5-Bayes-Learning.ipynb

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    "# Supervised Learning\n",
    "\n",
    "\n",
    "by   \n",
    "[__Michael Granitzer__ (michael.granitzer@uni-passau.de)]( http://www.mendeley.com/profiles/michael-granitzer/)  \n",
    "[Konstantin Ziegler (konstantin.ziegler@uni-passau.de)](http://zieglerk.net)  \n",
    "Jörg Schlötterer (joerg.schloetterer@uni-passau.de)\n",
    "\n",
    "with examples taken from the [scikit-learn documentation](http://scikit-learn.org/stable/)\n",
    "\n",
    "__License__\n",
    "\n",
    "This work is licensed under a [Creative Commons Attribution 3.0 Unported License](http://creativecommons.org/licenses/by/3.0/) (CC BY 3.0)"
   ]
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   "source": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt"
   ]
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    "## The Iris Dataset\n",
    "For introducing the different supervised learners we will use the IRIS data set.\n",
    "\n",
    "The iris data set characterises iris-flowers into three sub-groups according to length and width of the outer (petal) and inner (sepal) leaves of a flower.\n",
    "\n",
    "**Sepal vs. Petal**\n",
    "\n",
    "\n",
    "<img src=\"http://upload.wikimedia.org/wikipedia/commons/thumb/7/78/Petal-sepal.jpg/220px-Petal-sepal.jpg\"/>\n",
    "\n",
    "**The three classes (setosa, versicolor, virginica)**\n",
    "\n",
    "<div class =\"img-responsive\" style=\"display:inline\" >\n",
    "<img src=\"http://upload.wikimedia.org/wikipedia/commons/thumb/5/56/Kosaciec_szczecinkowaty_Iris_setosa.jpg/220px-Kosaciec_szczecinkowaty_Iris_setosa.jpg\" width=\"30%\"/>\n",
    "<img src=\"http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Iris_versicolor_3.jpg/220px-Iris_versicolor_3.jpg\" width=\"30%\"/>\n",
    "<img src=\"http://upload.wikimedia.org/wikipedia/commons/thumb/9/9f/Iris_virginica.jpg/220px-Iris_virginica.jpg\" width=\"30%\"  height=\"10%\" style=\"overflow:hidden\"/>\n",
    "</div>\n",
    "\n",
    "\n",
    "Images from Wikipedia\n",
    "\n"
   ]
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     "text": [
      "Classes: [0 1 2]\n",
      "Iris Plants Database\n",
      "====================\n",
      "\n",
      "Notes\n",
      "-----\n",
      "Data Set Characteristics:\n",
      "    :Number of Instances: 150 (50 in each of three classes)\n",
      "    :Number of Attributes: 4 numeric, predictive attributes and the class\n",
      "    :Attribute Information:\n",
      "        - sepal length in cm\n",
      "        - sepal width in cm\n",
      "        - petal length in cm\n",
      "        - petal width in cm\n",
      "        - class:\n",
      "                - Iris-Setosa\n",
      "                - Iris-Versicolour\n",
      "                - Iris-Virginica\n",
      "    :Summary Statistics:\n",
      "\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "                    Min  Max   Mean    SD   Class Correlation\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "    sepal length:   4.3  7.9   5.84   0.83    0.7826\n",
      "    sepal width:    2.0  4.4   3.05   0.43   -0.4194\n",
      "    petal length:   1.0  6.9   3.76   1.76    0.9490  (high!)\n",
      "    petal width:    0.1  2.5   1.20  0.76     0.9565  (high!)\n",
      "    ============== ==== ==== ======= ===== ====================\n",
      "\n",
      "    :Missing Attribute Values: None\n",
      "    :Class Distribution: 33.3% for each of 3 classes.\n",
      "    :Creator: R.A. Fisher\n",
      "    :Donor: Michael Marshall (MARSHALL%PLU@io.arc.nasa.gov)\n",
      "    :Date: July, 1988\n",
      "\n",
      "This is a copy of UCI ML iris datasets.\n",
      "http://archive.ics.uci.edu/ml/datasets/Iris\n",
      "\n",
      "The famous Iris database, first used by Sir R.A Fisher\n",
      "\n",
      "This is perhaps the best known database to be found in the\n",
      "pattern recognition literature.  Fisher's paper is a classic in the field and\n",
      "is referenced frequently to this day.  (See Duda & Hart, for example.)  The\n",
      "data set contains 3 classes of 50 instances each, where each class refers to a\n",
      "type of iris plant.  One class is linearly separable from the other 2; the\n",
      "latter are NOT linearly separable from each other.\n",
      "\n",
      "References\n",
      "----------\n",
      "   - Fisher,R.A. \"The use of multiple measurements in taxonomic problems\"\n",
      "     Annual Eugenics, 7, Part II, 179-188 (1936); also in \"Contributions to\n",
      "     Mathematical Statistics\" (John Wiley, NY, 1950).\n",
      "   - Duda,R.O., & Hart,P.E. (1973) Pattern Classification and Scene Analysis.\n",
      "     (Q327.D83) John Wiley & Sons.  ISBN 0-471-22361-1.  See page 218.\n",
      "   - Dasarathy, B.V. (1980) \"Nosing Around the Neighborhood: A New System\n",
      "     Structure and Classification Rule for Recognition in Partially Exposed\n",
      "     Environments\".  IEEE Transactions on Pattern Analysis and Machine\n",
      "     Intelligence, Vol. PAMI-2, No. 1, 67-71.\n",
      "   - Gates, G.W. (1972) \"The Reduced Nearest Neighbor Rule\".  IEEE Transactions\n",
      "     on Information Theory, May 1972, 431-433.\n",
      "   - See also: 1988 MLC Proceedings, 54-64.  Cheeseman et al\"s AUTOCLASS II\n",
      "     conceptual clustering system finds 3 classes in the data.\n",
      "   - Many, many more ...\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from sklearn import datasets\n",
    "iris = datasets.load_iris()\n",
    "print (\"Classes:\", np.unique(iris.target))\n",
    "print (iris[\"DESCR\"])"
   ]
