsM+4UXNxceHevXvNlrUt2EXDkZICqakVHD8+\njZqaKkaOnM8LL8wlJwfGj4eBA61dQiHsh5+fHwEBAeTl5Zl9XafTsXDhQiIjI/nwww+ZN2+e4Qu/\nubSufn5+vPjii6SkpPzunLW1tTg7O5Ofn8/gwYNNXjPXxeTn58f69esN3VPGLl26ZFKGxmVqrPGM\nK+P0r+Zmcfn6+pqcr7lz9+zZk4KCAsPzwsJCHB0d8fHxMRmTaW9svqvq+HFITq4jLS2K0tI8evUa\nRETEB5SWQs+eEBZm7RIKYV+ef/55XF1d2bp1K5WVleh0Os6fP8/p06cBiI2NxcHBgfj4eN555x0i\nIyNNul6aSus6YcIE8vLy+Oyzz6ipqaGmpoaMjAxyc3PRaDTMnz+flStXUlJSgk6nIy0tjerqary8\nvNBoNCapXBcvXkxsbCwXLlwAVPdS/UB7WFgYP//8M4cOHUKr1bJz506zmQTrNe5melD61+nTp7Nj\nxw6Ki4u5desWW7ZsaXL8ZMaMGWzbto2CggLu3r3L2rVriYiIaHZacXuImmzzDUdODly+vJtz5w7i\n6NiFOXM+oXNnF8rKYMgQScok7Ie3t5oya6kfb++WlUOj0ZCUlERWVhaBgYF4eXmxcOFCbt++zZkz\nZ9i2bZshFezq1avp1KkTW7ZsAZpP6+rq6kpKSgqJiYn06tULX19fYmJiqK6uBlSK2kGDBvHcc8/h\n4eFhGDtwcXFh3bp1jBw5End3d06dOsWkSZNYvXo1ERERdO/enUGDBvHtt98C4OnpycGDB1mzZg2e\nnp7k5+czatSoJv+95tZ4NJf+NSoqipdffpnBgwczbNgwJkyYgIODg9nGYP78+cyZM4cxY8YQGBiI\ni4uLYYZa/WebK4+1Wb8ELWM2H4dOB4sWZZGQMBytVl1coaFrCA6O4/59WLxYTcEVwtbYaz6OjpjW\n9ZtvvuGNN94w6ZJqbZI69iFcunSbL7+camg0vL2fYvTojdy4oWZQPWC8SwjRxuyxMWysqqqKY8eO\nodVqKSoq4r333iM8PNzaxWpVNtlwaLXw4491TJo0i4oK1a/p6RlAdPQPlJc7ExoKI0ZIN5UQ7U1H\nSOtaV1fHpk2b6NGjB0OHDmXAgAFs3rzZ2sVqVbbyGzTpqtq9G/bv38lPP6nAOs7Orqxdexqd7k84\nOMD69dYqphCtw167qoRlSOrYB6irgzNnTpOevgqAV15ZQ//+f8Hd/U/k5ak4VEIIISzH5hqOCxcq\nOHjwNXS6GsaOXUp4eBwVFfDLLzBgAAQHW7uEQghh32yq4airq+P11xdSUXGF3r2DmDr1P7lyBTQa\nGDcOJk5U20IIISzHphqOuLiPycg4QJcu3YiKOoCTkzP378Py5ZJbQ9gXd3d3ux9EFq3HOExLW7B0\nwxEKbAccgD3AFjPH7ATGA78B84BMcyf6/vscNmxYAcCkSbH4+DzF1avg6SmNhrA/5eXl1i6CEE2y\nZMeOA7AL1Xg8A8wA/tzomDCgH/AUsBD4qKmTTZv2V3S6+wCcP/89WVnw2GMSUuSPOHnypLWLYDek\nLluX1KdtsGTD8TyQDxQANUAi8NdGx7wKJOi30wE3wMfcyW7cKADAw6MvI0f+jenTYdUqFVZEPBz5\nz9l6pC5bl9SnbbBkw9ELMA4L+W/9vgcd02QMYjc3f8LDswkL68vYseDi0lpFFUII0VKWHONo6eql\nxiOAZt/n5vYMy5alMW5cV5qJRyaEEMLCLDltIxjYhBrjAIgBajEdIN8NnER1YwHkAi8C1zGVD7Qs\ng4sQQoh6l1HjyDbDEVVof6AzkIX5wfFj+u1g4F9tVTghhBDt03jgF9QdQ4x+3yL9T71d+tezgaFt\nWjohhBBCCCFExxaKGve4BKy2clnauwIgB7WA8pR+Xw/gOyAPSEFNd64Xg6rXXOBlo/3DgHP613ZY\ntMTtxz7UuNo5o32tWXddgH/o9/8L6NO6xW93zNXnJtSsyUz9z3ij16Q+m9cb+D/gZ+A88KZ+v1yj\nZjigurD8ASfMj5GIBldRF5KxrcB/6LdXA3/Tbz+Dqk8nVP3m0zBR4hRqDQ6o8af6yQ32bDQwBNMv\nutasuyXAf+u3X6NhMoi9MlefG4GVZo6V+nywJ4Ag/XY3VPf/n5Fr1KwXgGSj52v0P8K8q4BHo325\nNCyofEL/HNRfI8Z3cMmoyQm+wEWj/RGomW8dgT+mX3StWXfJwHD9tiNQ2lqFbsf8+X3DEW3mOKnP\nh3cYGIcVr9H2HEu2JQsIRYM64DhwGojS7/OhYWrzdRousp6o+qxXX7eN9xfRceu8NevO+FrWAhX8\n/u6wI1iOmgSzl4ZuFanPh+OPuptLx4rXaHtuOCT92cMZibqgxgNLUd0FxuqQOv2jpO4e3UdAAKrL\npQT4L+sWxyZ1A/4JvAXcafRam16j7bnhKEINCtXrjWlrKUyV6B9LgUOofszrqFtYULepN/Tbjev2\nSVTdFmEa8uVJ/b6OqDXq7t9G7/HTbzsC3YGOFv72Bg1fbnto6GeX+mwZJ1SjsR/VVQVWvEbbc8Nx\nGhU11x+1gPA14Kg1C9SOuQCu+u2uqFkU51D1NVe/fy4NF9xRVP9mZ9RfgU+hBs1+BW6j+jo7AXOM\n3tPRtEbdHTFzrqnACQuXvT3yNdqeTMP4h9Tng3VCde9dQKWpqCfXaBPMLSAUvxeAmkWRhZquV19X\nPVDjHuam661F1Wsu8IrR/vrpevmoXCkdwf8AxUA1qp/3dVq37roAB2iY6uhvgX9De9K4PucDn6Km\ni2ejvuCMo2BLfTZvFCpcUxYN05lDkWtUCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQghb5GDtAghh\npzah5synWbkcQrS69rxyXIj2ohMNYalbSmJbCbslDYcQ5vmjohYkoFba7gUyUCvzNxkdV6B/fga1\nMvppo9fqG48oVO4DZ8sVVwghhLX5AzoagvG56x8dUNnYBuqfX0VFIwZ4A/hEv12ff2IZKuikk2WL\nK0TbkTsOIZp2jYY0vK+h7irOAgNQWdbqfaV/PEtDjJ9OQCQqptBUoMbCZRWizUjDIUTT7ukfA1B3\nDy8BzwJfY9rtdF//qEOFpAbVTXUOlbvZOMS1EDZPGg4hHuxxVCNyGxXVdXwL3tMJFcV0MSpktW/z\nhwthO6ThEKJp9YPb2ahGIBf4HPixmePrGm2nAqtQdykdJb2pEEIIIYQQQgghhBBCCCGEEEIIIYQQ\nQgghhBBCCCGEEEIIIYRoa/8PyStUMKSFjoMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7d78f19390>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# 2. Compute cumulative rank distribution of known negatives\n",
      "\n",
      "The code below is analogous to what we did earlier for known positives, but now for known negatives. We will first flip known class labels, as described in the text."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# ranks of the known positives\n",
      "known_neg_ranks = [idx for idx, lab in enumerate(sort_labels) if lab == False]\n",
      "\n",
      "# compute rank ECDF of known positives\n",
      "known_neg_ecdf = ss.compute_ecdf_curve(sorted(known_neg_ranks))\n",
      "\n",
      "# flip class labels\n",