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EqKGxpSGCpgrkAmVXaz66kie1D/hRoJFA1l8iSxCZdM25/9gAIU3hNYc61uP2S+a1hzro\nbo7yiYfO8rprVici6mpQranmzOBjcNmzeCxbIFdwuTRRxFAFsZDKudEsqiLY154gYqgMZy06G8I8\ncHyoppEW6wS7xdPDOVxf4vuS9mSIvrRJSFPZ3R5nT1uC/rRJ3vLQhGSy6PKDwUmaIjqtiRA3bG8k\nU3AQU2aj43kbBFzX1cz1XY20zgg2d6VQubvPFWxcT1J0HCK6SmsixFjOnpVYZuZ4aUuEuJg25xQh\nlayBEiGN/R1JTMdja2OE1kSoLPKJhdTye81xg7CmTCt7NGutnfnoVIjpLwshbpNSPrrccmqF6/l8\n9flLvPJA26bZiaiK4Gfv3Ml/+9L3eeJcmls2ibfxYqaapQ6rCHjs9Chp0yUV1XhJVxMF2yOia4xk\nHcZMG01RsD3JD1/TgaIq7G1L0BwPlfUHqajBvdd3krXcuo6ghuQtj5ZEiKaowYXxPCcGM7QlIuRs\nhz1tCfZvSbK9OcpI1uL5foehTJFJ06ajMUp3c4zesTy265Ererzxxk7OjOTQVbUcJfNKXATg8kkq\nomuYjk93S4yOhjBFx8OXYDkek6aNGr0smp5l0glYjk+mYKMJozxeLMfj/mMDZWugVx9sx5WyvPkp\nhaWIGQr7tyTLY6Iyw1twL23tzEcr+CkhxFtnvDYJHF3LfASPnh1jNGdzz7UbXyxUyY/ftI0/eeAk\nn3zo7KZZCGB+E7XKHdPFcZMnzqWJhTQs16MlES7vQs+P5tBVha6mKAMTJudGTa7b3sRgpohpe2X9\ngeV67G5PcHBLwzp8yysT03Y5OZhhOGsxMF5gsuAwnnfwgVTUIGIEvi1RQyNiuLgSDFWlf6LAUNai\nP51HVxX6xgsUbZfBbJFbd6bY0ZK44sNIzDxJ7W6PIyVEdJWC7XFuLNAZnEvnp5k9V46X3rE859Im\ncUPj5HCWguvRmghzIW1StD12tiU4O5LliXNptqWijGYt2hLhcliKsyMWEwWH1kR4KrrrdDPV5ZiP\n1uJphYD9BApigDcB54DrhBB3Syl/pQb3WJT7jw0QD2ncvb9tLW5XM8K6yjtv6+GP/+Mkp4ay7GlP\nrHeVpjGfdcN8Di2VO6ZMwcG0PRJhDdv1yNsuXakIEkEyrFJwPCzXoylqsKUpXFYqj+UtfIIjdcHx\nuDRZwEfOufups3RKmbCu39bI8xcn2B6JsrUpyqVJk8ZIYP0ymivSlzZRAM9zOT+WI1906dnagOP5\njOVsLMdFEQLH9ckU3GnBBSutWK4kfEm5Dwsk125rJGIEYqCRrIVpe+QtDyGgYHvztoNZdMhbLgXL\npS3hoyAI6QJXSvrH87i+JBnRymPCtN1yWArb88t6gZL/QsSY2yKpWmrxlK4FjkgpPQAhxMeBhwlC\nTjxfg/IXxXI9vv7CIK851E5Y33yeuu+4rZuPf+c0n374HB9587XrWpf58qRWWjcs5NBSuWPKFR2E\nhIuTBWK6Rks8xHP9ExQcn4iu8P67dgfH23iIwUyxPJHsak+wvWmCouvTEtN58lyakK7i+5Ku5gia\nohIzFI7sab3iJpq1IB7SyBVsvn8pi5CQEw4t8RCKEDQnDL5zYojnLmQYNx2EkLQlw+xsTZAtehia\nQlgLJr4fDGbQhMD3JW+/rZstjZFyQpUrNfifIuDMcJ6C4xHRVW7f3VLR94PTUs72CWuCFy5O0Dxl\nzVPZDooIfGfytoeqCAxNYSxvoymCN9ywFVdKEiGNc6P58pjY3hxlLHdZLyCk5MxIDk1ITg768zr8\nVWs1VIsn1ATECcRBADEgJaX0hBBrYuLx4IsjZIvuprAWmotUzODHb+ri80/2859fs5e25PrIwWea\nuVXmSa088g9nLVxfsj0Vm5Uz1Zewuy1O2FDpH8tjuT5RQ0OIwAROSkEirOF6ksaowXVdgX30tlR0\n2k7/Hbf3MJy1mMjbPHl+nO2pGM9fHOfZCzY7m+P0j7vs7UiuSp7jq4GC6+P7Po1Rg1zRxXR9ooZK\nKhriG8eHuJDOE9J1DA0KjsednQ1sTUWIGYEIZDBTpCcVYW9HA5JgImpLhBnOFuc1Gb4SCMw6JfGw\nhutNN+scyVooQrCtMcxwJhDf7O1omJ2vO2chEHQ2RhjJFGmKGRza2kDR8WiMGWUxT2XmtsqwFIqA\nZ3oncG2Xguuja7Lc3pVWQ2N5a02Dzv0RcEwI8RkhxN8AzwD/UwgRY4FgckKIdwohvjkVgXRF3l/3\nPztAKmZwZHfLSopZV95zxw4c3+dvHz2/bnWYFbkQ5rQOakuE0BQxzZKnZFKnCMqmnyFdRVcVEBKE\nAsipv0EiGc/bHL80yWiuOCsJR0s8zMEtDeztSJTvpSCIG2o5amOd6qn08M5ZLsmwztamKJlioBvY\n1x4nU7D5zovDKPg0hHVGcwXylkcyrFNwXJoiOnvaEiTCOvs7EsTDOjnLIaSqZYXmlRr8r2wy6rgg\nBYoQCASXJkweOT1CfzpP1NDQNQVJMAbCujpnO0SNIDdDwfbQVUEyopf1DNM/N31MlP73JWUz1WRE\nnxbdtS0RWp+gc1LKvxJCfA24eeql/yKlHJj6+zfmumZq4n+5lPKVK71/3nL55g+GePNN24JJZ5PS\n0xLjdYc6+LvH+vjAXbuJrcMACkQGDv1ps2wmWJkntXKSfsvNXdNy0laeJHa0xMhaLk1Rne+eGsFy\ng0TcsVCwixo3bVQBX31uACEEEV3lHbd3z2kRVHmvREjjWP8E46ZNT3Ns1fIcX2kEiVBGydsuMUPj\nhu5Art3RECZqqOSLDt94YZAzw3kaowaKAqloiK7GCDtbE7xsX+vUjj941r1jeUzbY2tjlFTMoCM5\nfbLarMH/Fkokc9lk1MH1Payih+V4/N1jvWiqgqYI3vuyXdy0vZH+8SKHtiQ43JNiOGfRnZoeeK8l\nHqKtIUw6b9PZFOXle1sJTS0C1bRX5WIb0VVumhHfab2shiA4WYxMlbdbCLFbSvnQAp9/LaAKIb4J\nHAd+paRjWCoPHB+i6Pjce93GDSlRLT/3sp382/cH+cLRft51ZMea39+0XU4NZyk4PqO6wq27m2mJ\nz50qryUeLk/cleKAgUmTZ/omSEZ0LqRN2hsidDZEGc0XGclZaKpKW1ynbzzHpGnR3RKjf9ykL23O\naxpaupdpu4Q1hWQ4sJ2uUx0jWYsTgxkSYZ3+cZO9HYnyZG05Hn/73fNcmCjguD5tyRCXJgvYnkvE\n0MjbLl///iDXdzWWLVQO96Q4P5YHCZ2N0Vmij80Y/G8hb/nKk/JkwaG7Jc6WZIRn+sYZzFjsbU9w\nbjTL6eEsQxkbz/c5N2pyYbxISFd5tm9imh4tbwX6he7mGK7nB9Fa5wlONxeLLbZrHXQOACHER4Dv\nAr9DcAL4DeDXF7msHTCmTgQmQbiJmeW+VwhxVAhxdGRkZN6CvnzsIp0NYQ5XxOLYrNy4vYmX9jTx\nV4+cW5fENcNZC0VROLClAVVVqvbirdyhWE6w+2+OhUhEdRQhmCzahDWVlphR9paMGiq25wcxbByP\nqDFdyT9XsLqStcuu1ji6ptaTzyyFsrNi4ElcmkSylkvYUNndlggsVtImEU2hIRIib7kIIZBILMcv\nXxc1NHqaY0SMuUUfm5GFvOUr+3dUV0lFdXwk25rChDSl7AgZ1jV8X9LZFCVnu2SK9rwe8Y4rKdge\nrrc8EWet8xnXopQfA/ZJKZeiGJ4EvjP197cIopdOQ0p5H3AfwOHDh+dsrXTe5uFTo7znzh0omyhW\nz0L83J07ee9nn+Lfvj/IPWus/J5L9l8NlR7Eu1pjPHRqhGMXJtjWFOENN2wtH4+b4yFGsjam46Fr\nSYYyFqbjE9ODdJUl5tudrYb8udZ5jjdi3uRYKJi8MgWHuKFxeihDPGOUxXgRPdC73LIjxfVdDZwc\nyuPjM5qD1mSIJ86OMThRpDVhcFNPsOFaKxHQWrXnQvH/o4bGjpYYvWmTXa2JCiVuipt3NtObNulO\nBQmwvvb8ABcmTBxPsqUxPOdYUgQMTBbKItMJ0yZvL99hshZtVIuWPQvoVOQiqILvcTkMxfUEfgdL\n5mvPX8L1Ja+/AsRCJV51oJ2dLTHue+gsP3rtljUNOzFT9l9tpzRtt2yy9szEOF9+JvCOPCoEgkB8\ncG40T3M8VLZ8uJA2GRwv0pIIM5orkrWm7/znsjyp9eRT6zzHGzFvsmm7PNM7zoVxk96xAi2JEOOm\nzp17ouRtl5CuTnvmQSyhcSK6xsQWC88PNlyqIhictLhQIcJbbRHQ2rfn/PH/Sx6/JTFPSZQTTWl0\npYKc6MPZIi/b2wpSgJDsbU+W/V8qx1LWctneFKUlEaYvneOLT18gFQstK6hirdqoFq1qElgNfZPp\niWl+ab4LpJTHhBAFIcSDwCjwx8u58f3HBtjTFufAlo3lhLUSlKmwE//lX57n0bNj3L5rbS2hKmX/\nC1G5Cyk5kYUNlfMjgTPMgY4kJwYnOTmYIRbSQVzO3ARBuj5FgYFJk/CUIrLEQjv/5Uw+8+2YFoqO\nWm15lcxVXun1uTJ91Zq5vmfOcsnbPhFDIxFW0RUYyRV44twY3alIuV4tccrXRAwVX8pyAECBoCMZ\nYShTYDRv17ze87GW7VmK/5+Khig47rS+UIr/3xoPM5ov8lz/BIau0p2KlhcBCPppY9QoT8rzZWdr\nS4QIGyqTRRvXh4imlk2xS/kdqv1Oy+3DM6lFb7yfeZLLLISUcjE9woJcnCjwxPk0v/6avZsmWFu1\nvPHGrfyvB17k4w+eWfOFoBpmWqHs35Lg9HAOT0ocz0cRkhNDGTwp6U0XGMoEwQAPtCd4tm+CvO2i\nKoKmmMFQ1qK9Ybqss5Y7/4V2TMsRNc0sr5KZ5SniskPezExftd7dlupVsD0s1+f2KUV/PKShiUBh\nfHYkT9RQyRZcbEeSt12u297EiUuZcgybI3taOdyTom/M5PsXJ/F9H0VA3nJoS4TYt4ae7wu3pw9I\ndE2tSXtWOkJqipgSdQZewYmQxuBkgYvjJqbt8Vz/OI4nSUZ0fudHDpYXg5lBFuerT+XJWxOiHFTR\n83zOjeToSxeqdpislbi0FuajfyuEiADbpZQvrrS8avnKs4GF6pVgLTSTsK7yvpft4g+/9gO+d2Z0\nXReDyl1moMC1sB2P5y9MoGsqrhd4OnalIiAFWxpCdCSjTFo2vie5MG7SGA2RsxxOD2c5MzIVv30k\ny6VMkeZ4mOHJIjd2N7G/43I8oWp2/tXIRhfaMVUbPG/mDnuaw04FpfJGphSDo1mbdN5ha2OEi6YD\nSHY1rE48ntKpbDBTZLLgYLkeL9nWEIgpkDSE9cBU19AYmiygqQoXxws8cmqES5MWTVGj7KTXmghx\ncijLxYkCjVGDH71uCw1Rg+u2NU7bAa82lbL57lQQArvU9mdHc0gJuxpmWy0th8rQEZbn8djZMXQ1\n8GDf25Hk5h3NWJ7PC/0TfLt/goihcm7M5Knz4+U2qRSRBhZW8/fLypN3Km5MjSufh0+PEje0qh0m\na7VpWnFPFELcQ5Ca0gB2CCGuB35fSnnvSsteiC8fG+CG7UFy7CuRd9zWzV89co4/+vqL/MsHmtfl\n1DMz5O6p4TyKIkjnLUZzFg0RA8v1sF2f/nQB15cUHY/9WxIcaWnh2f40/eMFEMEuK2JoZesVy6Mc\nT6joeJj20qyHq5WNLrZjqiZ43kIK67noHctTsD2OD2SQSPrHTXakIoR0bdWsbOIhDcv1mSw4RHSN\nsyM5zgznAHB9n0uTFpmCg+0FCYCyRYfJgsNQxuLiuDlVn8AmI2e5hDSFxqjOZCHw2XjF/vY113fM\nlM3fe33nNOsdkDVrT0VQ7sPZooOuCtoSEfrHXVoTYUayVmD9k7fIWy6uJ7E9n0zRKZexXDFNaVHo\nHcuX4wktxWGyFrqaWjzZDxE4kz0IZfn/oqkqV8KJwQw/uJThQ/ccXM3brCthXeVXXrWH3/ri83zj\n+BCvXYccC5Udu2/MpOC4HNjSyGTBJhnW2dIQwfGC+DOlsBKTpg0IxvIW7ckwrzzQSt4OAsu9ZFtD\n4JZv+xzubuDEoErBcelIhtieqm5BLwW7UwQLDrrK3fzMHdN8AfPm++4LKaznuq5gexRdH19Kelpi\nDGaKbJt6wj1XAAAgAElEQVSymirtbms9qUYNjdt3B9Fri47HWA5SsRAIODWUwXY9tjdH8TyPnc0x\ntjfHsFyfm3qasFwP1/fZkbrspFdyOGuKGty+u3ldlN7DWYtM0SYRNshaDlnLndb2F9ImJ4ez7G1L\nrLh+laFR+tJ5LqYL5QnZl5LdbXEiuobt+JwZCiLnSmBb0+V+u5DlUTW0JkKzchCsFbV4uo6UcnLG\njnVVjeA//2Q/hqps6LzEteDNN23jUw+f5cNf+wEv39u65gH1Kne/qajGWE6jfzxPIqRzqDOJpqpE\ndZXtzdHyxNkYNTjYmSwrvGC6Qu/IntZyvJSQppVzDlQzkCuD3ZVCAAOzdoSBDmNkmty7ZOWxUMC8\n+b77UhTWJVlz0fE4N5rn5FAGRSiMZIpEDZWQrs1yMKoVLfEwrzrYPhWNUg2cvhBcv72JcyN5NBUE\nCm+4YSshXeXkYAbT9jBUlea4QUi/HH56I3gHa0LwXP8ktutjaApvvGFbue3703nue+gMri958MQw\nv/yqvSsSW8VD2pSSHDoSEZrCBh6wtTFS0b8l+7YkyFmt5CyfpqjGtV0zw6PPbXlUDZXxhNa63Wtx\npxeEED9F4Cm8B/glAvPQVaHoePzLMxd59aH2DZ+XeKVoqsLvv/4a3vbpx/nLB8/wa6/eu6b3nzkh\n3LrbnaYImy8ZxlyejpV/B4HrisQjOt0t8aqP0TOD3W1tirCtKTrrniNZqxy7faasdaGAeQt992oH\nZWlnGdE1NEXh2QvjdKci9KbztCUMbtnZsOB9V0rU0Ohu1mhNhMq6itZyLKjpp6DWRGheD+GN4B2c\ns12aYgZhTcXyPHIVzoW9aRPXl+xsCbx6e9PmihaCuU568/Xv23Y1zxuCXdeUFemB1qvda3HHXyTw\nKraAfwD+HfiDGpQ7J984PsSE6fCTL+1arVtsKI7sbuHHru/kEw+e4Z5rt6x5voLKjhk1tGkdf64J\nHqpT4i7H2qEtEcL3fU4MThLWFFrjCxyd55G1LuQ0N7PeyxmUl3eWkmQk+H1h0kQRENaVNUu5WVoQ\nIPhevoSe5tisZ9bTHJuW2nAjeAiXM9wBAkHR9RCIad7n3akomiLKXr3dVYoWF2Lm856vf1eOg8o+\ns5kD7tXCasgkWAh+p9prhBA9wOPADwBbSvmaaq/9wpP9bG2McGQDmlWuFr/zIwd5+NQov/gPz/Cl\nnz+yIXIuVBOgayEl7lJ23JWpL7enogxmLBpjOo+fGyNve6SiBq88cFmZ2ZoI0dMSKwensxyPR06P\nlO2+53Kaq5VjTqXl0MlLWS6OmxQdn21NUe7e346qKmUdwXKStyzVi3Sx77VRxEAlfCnL9Q0cDW0y\nBZdUTCc2Q7/zjtt6eGFgkkOdDTTHQzVNhlNNO8/VthupLZfCsmsqhPgKC6i2q7AaekBK+fal3PPc\naJ5HTo/yq6/ae8WElKiG1kSIj/7EdbzrM0/ye185zoffcM26+k5UG6BrseNxtSaipXuNZItBZNRo\niBcHswxNFmmOh7Acjz3t8Wnmp6XgdNmCw198+zRCgKaIsix5plimVo45pe9VcPI8eHKYwUkLT/oU\nHY8vPzPAa6/p4MSlDMvxKVjOYlXN99oIYqASlSaix3rHuThRIGroXJwo8nTvGBfGA9Ge5XggIKSp\nfOsHQ/SPmcQj+pp6iM/VtrWM/7OWrCTo3EeBjwH/CvQBeWAceAr4ZBXX3y2EeFgI8avV3vAz3z2H\noSq89ZarQyxUyd372nj/Xbv4hyf6+ORDZ1dc3lxB3ar9XLUBuhY7Hi9Uh9J7I1mLgu2hILAcnwnT\nZShbIFtwKNpBKOCC42La3rRrSsHpJgoOluuzsyWB50t60+acdanVsd60XXrH8pwdyZE1HXwkvg+2\nK0mbFhFdI2/75G13zvZbiLnavbIN52rPzSauKDmOjeUtHF/iuJJc0aXoegxmAg/fxohB2rQZy9s0\nRgwylkfatOdtl2oZzRU5fmmSvnR+3v5dyWZr24VYSc13EugHzhFM/seAMLAX+H0hxE8A/01K2TfH\ntZemPmcBXxZCfFNK+dxCN5s0Hf7p6AXuua5zSSFbryR+4zX7uDBe4P//txOENGXZoaorj98L7Xhm\n7oxK1kCKYMEAXdUcj2d6J3c3R6cFp6uM/35qOIuiKOSKDsPZAmQFluuRKdpkbY+QqqAKMcuLdyxv\n0Z4ITYsQOZ8suRYikpK10omhHKPZIpOWg2VLXMCXHn3jJv3juan+K5Y8gczlaVtqQ1URhDVllqdt\nNd9rIwXKU4SgIxnm5HCWlrjOeM7GkRJdCOIhjVNDOS6OmxSmTgTH+oNnfs2WxJweyNWeEEZzRT77\nvV4KjoumKBzoTE7VZ/7nsxzx5kZo47lYSY2iBLmKC3O9OeVYtofgtDCNqUil1tTn/hW4BnhuxvXv\nBd4LsH37dv7xyT4Kjse77+hZQZU3N4oi+OiPX4vtevzeV44zMFHgg6/bv+SEPJXH74XEIJU70IFJ\nk++dHiMZ0XHcwE5+PjO5akQNI1mLp3vTSASZYpGRjIuqimCBu6OnfN8J06GzKUpHQ5hTg1lylkNj\nJMSljEkqFmJHS4zclI155Xfa0RKbSio+PULkQpYlKxWRlOL6xA2NcUVBATQVPA8MXZAK6zREDY7s\naZ1mxVPtPWdOPJV5BgYzBXa2xDmwZWn5ATZaoDzb9fmLb5/Gcn0upPOoqiAZ0ik6Hum8w807U1iO\nxPY8QqpKIqIjkFzX1VROIr8cMV/fmElfOk9rIsylTIE79rSwuz2x6MS9VPHmRmjjuVi2aEhK+Rfz\nLQJT7x+TUn5zrveEEJWmL0eAM3Ncf5+U8rCU8nBrayt//3gft+5Mcahzpt3u1UVIU/nLt93EO2/r\n5lMPn+PNn3iUMyO5JZVRefxeaMczX56BvO3j+ZJdrQl0TVlWXoDxvM1zFyc5MZjh6b4MlzIFwrrK\ncNZiYLxQvm/MUEhFDaQMBt35UZNn+scZGC+SDGn4UpII6XSnotO+U2siVJbXdqVi3LG7ddXDI8RD\nGjFDIWe7ZAvB4iRlsFxatmQ4Z9E15YB0fCDDcMbi+EBmSeKLqDEjDv2UrshQFcQyxBQLifnWA8v1\nGM4WCetBbmTT9hg3g9DlcUNlJGOTzttkTJfGiEZDRKcxakx73ssR2UQNDUUR5G0XRQhSsVDN5P0b\nrY3nohYhJnYQiIh6KstbRFl8pxDiDwhOBQ9LKR9f7D6ff9+tZIsbrwHXA1UR/P7rr+GWHc389hef\n43V/8hDvOrKDX3zFbhJhfdHrFSGqOtJW7kAVEUxepcl5OaKNSnwpaY4bJMMGvu8xUXCZKNgoIrBp\nb44bU/Hfk+X478mIRt9YI7GITt5yeNneVhqjRtn6Z2ay77Wm5DDXlYrxTF+ai+N5To/kmTQdUnGD\nw9sbywtnLRTTrYkQ+9vj5G2frY1hbpiRsrAaNpqcW1UUFCGYKNgYusqWBoOQrqMiaIgZdBoaYUMN\nQpl0JMungJVaQm1vjnL33lbSpksqqtU0dM1Ga+O5qIXV0MsJxD+Zaq+VUn4N+NpS7relIcKWq/sw\nMIsfuXYLN+9I8dF/f5FPPXyWLz59kd947V7efFMX6iJWVdWKQSo/Ny0XKisLAby9OcqO5jiW53HN\n1iYaozrjBYdtTRGa4wb/fPQCBccr5zNuS4QDb2RdJT+VMH1ve2JVnLKWysyw1MPZIrGQRjJqsKsV\nzo7k2dWWQFFVEjW0Ny8tPCt5DhvNfDSsK7zxhq0MZS2KjsdXjl0kV3SJhBS2NkbIFFwmTIeortK6\ngFhtqWK+qKHxioMdq9IOG62N52IlNfro1O/dwC/UoC51lkFrIsRH3nwtb7t1O7/3leP85v99nv/z\naC+/+6MHuWVnc03vtZDDzVJpiYd5x+3d5aT0Jy5laJsKCdGfnsphnAhNy2ccNTT2tMXKu7bl+C/U\nmpmK9+7mGL6EpmjgMOZJ6GiMsLs1xsFtDYR0taYTQy1MPzeS+agiBD90bSc5y+Xp82m++twloiGQ\nMhAnqopASlhKULZqWc122EhtPBcr0RF8R0r5HeC/A3cBNpCt+Kmzhly7rZF//k+38advvYHxvM1b\n7nuMn//c06RXmEhkOWZ41dISD3NwSzA5VuYiBoEignsLKHuU5iyXeMTghu1NxCPGNFnreslhKxXv\n/tTc5Lgez12YwPeDLFWpWAhPSsKqWt79z5L11ylTahtfSnRN0JoIo2uCcdPGl5CaSv6yEWXtm5Va\n9MKXAe8EPsj0hSVSg7LrLAEhBPde18mrD7Rz30Nn+Ytvn+aJc2n+6M3Xcve+tiWXtxq77JlilJL+\noVJUsrcjzu27mxnMWFORSQMl70IilfWSw86seyykMll0yNsuri8ZzgbB5vZ3JNctiudm5SXbGuls\nCJPOO3Q2hDnY2cAjp0bLAQNL+ZPrrJxa9MqfJkhg/z+Be4B3sTJHtTorJGKo/PKr9vCaQ+38yj8e\n412feZJ3H9nBb/3Qfgyt+kdTS29bmL6wzMzYNTNiaTKsoyrqlGI6YCGRynrJYWcq3vvGTB49PYam\nKOSKLtd1NdLTEuO113RsCH3GZsPQVCIhiaGpSGQ5VHTR8consDorpxYTtgU8AwgpZa+U8kPAj9Sg\n3Dor5MCWJF/+hSP8zO09/PV3z/FXj5xb0vW13mVXLix52ydt2ggBhalBXRKVBFEcL4uKKkUAC4lU\n1kvcUrovwMVJE8f30XWBpirsa0+ytSlan7SWQEkceXIoS1hXuW1HCxFdZSxvEzFUpISIrm5I65vN\nSi1aUgAnAEcI8RxQBPbVoNw6NSCsq3zo3kO8fF8rty1ReVzrXXblwqIJybnxAkOZIqoQ3NTdNOfn\nNqq53UxKp5180UWgIAhk24YuNs132AhUKt8n8jZSUvYK39uWWHcT4SuVWrTkbxCYj8aBd0/9/o0a\nlFunhixHRwC1tXaoXFgKtoeuqUR0jYLjTtsxbwZzu5mUTjs7WhK88gCk4iG6U1FC+mw79zrzU6l8\nB3jXkR3kbHeaV3i9LWuPkHJlZ9Yph7JLBDmLJeAC7VLK8yuu3RQtLS2yp6enVsUtCV9KTMsrB1OI\nhlSUdYz8WQvOnz/PerXnlcZCbXkl9p3Vptq+WW/b6njqqaeklHJRFUAtltavMpWHfOr/DKACh2pQ\nNgA9PT0cPXq0VsUtieFskeMDmbLC9GBnctMHvTt8+PC6tWcJ2/V5pm+csK5y7baGdQ2rvRIWassr\nse+sNtX2zXrbVocQ4ulqPleLhWAH8Bop5cNTN74DeKAG5W4INqO8eqNzaijL+z77FGdH8wC8tKeJ\nv3zbTWuarHstqPed1aPetrWlFq3nAJUGvc1Tr10RbEZ59UZmcLLI2z79OBL4s7fewETB4cNf/QHv\n+psn+ML7brui2rfed1aPetvWllq03v8FPiWE+NTU/z7wT0KIGwGklFUdTTYStchdW2c2Ukp+64vP\nkS26fOnnj7CvIwhCu7UxzLv/5igf/feT/O49B9e5lrVjo8eg3wws1Ib1cVk7atGKPcBxAr0AgEeQ\ntOZjBMrjV9TgHmvGZogdvln52vODPPjiCP/fPQfLiwDAK/a38/Zbt/OZ753jjTdu5Zqtmz+6YL0f\nrZx6G64dy3YoE0K8XQihSCnvnvp52dTP3VLKu4GfBX63dlWtLfPF0NkMscM3I67n87EHXmRPW5x3\n3tYz6/0Pvm4/DRGdP/r3F9e+cqtAqR/FQirjpsNI1lrvKm0aKlOO1sfi2rCS5bUZeEYI8QLBqSAC\n/DFwK/BK4PvAby1UwFS+4jdJKe9YQT2WzEI7jboSanX40rEBzo7k+cTbb5wzRHYyrPOBu3bx4a+d\n4LGzY9xa48ipa008pOG4Po9dnAAEUV1ZMGxynYBKh7LKlKP1sbi6rCT66P8GbiQIQ30R2D71//PB\n2/JNUspT810vhAgB1y/3/ithoV1/SQl1sDM56yi6mpE4r2SklNz30BkObEny2kMd837unbf10JYI\n8effOr2GtastpT4CsLcjQVdTjFt3NM8KlVFnbiodynRNpSsVpS0Z4mBnsr6IriIrijUkpfQInNJ+\nHOiTUv6KlPLjBGEmFuM9wN+u5P7LZbFd/1wxa0qniOMDGY6eT9cXgyXw6JkxTg7lePeRngX9BcK6\nynvu2MEjp0d5/sLkGtawNszsI7GQSiqmT6U/rO9oq6Eymqvj+vSn88tK6VlnadQi6FxeCNHMVKYI\nIcStwIKjWAihA3dJKb+1wGfeK4Q4KoQ4OjIyUoNqXmauXf9orsjxS5OM5uZew+q6g+Xzme+dJxUz\nuOe6zkU/+9ZbtpMIaXzyoVlprDc8Zb2AoZHOO+Qtb1o/A+onykUoRXM92Jlkb0cCXVPnHXOLjdk6\n1VOLLcqvAfcDu4QQ3wVagTcvcs07gM8t9AEp5X3AfQCHDx+ueezGStOz0VyRzz/RX45z/pabu2aF\nDK7rDpZHf9rkmz8Y4v137SKsq4t+PhnW+albt/Oph87SN2bWNHfsahPoBTweuzgJUhIz1HJS9boF\nTPWUxqZpu/SO5eccc9WM2TrVs+ITwZSfwMuB24H3AYeklM8tctk+4P1CiK8Dh4QQv7jSelRLfzrP\nI6dH6E/ny68NZy1cX7I9FcOTkuEZFh4lW+aDnck5dQcbjbl0Geul3/i7x3oRQvD2W7urvubdR3ag\nKoJPPXx2FWtWe6KGxt6OJF1NEW7d1YyuKYxkLXrH8py4lGHCtFEQFGyPkax1VZ0OZva/avpj1NCC\n0BEVOoLSKeDkUJaC49EYMSi63qwxu1lZqF1WcwyveDYTQryVwGKog8BnoFMI8R0p5fvnu0ZK+ZsV\n1z8ipfyzldajGvrTef73f5ws7yJ++VV76UrFaEuE0BRB/3geVQjaKkIdbLad3Fz1Baa9tlYUbI9/\nfLKf1x5qZ0tD9Qnr2pNh3nDDVr5wtJ9feuWeTRV6ojURIhUzyFsejuvxfP8E59ImpuUwMGHRlYqg\nCoHt+STC+qboUytlZp882Jnk+EBm0TFl2m75c6NZix0tHvcfG8D1JTnL4dJEkYvjJqoiSFwBJ/SF\n5prVnodqoSO4D3gtsI3AjPR7wA9Xe/Famo72pk0sx6c9EcF2fXrTJqYdyHVffbCdG7ubuPf6zmlH\nzM2mG5irvjNfWyu+dOwikwWHn7l9x5Kv/U8v34Xt+fz1d5eWTGe9qdQ/7e1IMpwtMpwpYHuS5rjB\nnvYEW1MRPF9umj61Umb2v+Eq/QNylsuEaTNZcJgwbXrTZvnkrgjBnvY4N/akuGVnM6EqxI4bnYXm\nmtWeh2qxEGhSyrcQKIh/V0r5s0C6BuXWnLZ4iHHT5rkL46TzNomQxtHzaZ7pHeeB40Pkiy7nRvPT\njl6bTTcwV31nvrYWSCn52++d58CWJC9dRm7Zna1xfvglW/jso71MFjZX6KqS1ZnleDxwfIgnz6d5\n5OQovu8T1hSaIjoxQ9s0fWqlzOx/bYlQVWPKcjweOjnCgyeGeOjkCImQNu3kbrk+43mb4cza9evV\nZD1zcteitGEhxD8BNwEfmfIP2JA5ixtjBq+/oZOiIwnrQb5cX0LYUPGkJKJr+FJOy8272YJbzVff\nytfWgifOpTkxmOUjb3rJskNMf+CuXXz1uUt89tHz/MIr9tS2gmvAcM6iJR7iwJYGLqRNbt6R4obu\npvIz2Cx9aqXM1ScP92iLfv+s5bIlGaElEWY0V0TXFN5ycxfD2WAy7B0150xstFlZz5zcyy5NCPE8\ngcmoCbyBIEvZQ4AOrKlQd7HgXqX3FQHtyUhZztaWCDGatSg4HqoQFByXiDE7F+pGCG61lABmc9V3\nrb/D/3m0l4aIzr3XbV12GYc6G3jF/jb++rvnefcdO9b9GczHfM+mLR7CB0bzRZJRjZdsa5wWM3+j\nfp9asFjgxmr6Y1sihCclp0eyJEIabYkQLfEwLfHACms4Y+FLOeeY3aws1C7VjuHKtq+WlbTej67g\n2pqxmBJlLkWVL5m1M7mpu2na6xuJzaawHpws8vUXBnnPHTuIGCuT3f783bt408cf5XOP9/Gzd+6s\nUQ1rR2VIhMpnY9oug5kid+1rYTRr88oD7eVUi1c6te2vkiCL4vQt/2Y7qa8VM9seIaqSzqwkxESv\nlLIX+O+lvytfW265S2UxJUpJ4ZQxA4XTaNZmNGcxlrPKoQDaEsEuo+RNvNFCSWw2hfXfP96LLyVv\nv6V6k9H5uKk7xZHdzXz8wTMb8ntXhkQoPZvRXJGn+8bpT+eRCEKaQs5yN0x/Wm1q1V+HsxaW4xMP\n61iez3DWmuZENlcEgBIbbQyvFbMMQ4Ra1Rxfi2V0WkpKIYRKoC9YExZTopQUTq4vcT3J8xcmCOka\ng5MF7tzbSlPUWFMzreWwmRTWluvxD0/08Yp9bTVzBvvga/fz+r/4Lp966Cy/+uq9NSmzVlSGRFBE\n0N/uPzbAaM7m0TOjRHQFy/MZmCwylrM5sqdl3fvTalOr/uq4Po+dS+P5Pqqi8LI9rXz7B8OLOpFt\nxDG8VswyDJGeX811K9ER/DbwX4CIECJTehmwmfIIXgtKTifDWYu2qeiOo7li+f+s5ZIIG4QMhaGJ\nApmiR1ckRN5yyRRcwlPBwIIdRNB4pRV1LG9NUxzPxUxZaKU+olaips10DP7y1CT407f31KzM67oa\n+aFrOvj0w2d5x23dtMQ3jl9BKSRC6dmcH8vj+oGpqKaAJyW263NhwqQzHeb8WISe5kBEtFGe51IT\n6CzWx2vVX7OWS0xXsH1BSBVcnChQtD2akyHGchYnB3MMx6yy7qBE5a64mjG8WqxmYqKZeoDpivgK\nwxApV3chkFL+D+B/CCH+h5Tyt5dbzkpZyOlEUwSHe5o4NZTB8yWO79MYNcgUHfrSBbaM5cgUHHa0\nxHjg+BCuL/F9ye72OMCiu5n5HGUKtsfp4Ry72+JEDLUmO5KNoLBeDM+XfOI7Zzi4Jcmde1pqWvav\nv3Yf3zg+xJ9/6zQfuvfQ4hesIZXPpuScOJwpMpKzyZg2jgcjWYvBiSKJiMbFtAkEVmvrvWNd6u65\n9PnF+ngt+ut4rsj3L2XwpUQRgte9xONSpsCFCRPHkxQdj3hIn3U62Agn6NU8lVSW7bg+INE1ddp9\nlnqvlZwIbpz6858q/i6zVikqZ67+lU4n/eN5RnIWezsShFSV8YLFloYIuqbQGg9x3bYmwrrCcM6a\nds3WpgjbmqKLruQz711ylAkbKlnLZjhrkYzq8+5IKk8uV0KclAeOD3J2JM+fvfWGZZuMzseu1jg/\ncXgbf/94Lz99ew87Wjam4rUlHuYtN3fx2Nkx+tMmJ4eyWI5HLKxjqApFRzIuHQxNYVdDYl13rDC9\nDw9Mmpwfy9PTHJu3PqXPV5pcT5gWT/eNs78jUbboqcVOeGCySDys0RDWmSw6pE2bl+1tBSm4OGEy\nbtrlMds3Zs4wAlnfE3TOcinYHmFDpeB4y3rG87Vj5TM7O5pDStjVEC33pZJ0o20JHvkraaGPTf0O\nA4eBZwlEQ9cCR4HbVlB21cxc/btTUZ7tmyg7nXQ1RXnwxDCeb+N4PrmQS1hXMW0XgSSiq7Ou2Z6K\nVjUxz+UoM5q1GMoU+f6FDBfTBUK6yo1djbOuvdKCZkkp+fiDZ+hujvJD18yfc2Al/Oqr93L/sQH+\n8KvH+fRPv3RV7lELWuJhrtvWyL8+O4CPoOhJYkg8Hy6Om4Q0ld3t8Q2h8yn14YFJk9NDOZg6Wc+3\ngy19vmRyPZQ1efxsmi3JCM/2TXDv9Z2cG83XZCe8vyMJEtJ5G1URvKSzgbChTZUdoej49I/n8TzJ\nwLhJpuiuaFdcSxQBp4dzeFKiCsFN3Utzqqw2eVZUVwE5S0dVmldQ1KoaYSWiobsBhBBfBG6UUj4/\n9f81wIeWW+5izGWfXNIRaEKQtVxefbAdV0raEoHm/OYdzViej+N4xMM6HckIEwWL3e2J8u6n5KhS\nze68sg5zOco83TfOoa0NdDZE6RvP8eyFCSKGStS47ERTGeju7EiWE4NZbtx+Wd43U/660ROhP/ji\nCM9emOQP33ANWnWGCkumLRHmF16xh498/QQPnRwJdocbDNN26RszuTgROJAd3JLk0niRrc1RGqMa\nXakYRcdjf0eybP++ns+zNH5ODGZpTRqEDZUJ0552MpipEyiZYN/U3cSJwSwt8dxluf1wlrGsTVPE\nwEeu6LRzoLOB113TwcnhLPvaElzfnSIeujyGbt09pddDMJgprotOYD4dYcH2ArHZPA5v80kDKq+f\nT88RNTQ6kmFODmfZ25ZgWyo6S0dVOikJVdOr+R61aK19pUUAQEr5fSHEgRqUO4v5AqodH8gwbto8\nfHKEjoYIEV0t77BHc0HuU09KPG9qcUDSGDWmHYFLjirLqcNMJ6H9HQme7ZvgUsbkxUtZdEVwajDL\nnrYE8UgQaGxHSwxNEZwdyXJpskA6Z/HdU6OAxJdMk79WG6RrvfB9yUe+foLtqSg/flPXqt7r3Xf0\n8I9P9vEH/3qcr/3yneirtOgsB9N2+dbxIb794jCm4zKRdzjQ2YAjfdqTBsMZm9a4R2QqPPVGeIYl\nHduEafPE2TQt8RCjOQtJcDJYTO/VnfL4Us5mKGPhS0FzNMTzFyfwJWxPRblpGeFFSpwbyfGdF0fw\npOTSeJEfvraTW3a2TJsQy85l2eKan7AWCqbnuB6KEPjMdnibTxowXfY/f5rO/nSe+x46g+tLHjwx\nXA6eCcwKoCk9t6r4LLVoseeEEJ8G/m7q/7cBi4WhXhZzWQNAEOUyU3SxHZ/WeJjRfJETg1na4jYn\nh7M0RDW2N8UpOC77t6xsJ1aNRUKlnNhxPbY0xOhN50ibNt0tgUggpKvcsaeFx86OcjDWwI6WBGdH\nc4zmCliOJJ23iOiN+FNhsTeCFcR8fPnZi5wYzPK/f/J6DG11J+aQpvI7P3yA9372Kf7+sV5+5sjS\nAy370nEAACAASURBVNqtFjnLJW3ahHSViKHieCB9ybjpMJa36UpF6GqOLiiDX0tM2+X8WJ6C7dEQ\nNWhJhGgI6SAhomuMmw59YyYF28NyfArOlMzb9jhxKVPeAd+yM0VI1cgUHTwk+zqSWJ5HezK8rNAP\n/ek8vWmTY71pVFXQGoswbhY5M5Ljlp2zjRDWSydQ2rlHdI3ClFx+wrRBChCS67qa5pxrhqeiGZTm\nquGsRUs8PGtu6UiG8ZFla8gSvWmTouuztSHKpYzJyeEsIT24T2nuKZ02fsH3qnKkqEWLvQt4P/DL\nU/8/BHy8BuXOYi5rANN2OT2cI2vZpE2bvnSOyYLDyUtZPnHiNImwTrbocO+NW+lIhFe8E6vWIqEk\nJ37wxDDH+oNV/tCWZPm6ibzNZx89T9HxmDAdEmENx5X8xwvDeFKStzx2tsbKYbJHs9aGkCnPpOh4\nfOwbJznUmeSeaxfPQFYLXn2wnSO7m/nj/zjF66/fSlPMWJP7LkY8pJGKGliuh+36+L7Hd04NM1lw\nOTGY4dUH27l998bwI5hp/dOWNBjNWiAllzIWx/rGiYQ0XNelL13E9yWDmQLDmQIX0gVsVzKcK9IW\nD2FoCgc7G2g3QhRdn/OFPCBoiuhL7qu265dDxY9mLSbyDpOmg6oItjbOH8p8PXQCJT1AaWff0RAu\n+yxpiuCG7U3TpAUlEqHAj2lmCO3KucVxPfrTJrqmTOlsKizT4iEm8jZjWQsQDE4WUUWmLC2oVrpR\nyYpbTkpZBP546mfVKMnOdrTEyFpueZXMWW5ZFrerNU7E0JjIOwxMFsjZLj2tcTzp47r+ggmw55LB\nl+R4iZBWXnGjhsaOlhi9aZPuVOAwNZwtYjleuV6lhxDSVe7c2woIENAeNxjN23Q1RTk5nGXy/7H3\n5uFxneX5/+c958w5s2s02iVbluMtdmInTpw9ISQh0LCkQAspLfTLXmiBlpYutKWU0B8tbYHSUtrS\nshTC0pCyJQVK2Jp9dcjmOLZjW5asXSPNPmfO8v7+ODPj0WgkjWxtTnxfly575mzvvOddn+d+7idv\n0RkNkLNcLMclFvTRGjbojgUZmMrQFNQr9tja3z3fb1jKGIaF8M8/O8TgVJ6//dVdKCskASmE4C9e\neQ43fPouPvXjA9z8y+euyHMbwc71MVqjXj6CR48mODzhsdDypQjX1RRHK7cP03LoT+QYTeXpiHi+\ni6zpsKk9zKa2MAOJPOmCTVfUYCpvEQn4CGgCVRMEdY3u5iBHJzLkig5SEXQ3B4n4ffh9CmFDoycW\nQBFizgl6Pn9X0XHJmjYtYT8TGZOtHWF0TaUpoNIWXTpG0mJRj7efLzq0R/WKiGXatAnqKiAQSMYz\nZmXcKF8TLo0lm9sjjKTydEUDFQntan+nguCJwWlMx1OsLVs/MqaN4VO59uwOJnImfkUhpPtO2Vpw\nKvTRW6WUr68Sn5sBKeWuk713Lcp6LtV2yvIsGTY0ArqKKyUd0QCdUT+fu+s5EjmToak8ruvx210p\n2TeUmjGzllHP7p8r2vzXQwPkLWdGFPLG1lDFK//w4Um2tEdwkHX9E2FDozmoezEOmQJff2gQ13WZ\nyhW5oDfGgZE0RyayWLbLlZtayasOiiIYS+cJ6hpb2yOz7LO1q4Pa37AcMQxz4dBYhn/9v+d4ze4e\nLt+0tHEDC2FbZ4Q3XrqBWx7o5/V71nNuT9OKPr8WtfXfFPBx/3MTTOcsRpMmTUHPZ7dacsnl8k3n\nitx1YJxowMeBkTRntQU5OJolGvAWVZPZIkLC0HSeh45OEjFUXBfSBRtFgaxp0xML8NixaZJ5i6mM\nSWfE4MHDk7iuZDiV55Kz4oylimxuD9M/ObMNLsSvV4XgWCLPkYksBdsBwK+pTGYV0nlrVSKG5+Lt\nT2QK3HMwgRDeDuClO3w82j+N47oIBBvbwqTy9iyuv6Ep3P74UCVi+tJNLZV0pmUfw9BUntsfP44E\nNEWwtSNCMm/hSphM53l8MIkiPH9iT3PglK0Fp1KLZVPQsovPlfVcAj4N25X4dbWiYdIe8c+K7OyK\nBuhrDQOC3uagRyONhyrX1Daeenb/iVJsQVvYz/EpLwDIlcyIU9g/kiSRK9IU1HFK5yYLxYrNr9p2\n+eRxFyEkXc0BJjImjusNZtGgTipXpCVi0BTw8ZYrNpIp2myIBzF8KkPJQt3fPddvaOTcJXknruTP\nv/MkAZ/Kn758WbgBC+IPXrqNHzw1wh//9xN893euWDa2UiOorf+UaeH3aVy5uY1nRlK8aEsbl57V\nsmo7gnL5JALHlcSDBvGgSTigE/abtIYDxIIuPlUhHtTx6xqDiSzxsMFkuoCqKXQ1+VGEIBrwsb0r\nSmvIz2TOC5JL5m2awzqD0znMopyzDS7kYxMCLt0Yx+dTOTKeJmva9LVGSGRNxjMmYePUV78nW3e1\nvP2BRI54SGdDa5DJjMlEtkhvPEBLxGB4Kkem6NTl+j83niFkqKyLRRmazjIwleO89c0znvP0UJKQ\nobKp7cQ55d9+bDJHPOSjryXMRKbAxrYw6+ILxz3Nh1MRnRsu/fclgF5HeG7JUNZzyVu2Z6tMFrBs\ntzL7VYtPtUcM/LqKaTvEgzrn9ESJhw0KljPnjFnP7t8eMXBdybGpDEVbkipYWLbDhniw4pX3awpB\nQyWVt7Ac79xC0UFBlMxKJ0Sv1se860aSeUCUHIo+WsM+ogEfAokiYGtnhCs3t7E+HqribNtoiqBg\nOVi2S77ozBLTqnfucvoTvnDvER44nODPXrF91VJJNgV8fOTGc3h6KLXqmcxq67/J7+0AcpZNe9hg\ne090ReSS5xJbK5dPlNQ8+yczpEyLJsOHrqqMJHNMZorE/D7iIR8KoCgCXVVoixgYqkIyZ+HXVM7t\nbqI1bFBwbC8moi2CpggmMyaqIjB0MaMNKoJKmRbysWmqQjxsENRVeuMhwn4fk1kTn6qwtT2yKhHD\ntbz9sVSe2x49RjJrEfApjCTzKAjO6W5C1zQmM0X8Ph9dUaNyTUhXKuU+p7sJEDw3kcZFsLU9Mus5\nnVGjRDP3YpGqf3s8qBH1+0gWivh9Kr0twTnF9xrFUtRkL/BvQog+4FE8Z/HdUspfLMG9gRN6LuNp\nz4liS0EdaxTADK952ba/kM18LtbBlvYQI6kiCqCrCiBoCRsz7r9/OIXrWnQ1+YmHdNIFiwOjKX7y\nTJ518QCDiXzFTPPOF21iYCrHaDJP0NDpiRlsbIt4Hc03m11QXa4L+5rJmg4HRlIcmcjSP5mdsTWu\nPXc5fQT7R1L87Q+f5fodHbx+z/LSRRfCDed28pLtHXzyzgNcv6Nz1SKO670rAUzlLJqDPi7pa1l2\nyuh8Zpdy+cbTJomMxd0HxzE0heFkgfPWxTg4liKRtZjOF+mJBbhhVydIQUBXCRkqExmTXNGpBFsG\ndJX/e3acaEAjmbe48fxuT9erps8pglnU5/kYPmU6Zbl/PXR4kpGUNzCuiwdncOZXykdQ/W6PjGf4\n1t7jWK6LKgQ37uomGtSJBzV6mgNctbWlUt6rt7VX+iGc8BHkijY7uiKMp00vx3VYn/WcsBHn4o0t\nFV/k+nhoxm8vx1AslSrBUjiLPwwghAgA7wD+EPgHYEmTiAZ1jYBuEw7oC24NT8ZrXss6yJg2Pk2l\nPWIwnMxRtF2m82Yl0GZHl5+xdAGfptLRpHJ4Ig3SU99M5m1SBYtU3kciZzKe8hENamxoCdEVC2A7\nku6Yt00sb+nmkuqtLpcrveeVf/942vTqpCb5R9mxtRwoWA6/941fEA34+JvXnnz2saWCEIKPvvoc\nfukf7uY9X9vLf7/7cvyrlL+29l11NwfZuc57V+WAwuXEfGaXXNFmPO3Jr9uuS0eT58PKWw5ZyyYa\n1MkWXYqOZCxjEphW6WkK0hYxKnm9qyPuDZ9KNKCBFEznihi+6Ix8C+U2mDVnB0aVmTTlNlqPft0a\n9vpXS8TP1s6mGdeuJuvqmeEURcchHvIzls4zlMyza30zecsbmHVVYX1zEFGKB6qXiOjoZJaw38fG\n1ggT2QLHEifkMXJFzyytCGgJGzOczdWoHuOWwoF+yjUqhPhz4AogDDwGfAC4+1TvWw8rKSZVpoZN\nZk0ePJzg2FSOvOkgpaiE4JfLU5aU8Osqw9MFckWXgUSOVMHiiYEkQ1N5dE3Dsh3Cfp1DYxkQECit\nnBp1gNXSyw6MpGcJly2n2JWUkj/79lPsH0nzxbdcRMsaUQHtagrwydefx9v+8xFuvmMf/9+rz131\nCWo1hM/memauaHPvwXH2j2awLIe87ZA1LfKWQ2tIJ5kr8vRQkpGUyfGEj8d9Cu0RPwGfygV9zYwl\nCyiKMiP4qVrevUyVLKOec7WW8t1IG10L4nEw8/ckMhbj6SLjaROkIGdaPDYwNYM+6rgStaZOqlFN\nH5VScmQ8Qypvky5YHBrNoCiiIn4Z8ftmBastR39fipp9LWAD/wP8H3C/lNJcgvvOwlIGjiw0i7oS\n1sUDCAV6YgE2tYbZN5Jk31ASy3E5uytKe8TPju4oqYLFto4IsbCBT02yviVIQNcI+BQ6mvz0tYa9\n1VFRsrXTo5yuj3uBRYuRzK3+/fmiw5GJ7KzrllOC95YHj/Hfewf53eu2cM229iW551Lhuu0dvOvq\nTfzr/z3H+uYg737xplUtz2oEOc31zGOTOQ6MZrBsB92nEgv62L0+RixoEA/pPD44haootCVz6JrK\nZKZIxO+jaLscHc+SNi2ag550e1kKpZxPuCwtka7agda2wY2toRmBVWPpQkNtdKXrcD6Rt3LgmKLA\n9s4Qhs9H0bbpjofpaw2BmJ1jeTxt1jX5Gj61IntTtB2m8ha5oksi6wWabe9qqhBR+lrCMwQtl6u/\nL4Vp6AIhRBRvV3A98DkhxJiU8spTvXc9LEXgSCOzqCJgMJEnbRa9tIPJLM8MpTg+lefho1Oc29NE\n2NDYN+RJXCcLFj6fQkhXafL7ODyWwXFURpMF/JrAp2qEdFExE1RHly5m1VNt/umfzM66brlWUY/2\nJ7j59qe5Zlsbv3vd2kwk/0cv28bQdJ6P/3A/hqbw1itXN+p4NYKcap85kSnwgyeHODiW5uhknvXN\nAfw+ldaIge26tEZ04kGDkJEnoGvEgz4KlkP/RBZFBRXJk0NJAAqWS19rENeVbGwN4dc9ooS/ZEIt\no7YN1vpGFtNGV6oO5xsTqgPHpvNFECq24yLxdgT9k56cw/aOCH5dJVkoekJ+U/lZQnjl+5VlbxJZ\nk31DaVQBjoQd3ZESEUUlHtRnCVouV39fCtPQucBVwNV4KqQDLJNpaKmw0CxalnFdHw8QC8RYFw9x\neCxNe9SgNx5mLJ1nYCpHVyyAK+Gs1gim4xIsefdtKYn4NSQCTVPYGA8TDWp1Q85PdtUz13XVQSnz\nBZ8tBsPJPO++ZS/dsQD/cNPuFQscWywURfD3rzsP03a4+Y59DCfz/MkN21HXaHmXGvVWtGNpE0VR\nOLcrRqbgsKXDo1U3BXXylsNY2mT3hhhbOyPeqldXmcqZPHJ0io6In+fGM0zkLVqDBkcmM/hUjxJq\n+FRuPL+74sys9skt1KZrj3vlLKxqxHytXET1mOBKKoFjYb/CungQQ1Up2i6GphD1+0BIYiG94uie\nTwjPlVSCYPceSxD1a2xqizCc8oQK+1rDMwJmqwUt69XZUuyalqLm/waPKfSPwMNSyoZEjlYT882i\n1YFBA4k8skWQzFp0RPyk8zbPjaXQVJX1pXwFioCh6RzjSZPN7WFGUgV2dEeZKOmJxIMGbVFjXqGx\nk1311LuuNlFPveCzxSBj2rz1S4+QKzp8+W0XVwKj1ip0TeGzv3EhN9/+NP9+9xGeGEzyj2/YTUf0\n9JX4bgRzrWjLNOhnJzI40qVgOYR0jem8xeBkrq7sdFvEIJW3K+bRIxM5iq5DwKdi6EqFElqWmz4y\nkaUlPLNtL9Smq3e2M5KtrxJq5SKqxfJMy+HBwwlsV4KUXLW1jZawn0ze4uBYmslsEU0RXL75hBN3\nPiG86iDYcv2OpfPoqsLOntgMp3u9Ol1I+PJksOAIIYTYg7fi7wbywFPAnVLKKQAp5bIHlJ0s6q2Q\nyt+VpRvmsgf6dZW2JgNVeKsBQ9W4fHOc5rCf7liArligsrI5OpkFqDCBypIQ/Ykc1+/oIBbS687W\nyxEuv5Q+Attxec/X9nJgNM0X33yRpw9/GkBVBB/55XPZuS7Gh77zFC//9N38w6+dz1Vb1p5s9WLR\nSLKS6vfeGvZzzdlt/OxZuOSsFlRVcN66GC4Sv6rQHQsyND0zIU15V3lgJE13U5C3Xhnx5E3CRqUt\n1z6vlsHWKGrvs1oor9L9ukrBcphIF2eku632h3Q1BYiFdDqbDHyaUrnGlXNL1MOJFXz1rv3cnii7\nemIVSemWsDHjvHpYDj/gnFcLId4CvBc4ghcf8CxeEporgT8WQjwFfEhKeeyUSrBMmEuyuhHfwKGx\nDAXLYTiZZ3dvjMeOTdMa1rEcOLsjQiyozwhm62sJzbDf1SaHuOni9XUngeVg9yyVzVBKyV/e/jQ/\nf3acv37tzjWp/b8QfvXCdZy/vonf/upefvMLD/H7L9nK71yzec2athZCo8lKahlDg4kcg1M5jk1m\n6Y2HuG57O0FdYyJtMjSd81hsnNgZADxwaIKfHRjHLUXRv+nyDbMo2ScYbC4HRlKz0iU2gtpyrxZO\nrNLBslx+8ORQhSl1/Y6Oij9EQZDImBQdWZGalnJuBmBZOmIuuepy2tKw4aN/Mkf/ZHbBelwOP+B8\ndwgCV0gp8/UOCiHOB7YAa3IiqF7Zl1PFwcKJ6V0JbVGdiUyRpqBGxNDpigbY3BkB4a0aamWEa22e\ntckhypITteVbDnbPUjEt/v3uw9zywDF+6+qzeMPFvadcrtXC5vYI3/mdK/jTbz3JJ+48wN5jU3zq\npvOJBdeGYuliMJcM+1wr0DKZIGe5bG2PUnRcOpq8ZE1z7WbL90zkvKjhsKFhOs6sNtwIg60R1PMX\nrAaC+gkxyZBfw3UhHtKZyBSwpZzT9l/NiJqrT9d+X80Aem48A0g2NUXqpp1cKTbVnHeQUv7zfBcu\nZeTwcqC8sq9OFRfUF55JTcvhocMJipZLIlfkrFZvu+j3KQR86pxa8tU20drkEPVyhy4nR/pUmRa3\nPjzAx76/n1fs6uKPX3b2kpVrtRDUNT510/lcuKGZm+/Yx42fuZfP/eaFp42pq4zaNjPfCvTegxPs\nH0lhOS62I9FUgU9TaA7Mv5stH4sHNUzbIW/Z9DaH6rbhhRhsjWI12FW1mMgUKrv4TKHIcNJkcPqE\nTPRctv9av1+9Pl373qoZQCHdUyyol3ZyJdlUjfgINuKZiPpqzp9b5wGQUt54qoU7FVR75sup4hqZ\nSdOmTWdTgLawn+FUjg2tYV7WGVmUZENtcoh6Uc6rwTNvBN9/cpg/+dYTvGhrG598/XmnrRmlFkII\n3nRZHzu6m3j3LY/y2s/exydedx437Oxa7aI1jNo2M98KNFu0iZT0joKGyub2MC0hY9bANVc7vHZH\nJ5s7ouSKNr0t8+fwXqtteTGoTh27f8TzIfaUIoSNqkj1+X7rfEy+eilta2Wta/+/kvXYyJO+A3we\nuB1wl7c4jWMhR2u1Z14RVITaFppJ2yMGqhAMp3IYqsrZnZGT0vLwHHWzw+drz1lLnean+0f53W88\nxgW9zfzrGy/A0FZHqmE5ceGGZm5/75W865ZHefdX9/Keazbz/uu3LinFdDk182vbjGU7npqlrsxY\ngYZ0jYGSam5PzE9vPDhL+bS6nLWsk6CucXZX4zumleT7L0fdltlV+0eSqAJ6m4OVtLK1K/NqGYh6\n1NhGmIH1Ptf7/0qhkScWpJT/uOwlWQQacbSWZ+HxtFnR/a8VaquHoK6xpT1EImcTD55cY1tOmYfl\nwu2PD/H+//oF27uifP7NF6358p4KOqJ+vvHOS/nwd5/mMz87xL7hFJ+66XyaAqdOjV35d1/emJ+Y\nyIK6xhVbWtna6alahgx1ljwBNC5tslawnHUb1DU2d4RJ5IrEgzqXbmqpawWYK9/w6Y5GZKg/LYT4\nsBDiMiHEBeW/8kEhxBYhxG1CiH1CiMPlv2Us84wtcVnvvB6Curcr8GnKgudW3zsc0Nnd20w4oC94\n/kSmwL7hJBOZAjAzD2yjz1xNSCn50r1HeF9pJ/C1d1yyJAPiWoehqfz1a3fyV68+l7sOjPPLn7mH\new9NnPJ9G22bSwFPGFFhU1sEX1UWK/Da/oaWEBtavDwc+ZI8er7oESeqy5m3HI5OZmdJV88lab1a\nWM66zZg2uqrQ1xJC15SKYFztRFNtQnJK+cSrUTsenC5oZDrdCbwJuJYTpiFZ+gzwReDDeKkqr8HL\nYbysGUIW42hdrFN2MefXrg5uPL+bIxPZSpaqsrDcarIh5kO+6PCh7z7FbY8O8pLtHfzTG3YT0J9/\n5qC5IITgjZduYFtnhD+49XF+4z8e5GXndPDbL97MeetjJ3XPlRRKa/RZ9YKlysSJoWSOQ6OZWYFl\na3FXu5x1W49cUg/zEUFO591CIzX5OuAsKWVxjuMBKeVPhBCilJDmL4UQjwJ/sWSlrMFinFOLdWQt\n5vzq1cHAVJb+kpxsd2ymsNxqd6B6uPfQBB/81pMcS+T4vZds4X3XbnneOIYXi4v64vzo/S/ic3cd\n5t/vPsz/Pj3K+etjvOq8bl66o4P1pdzUjWAlHaeNPqs2WGoWfVTOpI/WozwupXjhyWI567YeuaQe\n5iOC1I4H9WjjaxWN1ORTQAwYm+O4KYRQgINCiPcAx/EkqeeEEOISvB2EiydL8f7Gi+xhMc6pxTqy\nGj2/dnWwIR7kyES2rrDcWkLBcvmN/3iQja0hvv6OS7lsU8tqF2nV4fepvO+6Lbzlij7+6+EBvrX3\nOB+9Yx8fvWMfPbEAF2+Ms7Onie1dUXZ0ReeV2lhJEkAjz6oOlqreoc5HH10rEtC1WK66rSaXLJRJ\nbq58J43QxtcqGqnRGLBfCPEwUDGIVdFDfxcv+Ox9wEfxTEb/b4F79gPXSikLQoivCiF2SimfXHTp\nG8RyMQ3qrQ5awsaap9H5fQp/8+u7ecn2jlVL4rJWEfH7ePtVZ/H2q87iufEM9xyc4KEjCe45NMG3\nHzteOa8nFuAb77x0FUs6G3O186WiPD6fEdRPXayxEdr4WkUjv/bD8x2UUj4MUNoVvE9KmV7ohlLK\nkaqPFuA0UI6TwnLbOmtXB2uNEjoXXrmre7WLsOaxqS3MprYw/+/yPsDTinlmOM2+oRT7R1JrSshu\noXY+X7tslPL4fMZSiTWeTHbEtYBGfukxYFhKWYBKSsqO8sGSKN0XgUjpcxJ4q5Ty0YVuLITYBbRJ\nKffVOfZO4J0Avb0nL3GwFm2dZ3B6oj3ipz3i5+o1qLt0pp2fGl7o9SeknDM42DtBiEeAy8vOYiGE\nDtwrpbyo9PkJ4HeklHeXPl8JfFZKuWuB+8bxgtVeX7NDmIXW1lbZ19fX2C86A1wpKytDpU7KxqNH\nj7LU9bnQM5+vWI66fCHjTH02hkb726OPPiqllAuyOBuZ8rRqxpCUsliaDMpwypNA6fg9Qoh5Cb5C\nCA24BfjAQpMAQF9fH4888kgDRT2DXNHmp/tGK4Ex1+7omLWy2bNnz5LW53xmieWMsl1M+ZarDEtd\nly90vNDrc762Wj6mCOrmL64HIcTeRp7bSK8YF0LcKKX8XunGvwxUR978nxDi34Cv48UX3AT8vBx0\nJqWsV5DXARcBf1tKMv5BKeX9jRT4DOZGrmjzi2NT3LlvjJBfxbQdNndEFiUVcDKYa1u9kN16JSaJ\ntciHX6v4xcA0//LzQ+w9No2mCC49q4V3Xb2JbaUI5TNYXtSTqy5HN8OJSPBU3sLQlFmU31NBI1e/\nC/iqEOIzpc+DeAFmZZxX+rfWqbybmYFnFUgpv443cZzBEqHciA6MphnP5IlHmshbzopEhc5FNZzP\n7rpSA/QL3fbbCKSUfPbnz/F3//ssLSGdF29rx3Zd7tw3yh1PDPGnL9/OW67YuNrFfN6juq0OJXPc\nd2iSaEnvqBwh3hIyMC0H03ZXLB8BAFLK54BLhRDh0udMzfFrTrkUZ3DKKDeibR1RnhxMYTsuvc0B\nelu8YKjq1fdSYy6q4Xxc9JUaoMOGVleY7QxO4DM/PcQn7jzAjed187HX7qzU0VS2yB/e9gQfuX0f\nWdPmPdduWeWSPr9R3VYtxyHq983I3FbuSwFd5cK+5kUpIi+EOe8ghHgj8DUppQuzJwAhxCagCzgI\nfAzollLeIITYAVwmpfz8KZfuDGZhLnNKedB1pOT67W10Nwcr8sErkRe2HtWw3gRRbedcuYCl2cJs\nZ+Dhh0+N8Ik7D/Ca3T188vXnIaocj80hnX9704V84JuP8/c/OkBvS4gbzztDO14KzG0W9dqqv5Tx\nrDrvQVtk+WKU5rtbC/BYSS7iUWAcL1XlZuBqPD/BnwBfwqOP/lnpugPAf+FJV5/BEmI+c8p8AUCr\nmRe2eoKYzwa6XOaaijBbU+SMaagGExmTP/32k+xa18Tf/MrOGZNAGaoi+Piv7GJwKscf3fY453RH\n2dQ2r3DAGSyAufpxbVutzn5W3c+XA3PSiqSUnwYuwLPltwHXlT4fB94kpfwVKeVBoFVKeSslQTop\npc0yBoi9UFFP1XQ8bc5QhwzqJ3Tlq79fzbyw1QqWteqRWXNpm0k9tcy1KpWwFvCR2/eRKdj8/evO\nmzf3hK4p/POve/kp/ui2J3DmEuI5g4ZQ2w/K/bh2l9wWMeoqoML8yrAnoxo7b6+QUjrAnaW/uZAV\nQrRQylYmhLgUSDZcgucpFsOIWYgyNp42eXJgmpzlcHzKSyGtCDgwksanKTNWFXOtNlYjL2y9HcCJ\nhOcOTwxO47iSUEk/v1b3vTrcf6G6nOt3v9CkEhrFY8emuP3xId537Wa2dizMCmqP+vnwq3bwb7Q8\nswAAIABJREFU+7c+zlfuP8qbzziPTxrVvgBNSA6MuJV+XMsUGksXZrVbLxXpONmiS0hXuGJL24xd\n970HJ8gWbUK6Bp7iw4JYil7x+8D3gE1CiHvxdg+/ugT3PW0x16BUO+CXB/l6A3r1fYaTBe47OE5v\naxjbcWiLGrSEjLoJw+dywi61XEAjE11tWVxJZVBOZE2+u3cQiYIQLls7I2xo8e5TLefrupIt7SHC\nAX1edtF8zucXklRCI5BS8jc/2E9rWOedV29q+LrX7O7h248d51M/Psird/cQC+oLX/QCxnx9pGC7\nJAtFNCFo1dQZfaScd7p2DAGvnScyRfaPZgjrGgNTNls7o5W+M5422T+SIuL3eRnqFK2hhn/KvUNK\nuVcIcTWwDc/T8ayU0jrV+57OqDcoAbNWxw8cmqA/kSdTsLh2RwdZ02E8bRLQZ+akDfpUxrNFVDWH\nEBD0abRFjLoJw1fCFNIo9bNeWcqD8tBUnieOp/CpCpbj8rJzimxoCQGenG+h6NASNeifzDEwladH\nChByThv/GRNQ47j74AQPHklw8y+fs6h6EkLwZ6/Yzss/fTef/slBPvyqc5axlKc35usj42mToxNZ\nIn4fo9kCuqZg1KFe54uOJ4tdWjD2T2ZLWkgFcqaFAGx7dvZgy5GkCzaW07gJ75R7ixDidcAPpZRP\nCyH+HLhACPFXcwSSPW9RPfuHDY1MvsixyRyaIon6vcGvenI4MJrmzmfGkdJlPF2kuzlIZ9TPgZEU\nPk2dYUrJWw5tYZ2e5iAKENDVVVWNnGuiq1eWja0h+hM5NsSDM3ZFOcsmHvTRFNRJ5osVu2bY0IgY\nGsOpPIPTOfKWw/B0jmdH02iK4OxOLzhuMQqbZzAT/3bXc3REDX7tosVreJ3dGeWmi3r5yv39vPny\nvsrk/ULFXKv+hejRluOSNr318s6eGPGwPuMe5ejhvOUQ8KlsaAlVJgaJLA32Fn5NwbQc9g0naY8Y\nhAwVgXcs4FNAug3lmV+wtwghDOBXgL7q86WUN5f++yEp5TdLGkPXAX8P/AtwSSMFeD6gdvbf2Bri\n4FiWRM7k2eEMZw+nCft9bGoLMp2zCOkKUgrG03miAR3bddEUL5HNSKowy5Ti7RLUyu6graRzvlqq\nkbWrb0XUz387kSnwvV8MYbuSx49NVzK4uRIy+SItET+ZgkVLyGA4mWcsbRLSNbZ2RnjR1jaQgsHp\nHOPpIhtag4wkczx0JMG6eHDRCptn4OGp40nuPTTJB284G107uUSC73/JFr61d5B//tkh/vZXz1v4\ngucp5lv1z7dDDRkq+aLD0HSe5qBOa0SfpViaNR2KjoMQUHRdCpZTyTJXsBy2dYbpiAQZTef49mPH\n8ftUNEVw3Y52dnQ3VZIQNUqZbqTXfBfP+fsoVfkIqlCmfrwC+Hcp5f8IIf6qoac/TzAjInA6x+OD\n0zhS0hw0SBamSBcdkgWbaMBHZ5MKCJpDOm3hAFJ4ae0cFwYSWUzLrUwW5RXChhZtWTnEi0Xt6nuu\n1c9cGdxaQgapfBEpJX6fZxraN5wmFtCxHYf1LQFiQR1XQq8IYFouqbyFQMHwiVLuXfsMFfQk8G93\nHSZsaLzhkpNX9G2P+nnDxb3c8kA/7712y6IyuD2fsJBfaq4d6kS6yFjaRBGCsbTJRLo4ayLIWzZD\nU3lUVcFxXHKWXckyN523KFoOiVyRdN5BE6LSx3JFZ0YSIqSzNDsCYJ2U8pfmOX68pDV0PfDx0g5i\nWXMWrzWUZ/+h6RyHxjK0RQxGknl8Gkjpks4VkUIhbKhsavM4ws1Bg+t3tNM/laMn5mdbZ5RE1iRv\nO/hUhdqZfK2tdmvLU7tDGEsXiBjanBncUnmbqOHjrPYIe49NcmQiS2fUwbQdkKKSJOTcniiXbm5l\nLG2iCcGd+0YZmjYruXfXMn727Bh3HRinNx7kpovWr/r7G0kW+P6Tw7ztyo1E/XNnWGsE77p6E197\n8Bif/fkh/vq18woNP2+xkF9qrj6bK9oVeuh4pkAiZ85mB0kBQiAlIARBn4bteIqjQU3Bth2ShaIX\neFbVx3pLJtgKQ7AUELwQGmmZ9y2QQez1wC8Bfy+lnBZCdAF/KIToAx4EngGKUsqXli8QQnTjqY/6\ngb+QUv64kcKuNgYS3qq2PWwQC+kzHDvlgQu8/K9CQM60GU2aOIChgu1KfjEwRXPAR1vE4NLNLXRP\nBhiaypEt2pi2i6EpxAIGeev0WfFWr34UAT9/doyRlEln1ODKLa0MTOXY2h5hfTxUyeC2qS3El+87\nyr2HxlCA9c1+Aj4fQmggJI/1T5Mt2hxP5LliSys7uvyMpQuzcu+uRUgp+cjt+/jSfUfRNYWi7fLV\nB4/x9XdcWjHrrQb+e+8gjiv59YtPfjdQRmeTn1+7eD1fe/AY7712C92xwBKU8PTCfJHz1WND7Y6g\ntyVIV1OATNGiNWxwdDzLodEM8aDOeb0x0qZN0XbYEA/i01Rsx6E5pLO1M1KXcXf11g5sKdkQD1Z2\nFosdN+aTmHgSLzZAA94ihDiMZxoSgCznG5BS5oBvla+TUg4Dw6WJ4E4p5Rvr3P5PgA8BjwN3AGt6\nIsgVbQ6MpPnivUdwXM90c+P5PTQHdUzLxpaCkK6we0MzE2mToWSOwUQOKQSGpnLBhjgjqTwHRzKE\n/BoTPoXzemPsH06TLdqoimBjawhFwPd+McQRN7dqK95G4x+qef6tYX9l9fOLgQTf3nscn6qQNS22\ndETpiPrpn8gRD+uVcwcSWQamcyTzFgFNpdcIIpEYqkqh6M6gwJWppXPl3l1r+M/7jvKl+47yliv6\n+NOXb+eBw5O888uP8o4vP8Jt77oMTV35DbOUklsfGeCSjXH6WpfGwfuOq87ilgf6+c/7j/LBG7Yv\nyT1PN9RGzpc5/Koi8GvKDOJHdRT99u4oiVyRgulw76FxdM2bRB44nCBoqGgKnNUexqeqFb9gPcad\naTm0RwJsbAt7dPLwyaXZnO+KV55k3VTjGiHE3cC3pJSfqvp+J/C7UkophEgLIaJSytQSPG9JcYLn\nn+LAaIaxdIGzO5uYzBQxHZdErsiRiSwdET+Hx4u0hA12dEc5Numt8Is2TGQshpN5HFcSCahs62xi\nYCrLgdF0ZbBLmxa71sUwfCrr4gFAgGDFV7yN0kInMgW+cl8/ecsm4NN40+UbKiuRyWwRy3GJBnxM\nZEyS+SLbOqKViaN83oHRNFOZIvGwn9Fkns1tCju6m0q/W0JF7uCEiex0YAYNJ/N8/IfPcs22Nj70\nih0oiuCqLW18/Fd38b6vP8YX7j3CO1/UOHd/qfDgkQT9kzl+97qlE45bHw9yw7ldlV3BWp2YVwrj\naZO9xxK4QN50OLenie1dwTmURCWxgM7BZIrRdJHWsGBoOk8yV2Rze5SUaXHllnY2d4RntXVXygrj\nbixt4kp5yuKNc14hpewHEEJ8RUpZLTuNEOIrzJSirodhYCveLuK7QoifSCmfKB1T5YnUaEkgBsyY\nCJYqVeXJojwoJrJFBqbybGwJcN9zHosFBJblIACBZCpXpH8yw8GxAJOZIo50eGowhV9XEUKys6eJ\nc7qbuHPfaMWW1xIyKoOdVZKUbRMGg4k8jpSoQqBsalnR39yoIuixyRzHElnaIn6OTWU5NpmrDPDr\nY0FUoTCWMtFUQaZg8X8HRwn6PFpoGSFdI5l3SOYzONJlOl+kf9KrmwvWx9gYDzKVt9gYD84wp6w1\nX0kt/u6Hz+JKyc2/fC5KlZ7Hq3Z18Z3HjvNPPznETXt6aQqemo1+sbj14QEihsYN53Yt6X3fftVG\n/ufJYb75yMALUqq6egc9lTN5YjBZWalvbA0xmTUxLc/kW+5XU9kiP3hymHTeRgpJLKAR1FWaAz5S\nBZvB6RyW4xLU1YpkTDV6W4Kc1RbBdByiAR8dEeOU42cauWpG1IgQQgUuXOgiKaVJiWUkhLgDOBco\nTwTVDowoMF3n+s8BnwPYs2fPiluDy4NiT3OAgakctit47e4eArrGdM4kaOg4jo0QgqlcEdN2yZo2\nRycy+DQVR0qiQR8hQ2VDa4itnVHiYX2GbMJgIstoxsR2JOMpk8FEnvXxALGAwXTeZCxtrujA12hQ\nVlDXUBRBtmijCDGjfLGQzmsu7Ma0JFMZk8eOTYELluuSNZ1Kx/HrChta/Fi2xBVwVmuY7lgQhKzs\nhMprhbWQ5awRDE7l+O7jQ7z58r5ZTBohBH/4sm3c8Om7+Y97DvMHL922YuVKFSy+/9Qwr71gHQF9\nbk2hk8Hu3mb2bGjmC/ce4Tcv60NdaTGrFUK9Npgr2vzkmRPZAFvCOk0BHwGfRsGy2dASpD1qsKkt\nVCFJKAJGkjmOjGfRfSqm5XDd2W10NQdxXJfjiQI+TUHgqb/WQ2vYz5su37AoCZaFMJ+P4IPAnwIB\nIUR5tS6AIqUBej4IISJSynTp4xXAP1UdfkIIcRnexLAmzULlQTFrOpzdEWVrZ6RC4dw3lKIlZPDc\neIYNLSFUBW59OMWPnxlFupJXnd+DqggyuSLRgI+28Anef2tJuHE8bSKFQFMVNFUQDxkkct7qIW/b\nDCTyGJrKRNpcsaxajZpeeluCXLO1jUTOJh7UKjkPyvXWGQ14sQIFm0zRIWRoJLM2w8kcAwnPbJYr\n2KyPh9BUQcF0mcgUMR2PStvbEuTIpBd5eXAsTcF2aY0Yaz7D2OfvOYIA3nZl/ZXx9q4oN5zbyZfv\n7+e3X7x5yQfluXD740MULJeb9qxflvu//aqNvOuWvfzo6RFu2Lm0O461gLlUc4emcvz46REURcF1\nXV5zwToEkMiaGD6FqWwRRVGYEOYMH8HP948iFOFpDjmevMoVW9pRBDzW72mKVccL1UNr2D+Dcnqq\nfWI+09BfA38thPhrKeUHT+LeVwkhPoq3K7hbSvmgEOKfpJTvBf4W+DIQYHZmsyXDqQi/BXWtwgSK\nGBqGz+u01avmkK7guA7PjKSxXcm6Zj+DkzkOT2Q4tyfKto4oCEnatJnIFLxIwaJToZiOpgqc3xsj\nlbc4Pp0nHvJx4YZmj30kWdJUdEuJoK5VKJ3lFUn1sfJk4tcUfrp/lHTBYxMVLIdnhtP4VJVk3vTC\n4F1JQFM5Z10T7dGAxwZyS5GXBZuM6eBIt7KtrpbgWEt1kivafPORQV51Xve8DJo3X97HD54a4XuP\nH+emk4jsPRnc+vAAZ3dG2LWuaVnuf/2OTnrjQf7jniPPy4mgNnPYz/ePo6mC/sksYymTppBOqmAx\nlTPRNYVUwSYgBHnLqcS8ZE2nMvHvXBdjc1uInOXQEgqxp6+lYgK6Ykvrqux+G3nSN8v5h6uQBPpL\nktN1IaX8PvD9mu/eW/p3kDopLJcSi0mFWG/Gz5oOB0a8BNGHxjJsbg8T0FX29MUrA51pOdz2yCDT\nWZNcwcZxXaQABYlEYNoOQ9MFpBQIAVG/t23MWw4I77lHJrL0tYTYtS42gxkwkTZXXDdnPqGr2i1x\nOXm2t2OZTZUL6hqJTJH2iI4rBYqQIOG5sSyulGRMC/BWRdmCNwnrOauyEhII0gUvN2tQ1yqKpXMJ\n9K02/vfpETKmza9dNP+q++KNcc7ujPCl+/p5/Z71dXMALCX2j6R4fDDJh165Y9mepSqCN1/ex813\n7OPxgWnOWx9bluesFqrVQrOmxYHRFFJ6/i9Nw8smZmgkcib3HJpASIEtXXxCMJm1cF1J0XGJ+H2V\ndvvHN2yvSK+sj59gca2WD6yRJ34WLw/BE3imoZ3AU0CTEOLdUsofLWP5ThqLSYVYGxl836FJXCk5\nPJ5lfTxAImcynvIRDWozOMLjaRNFEezpayVvuYQNjfaoQdRvcHDMG7COT+dpCuhkixbr40FM22Ek\nmcd2HEaSBXpiAfyaUpkEYPXYMbV1Vi10VZtAY77zyttggE3tEXyqiuU4CCEYS+dxpSBTsFGQ2BGj\nFDls0xwE8HwEO7qjlXiBszujBHQvLL+e4upawG2PDtIbD3JRafKcC0II3njpBv78O0/x1PEUO5dp\nlV7GrQ8P4lMFr9nds6zPed2edXzyzgN88d4j/MOv7V7WZ60GvDZaZCJtcs/BSYQAy5Z0xQxUDQKq\nQjLnoCmCWMggkS7g11XO740xmirguDOZPevjoRkTwGqjkV40BLxNSvk0QCkV5c3AH+HFD6zJiWAx\napTV55aDuoKGys/2jzGQyPD0UIYjsQwB3Rvo03kbn6aSyRdxXekFOrVFOL+3icf6p5F4A2JPLMDw\ndJ6i4+mN71zXhCtLiRsQ+NQ0vfEwLrNVNVdjZVAvgU29yXS+84amc/xs/xg+VUFVvGjinOXSHAhi\n+FRUoRDyq2SLFsm8hSUljguGqrCpLVzJoFYdL1CeJHNFu67i6mpjcCrHfc9N8nvXbZ3BFJoLr9rV\nzc237+O/9w4u60Rg2g7ffmyQl+7oJD6H43GpEPH7eP