      "labels_flipped = [not label if label is not None else None for label in labels]\n",
      "sort_labels_flipped = [not label if label is not None else None for label in sort_labels]\n",
      "\n",
      "# compute confidence interval in the same way as we did for known positives\n",
      "if use_bootstrap:\n",
      "    neg_cdf_bounds = ss.bootstrap_ecdf_bounds(labels_flipped, decision_values, nboot=nboot, ci_width=ci_width)\n",
      "else:\n",
      "    neg_cdf_bounds = ss.dkw_bounds(labels_flipped, decision_values, ci_width=ci_width)\n",
      "    \n",
      "# for reference, rank CDF of latent negatives\n",
      "latent_negatives = map(lambda x, y: x == False and y == None, true_labels, labels)\n",
      "sort_lns, _ = zip(*sorted(zip(latent_negatives, decision_values),\n",
      "                          key=op.itemgetter(1), reverse=True))\n",
      "latent_neg_ranks = [idx for idx, lab in enumerate(sort_lns) if lab]\n",
      "latent_neg_ecdf = ss.compute_ecdf_curve(latent_neg_ranks)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot rank CDFs of known positives and known negatives along with their CIs."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = list(range(len(labels)))\n",
      "plt.figure(1)\n",
      "plt.fill_between(xs, list(map(pos_cdf_bounds.lower, xs)), list(map(pos_cdf_bounds.upper, xs)), \n",
      "                 color='blue', alpha=0.4)\n",
      "plt.plot(*zip(*known_pos_ecdf), color='blue', linestyle='dashed', linewidth=2)\n",
      "plt.plot(*zip(*latent_pos_ecdf), color='blue', linewidth=2)\n",
      "plot_proxy('blue', 0.4)\n",
      "\n",
      "plt.fill_between(xs, list(map(neg_cdf_bounds.lower, xs)), list(map(neg_cdf_bounds.upper, xs)), \n",
      "                 color='red', alpha=0.4)\n",
      "plt.plot(*zip(*known_neg_ecdf), color='red', linestyle='dashed', linewidth=2)\n",
      "plt.plot(*zip(*latent_neg_ecdf), color='red', linewidth=2)\n",
      "plot_proxy('red', 0.4)\n",
      "plt.xlabel('rank')\n",
      "plt.ylabel('TPR')\n",
      "plt.legend(['known positives', 'latent positives', 'known negatives', 'latent negatives', 'CI for pos', 'CI for neg'], \n",
      "           loc=\"upper left\", bbox_to_anchor=(1,1))\n",
      "plt.title('Rank CDF')\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9+vXrR3R0NGvXriUzM5N169YRGRnJwIEDuXLlCj/88APp6elYWFhga2uLeQlm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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7d78ef8050>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# 3. Compute contingency tables for each rank\n",
      "We will compute contingency tables based on the rank distribution of known positives and based on the rank distribution of known negatives.\n",
      "\n",
      "Applying our approach to known negatives requires a few modifications:\n",
      "1. Flip known class labels, so negatives become positives\n",
      "2. Modify beta (new beta = 1 - beta)\n",
      "3. Run our approach\n",
      "4. Adjust resulting contingency tables (i.e., flip class labels back). Note also that the optimistic contingency table becomes the pessimistic table when flipping labels and vice versa."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute contingency tables based on CI of rank CDF of known positives\n",
      "tables_pos = ss.compute_contingency_tables(labels=sort_labels, decision_values=sort_dv,\n",
      "                                             reference_lb=pos_cdf_bounds.lower,\n",
      "                                             reference_ub=pos_cdf_bounds.upper,\n",
      "                                             beta=betahat, presorted=True)\n",
      "\n",
      "# compute contingency tables based on CI of rank CDF of known negatives\n",
      "# this requires flipping labels, changing beta and post-processing the resulting contingency tables\n",
      "betahat_flipped = 1.0 - betahat\n",
      "tables_neg = ss.compute_contingency_tables(labels=sort_labels_flipped, decision_values=sort_dv,\n",
      "                                           reference_lb=neg_cdf_bounds.lower,\n",
      "                                           reference_ub=neg_cdf_bounds.upper,\n",
      "                                           beta=betahat_flipped, presorted=True)\n",
      "postprocess_ct = lambda ct: ss.ContingencyTable(TP=ct.FP,\n",
      "                                                FP=ct.TP,\n",
      "                                                TN=ct.FN,\n",
      "                                                FN=ct.TN)\n",
      "tables_neg_post = ss._lb_ub(lower=map(postprocess_ct, tables_neg.upper),\n",
      "                            upper=map(postprocess_ct, tables_neg.lower))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# 4. Compute and plot performance estimates based on the contingency tables"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 4.1 ROC curves\n",
      "\n",
      "Start off with the easy stuff: the true ROC curve (unknown in practice), and the curve we obtain by assuming beta=0."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# compute the true ROC curve (we use Optunity's ROC function)\n",
      "_, roc_true = optunity.metrics.roc_auc(true_labels, decision_values, return_curve=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compute bounds based on the proposed method."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# we can directly use the contingency tables we already computed anyways\n",
      "roc_bounds = lambda tables: ss._lb_ub(lower=ss.roc_from_cts(tables.lower),\n",
      "                                      upper=ss.roc_from_cts(tables.upper))\n",
      "\n",
      "# bounds starting from known positives\n",
      "roc_bounds_pos = roc_bounds(tables_pos)\n",
      "\n",
      "# bounds starting from known negatives\n",
      "roc_bounds_neg = roc_bounds(tables_neg_post)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Plot the resulting curves"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "xs = [float(x) / 100 for x in range(101)]\n",
      "roc_pos_up = ss.zoh(*zip(*roc_bounds_pos.upper))\n",
      "roc_pos_lo = ss.zoh(*zip(*roc_bounds_pos.lower))\n",
      "roc_neg_up = ss.zoh(*zip(*roc_bounds_neg.upper))\n",
      "roc_neg_lo = ss.zoh(*zip(*roc_bounds_neg.lower))\n",
      "fig = plt.figure(2)\n",
      "fix_plot_shape(fig)\n",
      "plt.plot(*zip(*roc_true), color='black', linewidth=2)\n",
      "plt.fill_between(xs, list(map(roc_pos_lo, xs)), list(map(roc_pos_up, xs)), color='blue', alpha=0.3)\n",
      "plt.fill_between(xs, list(map(roc_neg_lo, xs)), list(map(roc_neg_up, xs)), color='red', alpha=0.7)\n",
      "plot_proxy('blue', 0.3)\n",
      "plot_proxy('red', 0.7)\n",
      "plt.xlabel('FPR')\n",
      "plt.ylabel('TPR')\n",
      "plt.legend(['true curve', 'expected region via known pos', 'expected region via known neg'],\n",
      "           loc=\"upper left\", bbox_to_anchor=(1,1))\n",
      "plt.title('Receiver Operating Characteristic curve')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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ycjK7d+/mww8/ZNeuXbi5ufHtt98ybdo00tLSePHFF7nvvvt47LHHjPevXbuW\n119/nfT0dLp06cKjjz4KQEFBAUOGDOGxxx4jLS2NyMhInnnmGc6fPw/ASy+9xMmTJzl06BCZmZks\nX74cpVLJgQMHAMjJySEvL4+ePXuyadMmli1bxsaNG0lPT6d///6EhYUBkJ6ezrhx41i6dCkZGRm0\nbt2agwcPVmu2joqKIjQ0lJycHMLDw5kyZQrW1tbExsZy8uRJdu3axddffw3Al19+yY4dOzh9+jQn\nTpzg119/LZe3qYk8IiKC77//nr1793L58mXy8/MrKbSDBw8SHR3N7t27WbJkidmtenv27ImDgwO7\nd+8u186lbVuRkSNHEhMTQ1paGvfdd1+V6Uy5cuUKISEhPP/888yePdt4ft26dXz33Xdcv34dlUrF\nu+++C0B0dDTh4eF8/PHHpKenM2LECEaPHo1GoyE4ONj4uyUnJ6NWqzl8+DAAly9fpqCggE4mITG3\nbt3KsWPHOHPmDD/99BM7d+6sUs6oqCjGjx9PVlYW4eHhjBkzBq1Wi1qtZvTo0QwfPpy0tDQ++eQT\nHn30US5dugSILZi//PJLcnNzOXfuHIMGDbphm1SkYQydJPWGXi8C2JV2oNVqEdzOoqQQz8uHaHXy\nFzzijqFBj9raAY1NMywcFFhYgK1pd1GnxaKokOS8TD7IvsYfhbnEqovLleXs3IwpU5bTrduDuLjU\n0/ZvJhQVCcUOoh0sDf8NNjZCsXt5iZG8s3PZNUv5H9PgOXr0KOnp6bz22msAtGrViieffJLIyEiG\nDh3KkCFDCA0NZdCgQWRnZ5cbYYHYc75fv34AvPXWWzg7O5OYmMjBgwdp1aoVkydPBsQ+92PHjmX9\n+vW89tprREREGEeyAL169QLMm/I///xz5s6dSztDtKW5c+eydOlSEhIS2Lt3L0FBQYwdOxaAmTNn\n3nA016dPH+OINCcnh+3bt5OdnY2trS12dnbMnDmTr776iqeeeoqffvqJmTNn4u3tbSx7z549ZvNd\ns2aN0WoBwrkuKCiI7777zphm4cKF2NjY0KlTJzp37szp06cJDAyslFdYWBjr1q3jgQceIC8vj+3b\nt1e5re+UKVPK5f/RRx+Rl5eHo6Oj2fTnzp3jjTfe4O233+aRRx4xnlcoFDz++OO0adMGgPHjxxMV\nFQXAjz/+yKhRoxg8eDAgOmwfffQRf/75JwMGDMDR0ZGTJ09y8eJFhg0bxunTp7l48aLxuilz5szB\nyckJJycfUTidAAAgAElEQVQnBg4cyKlTpxg2bJhZWe+//37jbztr1izee+89Dh06hF6vp6CggDlz\n5gAwcOBARo0axdq1a1m4cCHW1tacO3eOjh074uzsTNeuXc3mXx3y9XUXotNBXp7YbObkSTF6dXYW\nzmXWhdl0P/UTLfb+gFJTgs7CCnVTD1AqsQCMM4N6PZaFeeQV5BBVlMu54gIi87PIq7AJjZ9fe7p2\nHcaUKcuxrON49DdCrxeWi6Ii8d3RUWxU07w5ODmVBcORNG7i4+NJTk7G1dXVeE6r1ZZ7SU+bNo0V\nK1Ywf/78cukUCgW+vr7GYwcHB9zc3EhOTiY+Pp4jR46US6/RaJg0aRIZGRkUFxfTunXrGsv4wgsv\nlBuJAiQlJZGSklJOBhAm5OowTR8fH49arTZ2PEBYPVq0EJs+paSklMuvYlmmpKSk4O/vbzxu0aIF\nGo2Ga6VRpIDmzZsbv9vb21NQUGA2r/DwcPr06cPKlSvZsGED3bp1M1svrVbL/Pnz+fnnn0lLS0Op\nVKJQKEhPTzer8PV6PWvWrKFt27aMGzeu0nVT+ezs7MjPzwfEyL20TUD89n5+fiQZnEWCg4PZu3cv\nMTExBAcH4+Liwr59+zh06BDBwcFVlmFvb28swxym7V36vCUnJwOVf2d/f3+jPL/88gtvvvkmc+bM\noVOnTrz99tvGTmVNkQr/LiI/Hy5dgjNnoLgY9Do9LvosglRxOJy4QNOze3GKOwM6LeomrqibuFTK\nQ6FWkZ1znRVZqexSFRFtJnwtQI8eo3n66ZW4u9ehF1ctuXYNPD2hRw9wcxNmeOnce+fRokULWrVq\nRXR0tNnrWq2Wp556ikmTJvHpp58yZcoUo6LW6/VcvXrVmDY/P5/MzEx8fHxo0aIFwcHB7Nq1q1Ke\nOp0OW1tbYmJiypl6AbOm+BYtWrBgwQKjGd+US5culZOhokwVqeil7ufnh42NDRkZGWZXBXh5eZXL\nr7q8vb29iYuLMx4nJCRgaWmJp6dnOZ+DmtC+fXv8/f3Zvn07a9euJTw83Gy6tWvXEhUVxe7du/H3\n9yc7Oxs3N7cqfRgUCgWLFy9m+/bthIeHExkZWaPVED4+Pvz999/G49J29jF4ngYHBxMVFUVcXBzz\n58/HxcWF1atXc/jwYWbMmFGrupti2t46nY7ExER8fHyM5ev1euPvGR8fb7SW3H///fz6669otVo+\n+eQTxo8fX+vfQM7h36Hk5wvTfHo6XL0K27eLFXMn9+fR9uwGHtg2i3FfDGHYB8MI+vxZAqI+wCHx\nPCWObpS4NkdnZWPMS6fVsj/5Ep9ePkX3c/sIvHKKFdmpRmXv7d2WNm26MXXq+0REJBIVpee116Ia\nlLIvKhLm+CFDxJx7s2ZS2d+p9OjRA0dHR5YvX05RURFarZazZ89y7NgxAJYuXYqFhQURERG8/PLL\nTJo0yeiwBsI56uDBg6hUKhYsWEDv3r3x8fFh5MiRREdHs3r1atRqNWq1mqNHj3LhwgWUSiVPPPEE\ns2bNIiUlBa1Wy6FDh1CpVHh4eKBUKomNjTWWMX36dJYuXWp0RsvJyTE6AI4YMYJz586xceNGNBoN\nH3/8Mamp5peqQuUpAy8vL4YOHcqsWbPIy8tDp9MRGxvL/v37AWHW/uijj0hOTiY7O5t33nmnSv+A\nsLAwPvjgA+Li4sjPz2fevHlMmDChWoVa3WqE8PBwPvzwQw4cOEBoFWss8/PzsbGxwc3NjYKCAubN\nm1dlfqVYWVmxfv16CgoKmDRpUjkZqpInNDSUrVu3smfPHtRqNe+99x62trb06dMHEAr/999/p7i4\nGG9vb/r168eOHTvIzMys1px+o9UYx48fN/62H374Iba2tvTq1YsePXpgb2/P8uXLUavV7N27ly1b\ntjBhwgTUajVr1qwhJycHCwsLHB0db2olhhzh30FotXD8uJiPLy42hG/V67HLSqZZTjQDko7Q/Ohm\nFBoVOktrNLYOlLh4mtV8hRo1O9IS+DEjkf1mgt8ADB/+vzz00Iv4+jbAXV8qkJYGDz4Idnb1Lcmd\ni7t73S6dc69hfCWlUsmWLVuYPXs2AQEBlJSUEBgYyJtvvsnx48f54IMPOHbsGAqFgldffZWtW7fy\nzjvvMHfuXBQKBeHh4SxevJhDhw7RrVs3owe/o6Mju3btYtasWcyaNQudTkeXLl2M89Dvvvsuc+fO\npXv37uTn59OlSxd27tyJvb098+fPp2/fvqjVanbu3MmYMWPIz89nwoQJxMfH4+zszNChQwkNDaVp\n06asX7+e559/nscff5yJEycafQrMYW4d+qpVq5gzZw4dOnQgLy+PgIAA49zwtGnTiI6OplOnTjg7\nOzNjxgz27dtnVok/8cQTJCcnG1ccDB8+3LjiobRsc/JURVhYGHPnzmXEiBG4ubmZrcOkSZPYuXMn\nPj4+uLu7s2TJEr744osq8yzFysqKDRs2MGrUKKZOnWpcaVCVQ2K7du1YvXo1M2bMICkpia5du7J5\n82YsDY46bdu2xdHRkf79+wPg5ORE69atadasWaU8K9a/qjZQKBQ8/PDD/Pjjj0yePJm2bduyYcMG\nLCwssLCwYPPmzTzzzDMsW7YMX19ffvjhB+655x7UarVRVq1WS2BgIGvWrLlhm1Qqv9Z31I7hwIeI\nqd+vgXcqXG8KrAaaIzof7wLfmclHhvG8AYWFYnO5xERhtrayAsf4s7Tc+inOsceFUtfrUTVxM7+3\nu17PsawUItMSiFOXcNCMkh84cBLt2/elQ4d+tGjR4TbUqvaUrpEvLBS+CiA6Qi1bCoUvR/W1424L\nrfv444/j6+vLG2+8Ud+i3Da2b9/O008/Xc50L6kbFi9eTExMDD/88EOdlVFfoXUtgBXAA0AScBSI\nAs6bpHkOOAnMRSj/i4gOgKYO5bpjyM6GTZvKgsDY2ICvL9hmJBHw6/u4nduP3sKSEmfz9mt1SREH\n0hL4u6SQHQVZnKoQp75Zs5ZYWdnwyis/0apVp0r3326Kisor8lI0GuGEp9eDtbXo8AQFiXXy1oZQ\n/c7OUtlLbsyd2ImpSHFxMXv27GHo0KFcu3aNxYsXG73GJXVLfT9fdanwewAxQJzhOBJ4mPIKPwUo\n1SROQAZS2deYv/4So9dSp0+FVoPPf3/Af+eXoNdT4tLMEP3GgF5Pen4Wv2Uk8d/CXPYV5VKg05bL\nMygomKCgEB58cDqurs2pD0q96QsKhJIuVdQuLmI7WesK++04OAgnPGdn8V0qdsnNcjeEadXr9Sxa\ntIgJEyZgZ2fHqFGjWLJkSX2LdVdQ389XXZb8H2AYMM1w/BjQEzB1b1QCe4B7AEdgPLDdTF53pPnw\n35CaChs2CGWvUIBNZgqBq+fjdOUMJU7u6A270On1enZmpbIyOZrYkiIydOX7U02b+tK6dTf8/YMY\nOnQazZr5myvutqEXO+ji7w8dO5Y515nuIS+5fdxtJn2JpLFTXyb9mrwN5gGngBCgNfAb0BmoNIG8\naNEi4/eQkBBCQkJugYiNE50ODh40rB0vysV7/zr89qwCnZZi1+bogQM5aRwryGJdWgKJqvIBcAIC\nutK0qR9jx75Chw5966cSVZCcLMzx/fvLkXp9sHfvXvbu3VvfYkgkkjqgLl+pvYBFCMc9EPP0Oso7\n7m0D3gIOGo53A68CxyrkJUcTBoqK4ExUHHnbDtA64whOsSdRatWoHFzJUsCUS8c4kp9Z6b572nYn\nLHwxnToNwspkyV1D4vp1Me8+cqSMaNdQkCN8iaRxUV8j/GNAW6AlkAw8AlSMMnEB4dR3EPAE2gGX\n61CmRotOo+Pqz0coXPk9AQknsLTQobO2RWPnyN+qQubFHOVofla5e9q7NKfHA1MYMmY2Tk5N60ny\nG6PXizj1Hh5inbxU9hKJRHLrqctXqwbhhb8T4bH/DcJh738N178AlgIRwGnEfP4rQOXh6d2MSkV2\n5HYKP/kG27RUHGws0TT1QKtQEpWZzP+eP1jplpVtuhP43JfkBXSpB4GrR6cT8fpBeNfn50NJiZiv\n791bztNLJBJJXdFYZknvOvOhqkBNxo+/ofjkExSZ6ejsm6BwbIJer+dIfiZvJ14sZ7q3VSiYH9iH\ngeFLyOrQD72VdTW51w/FxcJs7+ZmcDS0EdvLennV7T7qkptHmvQlksZFdSZ9qfDrmdL143q9mJ/P\nSS4g7+edOKz9Epu8DPQOTdA3acLpgmxmXD7FpeLymzK0tG3CZ1OWY9FrDCX1tK2sKVqtWCtfXN5P\nEI1GKPkhQ0QQHEnjQCr8hkFISAgTJ05k6tSpdV7WiBEjCAsLK7c/fV2zbNkyLl++zFdffVXre29n\n2zQG6msOX1INubkQGys2sikqgiaZCbQ5uo6Wf0fhrlWhb+KIzrM5B3PTefbUIa6pS8rd38M3kGee\nXolbxxA01F/wgvx8scVsaVhnCwsR+CYgwBDa14BSCW3aiLX0kjuUBx8UOxTVFZ6eYlOIRkZcXBwB\nAQFoNJoabepijtu5fnvbtm23pRxT5s6de9P31vfa9saEVPi3gYICEUgmPV3EGk9NBZVKKEE3Zy1B\nZ36k1dZPUOi0qJzc0FpacbEoj+fO7edsYa4xH78mbgx+cDqjJyzEqh5N9vn5YhSvUolgNw89JNbL\ng3C4u8l3mqSxc+1a3c7N1GWg/tvA7bKIaLXam9pYRXLnI1/NdURhoVgr/9138MMPsGWLiIyXlQWu\nruK92EZ/iZ5fPkHrTe+htnOkxMWTLbnpeB3dQsjZfUZl39u5GVHv/MGnazMYO/Gt26bs9XpRj9xc\n8UlNFUFxbGyEk92DD8L48SL4j7W1+EhlL2kIJCcnM27cOJo1a0ZAQIBxw5fMzEz8/PzYsmULIHZm\na9OmjXGDnClTpjB9+nSGDh2Kk5MTISEh5bYgvXDhAkOGDMHd3Z3AwEDjDncARUVFzJ49m5YtW+Li\n4mLccGbAgAEAuLi44OjoyJEjRwD49ttv6dChA25ubgwfPrxcOb/99huBgYG4uLgwY8YM9Hp9lR2G\nRYsW8Z///IeJEyfi7OzM999/T05ODlOnTsXb2xtfX18WLFhg3BFQp9Mxe/ZsPDw8CAgIYMWKFSiV\nSuP1kJAQ48Yzer2eN998k5YtW+Lp6cnkyZPJzRXvpbi4OJRKJatWrcLf3x8PDw+WLl1qVsYjR47g\n5eVVrg4bN26kc+fOxjqYTiGEhobi5eWFi4sLwcHBxl0Fb0RKSgqdOnXivffeM9bl9ddfp1+/fjg5\nOTFs2DAyMjKM6aOiorj33ntxdXVl4MCBXLhwAYCIiAgeeughY7q2bdsyfvx447Gfnx9nzpwBxGZN\nX3zxBffccw+urq4899xzVcq3aNEixo8fz+TJk3FyciIoKIjjx48br1f13IJ4viZPnoybmxsdOnRg\n+fLl+Pn51ahdSpGv51tMcTGcOwdr18L58yI4jo8PeHtD8+bi2L4gjVa/vk/X9x7FISmaYlcvTquK\nGf3PQZ6MPV4uvy8nL2fud8nQvu4D5KjVYivd5GTxSUkRXvNNm4pPp04wYQKMHSv2lG/ZUi6hkzQ8\ndDodo0ePpmvXriQnJ7N7924+/PBDdu3ahZubG99++y3Tpk0jLS2NF198kfvuu4/HHnvMeP/atWt5\n/fXXSU9Pp0uXLjz66KMAFBQUMGTIEB577DHS0tKIjIzkmWee4fx5ES38pZde4uTJkxw6dIjMzEyW\nL1+OUqnkwIEDgNgCNy8vj549e7Jp0yaWLVvGxo0bSU9Pp3///oSFiVXL6enpjBs3jqVLl5KRkUHr\n1q05ePBgtWbrqKgoQkNDycnJITw8nClTpmBtbU1sbCwnT55k165dfP311wB8+eWX7Nixg9OnT3Pi\nxAl+/fXXKneUi4iI4Pvvv2fv3r1cvnyZ/Pz8Sgrt4MGDREdHs3v3bpYsWWJUmqb07NkTBwcHdu/e\nXa6dS9u2IiNHjiQmJoa0tDTuu+++KtOZcuXKFUJCQnj++eeZPXu28fy6dev47rvvuH79OiqVinff\nfReA6OhowsPD+fjjj0lPT2fEiBGMHj0ajUZDcHCw8XdLTk5GrVZz+PBhAC5fvkxBQQGdOpXtL7J1\n61aOHTvGmTNn+Omnn9i5c2eVcm7evJmwsDBycnJ46KGHjO1Z3XMLYuOdhIQErly5wm+//cbq1atr\nPZUhFf4tIj0d/vgDVq2CAwfEKL5017pSbNMTuWfdYnosGYXP/nWoHN3Zodcx6Nx+hv1zgGMFYh29\np20T1r38I5s3qGg+7uWyCfI6JiVFRLibMEF8pk4Vyn3YMPHp2VPUSyJpyBw9epT09HRee+01LC0t\nadWqFU8++SSRkZEADBkyhNDQUAYNGsSOHTsqbb06atQo+vXrh7W1NW+99RaHDh0iMTGRLVu20KpV\nKyZPnoxSqaRLly6MHTuW9evXo9PpiIiI4KOPPsLLywulUkmvXr2wtrY2OzL//PPPmTt3Lu3atUOp\nVDJ37lxOnTpFQkIC27ZtIygoiLFjx2JhYcHMmTNp3rz6fS369OljHJHm5OSwfft2PvjgA+zs7PDw\n8GDmzJnG+v/000/MnDkTb29vXFxcmDt3bpXWgzVr1hitFg4ODixbtozIyEijNQBg4cKF2NjY0KlT\nJzp37szp06fN5hUWFsa6desAyMvLY/v27cZOTkWmTJmCg4MDVlZWLFy4kNOnT5OXZ36bboBz584x\naNAglixZwpNPPmk8r1AoePzxx2nTpg22traMHz+eU6dOAfDjjz8yatQoBg8ejIWFBS+99BJFRUX8\n+eefBAQE4OjoyMmTJ9m/fz/Dhg3D29ubixcvsm/fPqPVppQ5c+bg5OSEn58fAwcONJZhjv79+zN8\n+HAUCgWPPfaYsb1u9NyuX7+eefPm4ezsjI+PDy+88EKtp4nk+OxfkpgIR46I5WbW1mIuu6J+tszP\nxnfvanz2rkah16FydCdFq2HY379z3cQZz8XGgQ/e+C/ugb2AmsUmvlVcvy6c6oKCZEhbSeMmPj6e\n5ORkXE16p1qtttxLetq0aaxYsYL58+eXS6dQKPAt3Y0KcHBwwM3NjeTkZOLj4zly5Ei59BqNhkmT\nJpGRkUFxcTGtW7eusYwvvPBCuZEoQFJSEikpKeVkAG5oujVNHx8fj1qtxsurbNWOTqejRYsWgDB7\nm+ZXsSxTUlJS8Pcv21+jRYsWaDQarpk4Z5p2Ruzt7SkoKDCbV3h4OH369GHlypVs2LCBbt26ma2X\nVqtl/vz5/Pzzz6SlpaFUKlEoFKSnp+Po6FgpvV6vZ82aNbRt25Zx48ZVum4qn52dHfn5YqVTcnKy\nsU1A/PZ+fn4kGXxFgoOD2bt3LzExMQQHB+Pi4sK+ffs4dOgQwcHBVZZhb29vLMMcnp6e5dIWFxej\n0+lu+NwmJyfX+HerCqnwbwK1WjjhnTgBMTHC89xc27tE/4XP3tW4XjwCiL3o0/V6PkuO5rPU8gEF\nI974L+6dB9+eChjIyhIrBADs7GDAAKnsJY2fFi1a0KpVK6Kjo81e12q1PPXUU0yaNIlPP/2UKVOm\nGBW1Xq/n6tWrxrT5+flkZmbi4+NDixYtCA4ONppYTdHpdNja2hITE1PO1AuYNbu2aNGCBQsWmB3h\nXrp0qZwMFWWqSEUvdT8/P2xsbMjIyDC7KsDLy6tcftXl7e3tTVxcnPE4ISEBS0tLPD09y/kc1IT2\n7dvj7+/P9u3bWbt2LeHh4WbTrV27lqioKHbv3o2/vz/Z2dm4ublVOZpVKBQsXryY7du3Ex4eTmRk\nZI1WQ/j4+PD3338bj0vb2cfgeBocHExUVBRxcXHMnz8fFxcXVq9ezeHDh5kxY0ZV2VZLdSZ4Pz+/\nap/b0t8tMDAQqP53qwpp0q8F+fliVdC334qd6pKSoEULMS9vikKtotWvH9Bx5dM4xxyjxMmdlCau\nTL5yiqBTu4zK3lZpwZuh89i8UX3blX1RkVgbP2oUjBkjTPd2drdVBImkTujRoweOjo4sX76coqIi\ntFotZ8+e5dgxsUXH0qVLsbCwICIigpdffplJkyaVM1Fv27aNgwcPolKpWLBgAb1798bHx4eRI0cS\nHR3N6tWrUavVqNVqjh49yoULF1AqlTzxxBPMmjWLlJQUtFothw4dQqVS4eHhgVKpJDY21ljG9OnT\nWbp0qdEZLScnx+gAOGLECM6dO8fGjRvRaDR8/PHHpKamVlnfiorQy8uLoUOHMmvWLPLy8tDpdMTG\nxrJ//34Axo8fz0cffURycjLZ2dm88847VSqisLAwPvjgA+Li4sjPz2fevHlMmDChWoVanZk5PDyc\nDz/8kAMHDhAaGmo2TX5+PjY2Nri5uVFQUMC8efOqzK8UKysr1q9fT0FBAZMmTSonQ1XyhIaGsnXr\nVvbs2YNarea9997D1taWPn36AELh//777xQXF+Pt7U2/fv3YsWMHmZmZdO3a9abqX921Gz2348eP\nZ9myZWRnZ5OUlMSKFSvkHP6tRqUSoV9TUuDnn8VfLy/hhOfhUTm93bU4On8yFZ99ayhxbkamvRMP\nXzzCvSd3sTO7zAw2c+SzRK4votPEt9Bb3F5Di04HaWkweLBwKPT0hCZNbqsIkjsRT0/RC66rj4kp\ntDqUSiVbtmzh1KlTBAQE4OHhwVNPPUVubi7Hjx/ngw8+YNWqVSgUCl599VUUCgXvvCP29FIoFISH\nh7N48WLc3d05efKk0YPf0dGRXbt2ERkZiY+PD15eXsydOxeVSgXAu+++S8eOHenevTvu7u7GuXF7\ne3vmz59P3759cXV15a+//mLMmDG8+uqrTJgwAWdnZzp27Gh09GratCnr169nzpw5NG3alJiYGPr1\n61dlfc2tQ1+1ahUqlcq4CiA0NNTYaZg2bRpDhw6lU6dOdOvWjZEjR2JhYWFWiT/xxBNMnDiRAQMG\nEBAQgL29fTnPcXMKpzolFBYWxv79+xk8eDBubm5m6zBp0iT8/f3x8fEhKCiI3r1710ixWVlZsWHD\nBq5du8bUqVONyrUqh8R27dqxevVqZsyYgYeHB1u3bmXz5s1YGjyR27Zti6OjI/379wfAycmJ1q1b\n07dv30p5Vqx/VfKau1Z6bGFhUeVzC/D666/j6+tLq1atGDp0KKGhoVhb127FVmMx4NZ5VC+9Hi5e\nhJwccZydLZR7cbEwc2u1wmGtSsWo1eJ94EdabfkYFAqKm7jxbVo8CxLOGZN4WNsxqPMDhL38I0rb\n+htOJydDhw7CQU8iqY67LdLe448/jq+vL2+88UZ9i3Lb2L59O08//XQ5072k4bNy5Up++uknfv/9\n93LnZaS9G1BSAvv3w6VLYGsrzllZCVO9u/uN77fKy6Td6tdwjf6LEkc3jpcU8j8ndqDSCzOhh7Ud\nkye+xYCHX6zDWtSM9HSxxK5nz/qWRCJpeNyJnZiKFBcXs2fPHoYOHcq1a9dYvHgxY8eOrW+xJDcg\nNTWV2NhYevfuzaVLl3j//fdr7Utw1yv8lBT4/XcRDa9WMQx0Ouyvx+EUe4KWOz7HoiiPaHsnXrty\nmt9yrhuT+Tg15cMvr2BjX/8289xcsYJg2DCxokAikZTnbgjTqtfrWbRoERMmTMDOzo5Ro0axZMmS\n+hZLcgNUKhXTp0/nypUruLi4EBYWxjPPPFOrPBrLk33LzYfFxXDoEPzzjzDVm1ntUSV2aQm0+2E+\nTZKiQa9DY9uEc3odA8/tN6ZxsLBi+sS3CB778i2V+2ZJSxPTFg8/LEb4EklNuNtM+hJJY0fulleB\nzEzYsUOM6j09a7EUTaej2V+babtBOPiomrhxsTifpYkX2GXikPf66Bfo9sR7KBpAPOuCAsjIEGvs\ne/euvKJAIqkOqfAlksaFVPgmJCXB1q1gby82fqkpthlJtP3xTVwuHUXVxJUcCwueijnB3tw0Y5pm\n1nYsnvMzPvePuCWy/hs0GhFMx94egoPF8kGJpLZIhS+RNC6k056BzEyh7J2dhSKsKa7//EH77+eg\n0GoocvHk9cTzfH3tivH6oBZBTJj8Ns27j6wDqWuHXi8c81QqEe++Y8fy4X0lEolEcndy1yj8wkIR\nNMfevnbKvvmfG2jz81JUto5sU5fw5PFt6EyuTx77CuOmvHPL5b0R+fli6aBCUX5KQq+HVq2gV6/a\nWTAkktpgaWmZp1AoauH5IpFIbgeWlpZ5Go3G7LW7wqSfnAz79onocuaC5VRRIn6/fUPL7Sv5LxAa\ne6Lc5dG9x/HEK5FY3KagOWq1sFBotUKpu7tDly4icE7FHeukB77kVlGdeVAikTQuGss/cq0Vvl4P\n167B2bMioE6tPPH1evy3r6TFb9/wvUbFzPizxksBzh4s/L/DuDYPqJU8taW4WDjblY7eLSzg3nvB\n31/URYbBldwOpMKXSO4c7kiTfkKC2Ko2JwdsbMT6+tosrfXd/R2+u75mTFoC+/IyjOe3vByJrv8j\ndSBxeXJyxBTE4MGik6JQgJubnIuXSCQSyc1zRyn8wkKxF31MjDB538TugTgkXqTl9pUMvXaFYwXZ\nAHS3c+Ktt/dT3KrzLZa4MteuCR+D//xHKHmJRCKRSG4Fd5TCP3gQ4uNvfgmaUl1Cq+9fpVf8WaJV\nYt/Yz/zu5Z7XNlHoVbN9rm8WjUZE/QsIgJCQshC/EolEIpHcCu4YhZ+YKGLh38yovpSmWz4h4Mgm\n4/EIBxfavxJJXh0pe7VaRMAD4XjXsyd07Qo12MpZIpFIJJJacUcofLUa9u4Vzmw3GwZbe/BnekWU\nhcH9yrMVPcbMJt4/6NYIidiWNjdXOBSqVMLjvlcvMapv0uTmZZdIJBKJ5EbcEQr//HmxLt3H5+bu\nTz66hefeGW88jvQJpL9/ECeGTrtFEgpSUoSMTZqIpXMdO8pQtxKJRCK5PdwRCj86Wozub4bM2BNM\nf2M0ANYKJX+07kor2yacnvIOeqtbt6D92jXhWzBsmFhiJ5FIJBLJ7aTRK/ziYhFK9mZG9zlXzjDl\nxSkVy8IAABNqSURBVG7G40Nt7sffypozz3xO4U2us9fphEx6vfiUlIiAP25uMGiQVPYSiUQiqR8a\nvcI3DU5TGyzTE3nl5V4AuFtas6FlR1paWHJm+mfk+wbWOr+CAhEJz8pKKHdLSyGXry94e4OXl/S8\nl0gkEkn90egVfnJy7UfNjhf/4qXXHyDFsPQu0r8jQRbW/D39U/Jadqy1DAUFwhnv4YeFYpde9hKJ\nRCJpaDR6hX/5cu0c3zwP/kzPd0KNx7PdfbnPyoazT31MbkCXWpdfquwfegiaN6/17RKJRCKR3BYa\n9Vi0sFCY0WsaV775wZ/Z/80s4/GLrl68FNCVUzO/I6dNt2ruNI9U9hKJRCJpLDTqEX5t5u89D2/i\nyvdzeTn9KgCPObrzbP9HOBG+BK197Xf5lMpeIpFIJI2JRq3wExNrthWsXVoC136YxyOpMcZzCwZN\n5vzkt9Fb1n5HmpISsRf9mDFS2UskEomkcdCoFX58fA22vNXpCFi3iNZX/wHEPp+nRj5H9KRlN6Xs\ntVqxpn7oUKnsJRKJRNJ4qOs5/OHABeAS8GoVaUKAk8BZYG9NM1apxDayN1rq5vlXFI/+sd54/NvA\nSSQ88d5NBdVRqyEpCbp3h7Zta327RCKRSCT1Rl2O8C2AFcADQBJwFIgCzpukcQE+BYYBiUDTmmae\nm3vjNLbpiVj8+CaHi/MBCPfrQPGzX9Ra2Wu1wl9Aq4V+/URIXIlEIpFIGhN1qfB7ADFAnOE4EniY\n8go/HPgFoewB0mua+Y0UvkKtov33c+gef6assHePoLOuWfQbjUY45uXnC8fAdu2gW7caTCFIJBKJ\nRNIAqUuF7wNcNTlOBHpWSNMWsAJ+BxyBj4AfapJ5aqqIalcV/ju/4NO/95CqUWOjUPDVnA3o7JrU\nSPDUVBHMx9sb7r8f/P1rvvRPIpFIJJKGSF0qfH0N0lgB9wGDAXvgEHAYMedfLamp4OBg/prr+T9R\n7vyKtzNTABjZtgcuvcfUSOiiIrCxgQkTarYCQCKRSCSSxkBdKvwkwM/k2I8y030pVxFm/CLDZz/Q\nGTMKf9GiRcbv/fuHkJ4egqdn5ULt0hJo//0cfBLOAeBiYUX4gi01FjojQ3jgS2UvuRvZ+//t3XuQ\nlfV9x/H32bMs7qIgF0FuQlAsWBRvQYqGrsEbMZGWtmONsYmmEzsZE9vYeum0qZ02bTOtubROjRXj\n2GasSUzaMRmjaZtuTIyiwXu8gfWCgAIuyxJwb3D6x+/ALrvnxgPPOefHeb9mznie5/mdh+/sePaz\nv9/ze35PRwcdHR21LkNSChI8dqZizcDLhN77RuBx4DL2v4Y/jzCx70JgNLAauBR4Ydi5crnc4IBB\nVxd885thyH2obM9OTv3yx/nhG89x5cZXAPin67/FrHN+h0p0d4fe/cqVrocvAWTCylZp/p6QVCVp\n9vAHgGuAhwgz9u8khP3V+eO3E27ZexB4FtgD3MHIsB+huzs8ena4aQ/fS9vm1/aF/ZSjJpYM+1wO\ntmwJt9tlMiHkly0z7CVJh5+0F975Qf411O3Dtv8h/6rY1q0jn5CX6e9j+sP3cEfPzn37rvuz+4ue\no78/zAM48URYtCjMB9gb+pIkHW6iXGlv06aRE/YmvPgIXTs6uX7DywAsOfNi5s1fUvQc27fDggWw\ndGmalUqSVB+i68/mcmFp27a2/ffP+NHdnLt+8GrAtX9yb8nz9PXB9OlpVChJUv2JLvDfey8Mxw8d\n0h+zcS39rz3DhoE+AK644gu0lrnnPpOBcePSrFSSpPoRXeDv2jXykbhTHv0Pzs7fhpdtyrJy5fUl\nz5HLhZeBL0lqFFEG/n4z9HM59qx5gHd29wOw7IMfJ5stPTWhpwfGjy+9Up8kSYeT6AJ/79r2e7Vu\neZO/eeP5fdtX/f6Xy55j586R9/BLknQ4iy7wOzv3XwVv7NonWJ1/Gt4V511JW9vYsufo64OpU9Oq\nUJKk+hNl4I8ePbh933/ewmv9vQAs/72/q+gcTtiTJDWa6AJ/27bBwG/q7+XvX34MgOWzTubIoyeX\n/bwT9iRJjSiqwB8YCBPu9k62a1m3hiPyF/R/Y8XnKjqHE/YkSY0oSeBnCA+4qbpdu/bffvKHq+jJ\n5ZjW3MLUpZdVdA4n7EmSGlGpwD8SuA74Z+DT+ba/CfwCuDz90kYaHvg3/s9dAFzwvoXQMrrAJ0bq\n6zPwJUmNp9QN6/8KdAOPAhcAnwB6gI8CT6deWQFDA3/P1rf2vf/ghVcXaF3cxImHqiJJkuJQKvBP\nAE7Jv18FbAJmAe+lXVQx27cPPs3u21+/DgjXFyZ+4FJ2V/D5/v4w4W9s+Tv3JEk6rJQa0t897P0G\nahj2sP8teW+sexKA8yfPZneZdfP36u6G2bNHLs0rSdLhrlQP/xRgx5Dt1iHbOaDq/eTOTjjiCCCX\no7PrbQBOPWN5xZ/v6YFZs1IqTpKkOlYq8LMljtXE9u0waRLk1r/AC/nV9RZVeDveXl6/lyQ1olKB\n3wr8AXA88BxwJzBQjaIK6emB3bvDY3E3P/H9fftbpp1Q0ef7+6G11ev3kqTGVOoa/t3AGcDzwIeA\nW6pSURFDZ+g/9tNvA3D+/CUVf7672+F8SVLjKtXDnw+cnH+/Cngi/XKK6+kJ/83sHmDVq2sAOGf5\npyv6bH+/gS9JamylAn+gyPua2J2/Z2DHK4N/d8w57YKSn9mzBzZtCsvonnUWTJ+eZoWSJNWvUoG/\nkDqapb838L+66loATp5+IuPGHVPyMxs3woIFsHixa+dLkhpbqcB/BjitWoWUszfwV68NPfz5p5bu\n3W/eDDNnwpIlYaKfJEmNLJqn5Q0MQF/f4My981b8UdG2nZ3Q1gbLlhn2kiRB6R7+McDnCKvXDpcD\nvpRKRUX09cG6dT/Zt33ssXMKtuvshOZm+PCHw214kiSp/MI7R1WrkHL6++HJJ+4BYOpRhVfP2bYt\nhP0ll8BRdVO5JEm1Vyrw3wb+slqFlNPXB5veDOvnnzRrwYjj27aFNfI/8hHDXpKk4aK5ht/bC727\nugC48Nwr9jvW1RXCfsUKV9KTJKmQUoF/XtWqqEBv7x42bw8PzDlu4fn79udysHMnXHyxYS9JUjGl\nAv/dqlVRga6uLvr2DHBUU5a2ycft29/ZCXPmwIQJNSxOkqQ6F82Q/tatmwFoze4/7WDXLli4sBYV\nSZIUj2gCf+fbbwHQOdC/b193N0ydClOm1KoqSZLiEE3gr/nptwA4fsrsffu6u+HMM2tUkCRJEYkm\n8N/d8iYAo9vGAeHBOM3NMG1aLauSJCkO0QR+5/ZwDf+cJb8NhGv3xx7r0rmSJFUimsB/cv1TAMw7\n82IAfvnL8HAcSZJUXtqBfxHwErAWuKFEu/cDA8DKciecfOz7gDCkP3nyIahQkqQGkGbgZ4FbCaF/\nEnAZML9Iuy8CD1L4QT37jM8209oa1s3N5WD8+ENZriRJh680A38RsA54HegH7gVWFGj3GeA+YEu5\nE/blcmQyGXp7w6p6Pg1PkqTKpBn404H1Q7bfyu8b3mYFcFt+O1fqhNPyvfsdO+C440q1lCRJQ6UZ\n+CXDO+8rwI35thnKDOl/YMY8IDw5b/rwPx0kSVJRpR6Pe7A2AEPn0c8k9PKHOoMw1A8wCVhOGP6/\nv9AJn+7azK57bmbq1HYuvbT90FYriY6ODjo6OmpdhqQUlOxRH6Rm4GVgGbAReJwwce/FIu3vAr4H\nfLfAsRzAH7Z/jKWf/Tc6O+HKK6EpmpsKpThlMhlI9/eEpCpJs4c/AFwDPESYiX8nIeyvzh+//UBP\nOH3GPLZtgxNPNOwlSToQaQY+wA/yr6GKBf2V5U6WGXsMvb0wd+5B1yVJUkNJO/APqTGTjqe1zQV3\nJEk6UFENjGdaj2fBAofzJUk6UNFEZwbItU1l9uxaVyJJUnyiCfwccPTk0UycWOtKJEmKTzSBP7dl\nDFOn1roKSZLiFE3gj8lkGTWq1lVIkhSnaAJ/dFMTzVHdUyBJUv2IJvDfGeg18CVJSiiawJ/TMoZs\nttZVSJIUp2gC/8imZnv4kiQlFE3gd4KBL0lSQtEE/qyxUx3SlyQpoWgCP3PEkS6pK0lSQtFEaKZ1\nrIEvSVJC0UTojkyTgS9JUkLRROicWWca+JIkJRRNhO4ZM8HAlyQpoWgiNDt+hoEvSVJC0URoU9t4\nb8uTJCmhaAI/0zzaHr4kSQlFE6HZbLOBL0lSQtFEaCaTNfAlSUoomghtajLwJUlKKpoIzWZHGfiS\nJCUUTYS2tLQZ+JIkJRRNhDY3txj4kiQlFE2EZrOjvA9fkqSEogn8piZ7+JIkJRVNhDY1OWlPkqSk\noonQ5uZaVyBJUrwiCvxMrUuQJCla0QS+w/mSJCUXTYw6pC9JUnIRBb5D+pIkJRVR4Ne6AkmS4hVN\n4Gez9vAlSUqqGoF/EfASsBa4ocDxy4FngGeBR4BTCp3EHr4kScmlHaNZ4FbgPGAD8ARwP/DikDb/\nBywFthP+OPgXYPGIQg18SZISS7uHvwhYB7wO9AP3AiuGtXmUEPYAq4EZhU7kpD1JkpJLO/CnA+uH\nbL+V31fMJ4EHCh2why9JUnJpx2juANqeC1wFnF3o4De+8Vf87Gfh75P29nba29sPujhJ++vo6KCj\no6PWZUhKQdrj5IuBmwnX5gFuAvYAXxzW7hTgu/l26wqcJ/fjH/ezdKndfKmaMpkMpP97QlIVpD2k\n/3NgLjAbaAEuJUzaG+o4Qth/jMJhD0A2m06BkiQ1grS7zAPANcBDhBn7dxJm6F+dP3478HlgPHBb\nfl8/YbLfflpa7GRIkpRULCmaW7NmgNNPt5svVZND+tLhI5qV9kaN8neOJElJRRP43pYnSVJy0QR+\nUzSVSpJUf6KJUR+eI0lSctEEvj18SZKSiyZGXUtfkqTkogl8e/iSJCUXTYwa+JIkJRdNjBr4kiQl\nF02MGviSJCUXTYwa+JIkJRdNjBr4kiQlF02M+nhcSZKSiybw7eFLkpRcNDFq4EuSlFw0MWrgS5KU\nXDQxauBLkpRcNDFq4EuSlFw0MWrgS5KUXDQxauBLkpRcNDGa8em4kiQlFk3gS5Kk5Ax8SZIagIEv\nSVIDMPAlSWoABr4kSQ3AwJckqQEY+JIkNQADX5KkBmDgS5LUAAx8SZIagIEvSVIDMPAlSWoABr4k\nSQ3AwJckqQGkHfgXAS8Ba4EbirT5x/zxZ4DTUq5HkqSGlGbgZ4FbCaF/EnAZMH9Ymw8BJwBzgU8B\nt6VYT1V1dHTUuoQDElu9YM2SdCDSDPxFwDrgdaAfuBdYMazNJcDd+fergaOBKSnWVDWx/WKPrV6w\nZkk6EGkG/nRg/ZDtt/L7yrWZkWJNkiQ1pDQDP1dhu0zCz0mSpDqwGHhwyPZNjJy49zXgd4dsv0Th\nIf11hD8EfPnyVd3XOiSpjGbgVWA20AI8TeFJew/k3y8GHqtWcZIk6dBZDrxM6CXclN93df611635\n488Ap1e1OkmSJEmSlI7YFuopV+/lhDqfBR4BTqleaUVV8jMGeD8wAKysRlElVFJvO/AU8DzQUZWq\nSitX8yTC/JanCTV/omqVFfZ14B3guRJt6ul7JylyWcLQ/mxgFOWv+Z9Fba/5V1LvrwHj8u8vovZz\nFCqpeW+7HwHfB36rWsUVqaNcvUcDv2Dwds5J1SquiEpqvhn42/z7ScC7hDkvtfIBQogXC/x6+t5J\nSqie1tKPbaGeSup9FNief7+a2q8xUEnNAJ8B7gO2VK2ywiqp96PAdwhrOABsrVZxRVRS8yZgbP79\nWELgD1SpvkJ+AmwrcbyevneSEqqnwI9toZ5K6h3qkwz2kmql0p/xCgaXOc5Voa5iKql3LjAB+F/g\n58AV1SmtqEpqvgP4VWAjYYj82uqUllg9fe8kJVTLYcThKg2Welmo50D+3XOBq4CzU6qlUpXU/BXg\nxnzbDCN/3tVUSb2jCHd3LAPaCKMqjxGuN9dCJTX/KWGovx04HvgvYCGwI72yDlq9fO8kJVRPgb8B\nmDlkeyaDw7TF2szI76uFSuqFMFHvDsI1/FLDptVQSc1nEIahIVxfXk4Ymr4/9epGqqTe9YRh/Pfy\nr4cJ4VmrwK+k5iXAF/LvXwVeA36FMEJRj+rpeyfpMBDbQj2V1Hsc4Xru4qpWVlwlNQ91F7WdpV9J\nvfOA/yZMlmsjTDw7qXoljlBJzV8C/iL/fgrhD4IJVaqvmNlUNmmv1t87SYeJ2BbqKVfvKsKErKfy\nr8erXWABlfyM96p14ENl9f4xYab+c8Bnq1pdYeVqngR8j/D/8HOEiYe19O+E+QR9hBGTq6jv750k\nSZIkSZIkSZIkSZIkSZIkSZIkSZIk1bPdDK4z8BQwi7Bk7Pb89gvA5/Nth+//6+qWKkmSkiq0/ns7\nYWEZCKvfvUJ4/OqvD9l/BPAiYSlfSVLK6ulpeTo87QLWACcM299DWHZ2TtUrkqQGZODrYLUyOJz/\nnQLHJxLWX3+e/Z+4NoHw7PgX0i5QkiQdvGJD+l3Ak4QnwH1q2P6ngZ3ALemXJ0mSDoVy1/CL7Z9N\neCzszALtJEmHmEP6qpXXga8Cf17jOiSpITTXugBFL1dkXyX7v0aYwT+D8Ex4SZIkSZIkSZIkSZIk\nSZIkSZIkSZIkSZIkSZIkSTp4/w/8DgngUqGIZQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f7d72544b10>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The resulting curves show clearly that in this case computing bounds based on known negatives is better, because we have far more known negatives."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 4.2 PR curves"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# we can directly use the contingency tables we already computed anyways\n",
      "pr_bounds = lambda tables: ss._lb_ub(lower=ss.pr_from_cts(tables.lower),\n",
      "                                     upper=ss.pr_from_cts(tables.upper))\n",
      "pr_bounds_pos = pr_bounds(tables_pos)\n",
      "pr_bounds_neg = pr_bounds(tables_neg_post)\n",
      "\n",
      "# an alternative without all these intermediate steps would be:\n",
      "# roc_bounds_point = ss.roc_bounds(labels, decision_values, beta=betahat)\n",
      "\n",
      "# compute the true ROC curve (we use Optunity's ROC function)\n",
      "_, pr_true = optunity.metrics.pr_auc(true_labels, decision_values, return_curve=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pr_pos_up = ss.zoh(*zip(*pr_bounds_pos.upper))\n",
      "pr_pos_lo = ss.zoh(*zip(*pr_bounds_pos.lower))\n",
      "pr_neg_up = ss.zoh(*zip(*pr_bounds_neg.upper))\n",
      "pr_neg_lo = ss.zoh(*zip(*pr_bounds_neg.lower))\n",
      "fig = plt.figure(3)\n",
      "fix_plot_shape(fig)\n",
      "plt.plot(*zip(*pr_true), color='black', linewidth=2)\n",
      "plt.fill_between(xs, list(map(pr_pos_lo, xs)), list(map(pr_pos_up, xs)), color='blue', alpha=0.3)\n",
      "plt.fill_between(xs, list(map(pr_neg_lo, xs)), list(map(pr_neg_up, xs)), color='red', alpha=0.7)\n",
      "plot_proxy('blue', 0.3)\n",
      "plot_proxy('red', 0.7)\n",
      "plt.xlabel('Recall')\n",
      "plt.ylabel('Precision')\n",
      "plt.legend(['true curve', 'expected region via known pos', 'expected region via known neg'],\n",
      "           loc=\"upper left\", bbox_to_anchor=(1,1))\n",
      "plt.title('Precision-Recall curve')\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9B+vWrdN7Lezs7Jg/fz4bN27UewMAZs2ahZWVFW3atKFt27acL6HOdEhICBs2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\n0Ifd8tptBSpJkuLEBP6jwPcJY/dnEbr37y+zqBi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       "text": [
        "<matplotlib.figure.Figure at 0x7f7d723adc90>"
       ]
      }
     ],
     "prompt_number": 17
    }
   ],
   "metadata": {}
  }
 ]
}