2e9Xz5/qN88OXb6YjOZrusdcxlSh5PmxxJ\n5AjrGgdHU6RyRQxDwzRtQnqQF23pYCJbYF3cj6ooTGeLqKrCpvYwUkJzwAeINdduq9FIibaWJwEA\nKeU+IcTZUsrDy72tPRUsZlVdGxl7/3OTPHM0hWk7hA1P7c9v+BhLFfjxvjGCusZVW9oAuObsEJmi\nTXvYwPCpZEyHXNHBdlwifo3eeIiOJoPmgE5vaQUwkTbJWw5+n+px8fW1ERxV7Rcp2/4PjKQ5PJEh\nWBXAVf+8FM+NZ8gVLEZSBeJhg0TWpDnoQ1EVpIDmoE5H1I+iCIqWgyoETQED07ZBLJyfda3GEdzx\nxDBSwmsvaGzV3RT08ZId7dz++BB/9ortJUmRpceP940xlbN43Z51y3L/Wrz58j6+eN8RvnJ/Px94\n2cqxopYCtQldahMlWZZDRoINFFxJMe+ZNg1N9aQeNJVdPXHedqXDeKZIW1jn2u2dM/r2Wmu31Wik\nRE8LIf4F+Ebp803AvpKm0JrOOzDfqrqec7ismHloNMNoKs9kpkjUr6EKKFo26YJFthRk1tMcIB70\nMZ52caXkzmPTnvyBprBrXYyQ4a1oL9/cOisvb3kwu3BD87Ln7F0Mam3/O7qjgPT0TpAzzquWgNi9\nIUY56bYUkLNsiilPKC5jOvTGgxydzLKlI8z1OzqYylvkimGeGEiiayqu1Ll0UwvdseCC+VnXYhzB\n26/cyJ4NzYsSX3vN7nV8/8kR7jowznXbO5alXLc+MkB3k7+yaFlu9LYEuX57B199sJ/3XLsZv29l\nWFFLgdqELuvjwYo0dMhQsaUkkc7jOi4KoCieDtCFfc1s62piQzxIS9hgLB1hYxuVBU3tLn+topGS\nvRn4beD3Sp/vBT6ANwlcszzFWl7M50geS5u4rmR9PMRzYzmKtkNfa4iupgDJvIVTSvawvjlIT3OA\nIxNZFAS2K/HrKlJ6Zo1aNcFqrMXBDGb7CMbSJj5NZVNTcAZjJ5Gd2Wlawnol6fb+kSSDU3mPZ+xK\n+lrKg4Eg4NO4dkdHZefV0+QFjTUHfGztiK7JOmkEmqpUHOuN4uqtbcRDOt/ae3xZJoKh6Tx3HRzn\nvddsXlFu/1uv3MiP9o3ynceO82tLoGm0oqgEeEoe7U8QMnyEdIX1LUE0RdARCTCZNokFfMQCOhnT\nZjprYzuyIu+wFnesjWDBkkop88AnSn+1yCx5iVYA8zmSI4bGsak8qUIRhMuVW9vRVYWQX8PvUwga\nGpbt0tMcqGQJyxdtNEVQKCWRWAtmnpNBre2/PWJU2EuW7fDkwDS2hKxpYVXUbUXFgVyOouyLh+iK\nBRlOZWkPe5LSPTH/DFYUUJkUTrdOsxTQNYVX7eriGw8PkCpYp6wGWovbHh1ESvjVC5cndmAuXLIx\nzo6uKF+49wg3XbT8rKilQlvEYGM8QCJn0xz0MZoq0ByUDEzZhAwNn6YSMTS640EKtosA2poMelsD\nM8aRuZLNr3U0kpjmCuAvgQ3MTExz1vIVa2lRawaaz5HsSuiOGbRYOseTOZI5m46IQU9TkHyXgy0h\npJ9g+VTMPH1ry8yzEOo5xurZ4Pf0aZU8qXc+M0pY90LpO6J+QoaPnpif3pYgrREvarq7yU8yb5Es\nFIkYOtef04FRmhxr1RnX6s5opfDq3T385/39/PCpEV6/hMFeriv55qMDXL6pZUaw30pACMFbr9zI\nB775OPcemuTKLa0r+vxTgem4pEwLX2ny8v6RxEMGZ3eEyRZdemJ+btzV7ZmPmoMk89aadgI3ikZK\n/nng/XiJaZwFzl1zmMsMNN8WLqhrNIdUJrMFTNupUEENn8LOzugsqufpNpi5Us5pGqv9PeXP+aID\nUiIE+DSFC/uaiYeMSuMv+xYUATee303atCvKpGUsJrbjhYDz18foawnynceOL+lEcP/hSQYSeT6w\ngjIW1XjVeV38zQ+e4Qv3HjltJoJjiSz3HZrE8KlkTZvze5toDun0xAL0tgTpbQlWTJr7hlKEDR/J\nvDVLVfR0RSN0haSU8gdSyjEp5WT5b9lLtgTIFW2OTmaZzhVLEX5OJb9uUNfqbuPaIgZnd0bx+xQ2\ntITY0hZBURT8uopPUyv5gk9nuPIE3dOVVOqkHsq5hEOGSl9rCEWBvpYQvfFQpf6qTW2uBMOnsqOr\naZafpPa8+Z77QoAQglfv7uH+w5MMJ/NLdt+vP3SMpoCPl53TuWT3XAwMTeWNl27gp/vHODx+eliP\nc0WHQtGhYHuMv22dUS7b1FJhD5XHi9q+40pOW3NQNRqZCH4mhPg7IcRlQogLyn/LXrJTRHn1eWg0\nzV0Hxnn46CSHxjIs5DcLlqhjV29tZ2dPEy6yYv8/3bd/ZZSziC20pS3X4b6hFI/1TyOkJOrX8dfk\num00ZmMxsR0vFLz6/B6k9PJQLAUS2SI/enqU1+zuWVXWzm9csgFdVfjSfUdXrQyLQVjXSOSK9E9k\nSWSLtIaMugP887UNN/Irykno91R9J1lmiYhTRXn1GQsYdEUDbO6I4PcpDWn8B/WZeYJPN/v/QlCE\naIjdUL2CPzyRQUpRCfpqND9rNdZqHMBqoq81xO7eGN9+7Di/dfWp5yn41t5Bio7LG1aZsdMWMbjx\n/G6++cggf3D9thWX3V4sbCk5b30TYUMnUyxiy/oDxfO1DS+4I5BSXlPnb01PAnBi5s5bNn5dxe9T\nCPjUSj7dXHFhs0R5O9ga9j8vtn/VmMs0Vo3q1U/QpxLSlVl5icv12Mj9FnPeCwmv2d3D/pE0zwyf\nmgivlJJvPDzA7t4Y2zojS1S6k8dbrugjbzn81yPHVrsoC6I9YhDx67hIIoZOxNDmHCeej224EdZQ\nB/AxoFtKeUNJYuIyKeXnl710p4B6jJ6yo+eMs7Ix1K5+gBkOszP1uDR4xc4uPnL7Pr7zi+Ns74qe\n9H0e7Z/i0FiGj//KziUs3cnjnO4mLj0rzn/e189br9i4Kik6G0Vr2M9NF6+vqA0fmZitsfV8RiNv\n5kvA/wLdpc8HOBFctqZRu6JfjJP0DDxUr37mcpidqcdTQ0vY4OqtbXzvF0O4p5Cf9Iv3HSXi13jl\nru6FT14hvPWKjRyfzvOjfaOrXZQF0Rr2s6OrCcOnvuDadyMTQauU8lZKWcVK0tML0kiFEJcIIe4T\nQtwjhPhUzbG/FEI8LoT4uRDi90+q5CeB56ujZ6Vxph6XHq/e3cNwssCDRxIndf3x6Tw/fGqEN1zc\nS2gNvY/rtnfQGw/yhXuOrHZRGsYLsX038guzQogWSmIzQohL8fIRLIR+4FopZUEI8VUhxE4p5ZNV\nx/9ASvnjxRf55PF8dfSsNM7U49Lj+u0dhHSV7zx2nMtOIlf1l+8/ipSS37xsw9IX7hRwOuYqeCG2\n70Z2BL8PfA/YJIS4Fy+z2HsXukhKOSKlLJQ+WszeRXxcCPFjIcT5iynwqeL56OhZDZypx6VFQFe5\nYWcXdzwxRLqwOC3HrGnz9QeP8UvndrKueWUjiRvB6/asI2xofPHe02dX8EJr342whvYCVwOXA78F\nnCOlfGL+q05ACLELaJNS7qv6+h+llBcC72ZmLuPq694phHhECPHI+Ph4o487gzM4bfGbl20gW3S4\n9ZHBRV335fv7SRVs3n7V2lR9KecquOOJYQYSudUuzhnUwZwTgRDiteU/4EZgG7AVeFXpuwUhhIgD\nnwHeVv29lDJR+vfgXNdKKT8npdwjpdzT1rYyMrpncAariV3rYuzZ0MyX7juC06DTOGPafO6u57h6\naxsX9DYvcwlPHu980VkoiuAzPz202kU5gzqYb0fwqnn+Xll9ohCiWQhxjhDiLCGEUvpOA24BPiCl\nHKk5P1r6t5XG/BRncAYvCLz1yo0MJPL86OmRhU8GvnjPEaZyFr/3ki3LXLJTQ2eTn9+4pJfb9g5y\ndCK72sU5gxrMOQhLKd8y34VCiCbgd4A3ADowDviBDiHEA8B+4CLgb0tStB8Efr2UwP7vhBDn4k1E\nf7IEv2MG5ko5t9CxM1j7OJn3dzq985fu6OCsthCfuPMA1+/omJd7f3w6zz///BAvO6eD3Wt4N1DG\nu1+8ia8/dIx//OlBPvn6xlyDZ/ryyuBUau82PMfxVVLK6eoDQogLgTcBf1ITeHY/gJTyt07hufNi\nPoXLM+qXpzdO5v2dbu9cUxX+6GXbeNcte/nmo4NzSkVIKbn5di+D7IdeuWMli3jSaI/4+c3L+viP\nuw/z2y/ezOb28Lznn+nLK4eTDvWTUl4vpfxK7SRQOvaolPL3ViP6eD6Fy4xpky86CAF5y5lxbCJT\nYN9wkolMYdY9ywqcjchSnMHSo1z/42lzzvc3F+q987X+Pl92TicX98X52PefYWi6virpNx4e4H+f\nHuX9L9m6JplCc+G3XnQWIV3jY99/ZsFz53t3tW1hPG2u6Xe61rEkU2iJGdTHzMQ131qKey8GuaLX\ncCbTBQYSOZoDPsKGxkAiS38iR8TQ2DeUomA7+DWVCzd42+mJTIH/emgA2/WURm+6eH02/ilEAAAg\nAElEQVRFQvnMymP5UL21h5nJvcvHquUsMnmLxwenKdg2EUNnR1eUsXRhXtNA+fryO9/RFWX/8NqW\nxxBC8Hev28UNn76b93xtL7e8/ZIZZbzn4AQf/u7TXLWllXesUabQXGgJG7z3us187Pv7+fmzY7x4\nW/uc5yoC7jowxmgqT0c0MOPdZfIW+4aTOBJUAZblEg74Ku8U1nay+LWGOWtoIWZQeaAXQnwB2AU8\nTSn6GC/4bMUmglwpofyBkTR5y+augxPEQwZSukzlitx1cBxV8fIKRw0fQvECXX4xMM22jgj9iRyJ\njElzyCBdsBhLm5WJoLwq8etqZVVypmGdOqonWMt2OD6dZzRtsq45wMvO6awM/qm8haEpdMeCDCRy\n7B9O40qJ7ivw432jNId0QiXp8Or3Up78NSEoOg5CQtFxGM+Yc6YpbdTmXDuBLQc2tIT4xOvO43e+\ntpc3/PuDfOTGc+iJBfjW3kE+8aMDnNUW4p/esBtlBfMRLxXefPlGvv7QAB+9Yx9XbG7FV+MHOTCS\n4sBYmmTO5H+fHqZgS/zaNBf1NRPQfQR8GtMFi4lMEelKhAJZy2ZDa7iSW7t/8oWlFXSqmK92XjXP\nseqB/lIp5YoZKWs7a65o89N9I/Qn8mQKFme1Ryg6DkXX5sHnpnjg8CQjqQLbO6IkckVSpo2hKaRy\nFum8ha6pbO+K8sCRBCFdRdcUbtjZVVlpKgIOjWVwpEQVorKLOIOTQ/n95YsOI6k8piU5PpXlp/sn\nMDQFR0riQR+KUAj4NECSKljkxzMMJnIcGkujqgpFy0VXBX1tYRRga2eEtgilhOJFPnfXc9iuJFuw\nUBSFlrCBaTko1M/FUG/nB7NXlbXnLSdu2NnFZ3/jAv7otid49T/fW/n+Jdvb+fvXnUcsqC9vAZYJ\nuqbwZy/fztu//Aifv+cI76qS3y5YDh/+7lOYjmRwKstE1otDzZjwwHOTRII6iWyRgmlzaDyLrqkU\nbYdN7eHKOwXmnOzPoD5OmjVUhfuFEDtqAsaWBeVBP5GzCemCPRtbmcoW+dmBcVQUBqaymI7DkfE8\nB0ezjKYK9LUEyZoOB8a8laQAFHzkLJvpnA3C4qy2ED2xAJ0xP0jJo0eniIdzhHSFrZ1RNreHCfg0\n8pbdUD6D5xOWkplRPYgOTeX49mPHcaVkOmvjSpfumJ+RVIGxtMlo0iRt2vg1hbO7IoAkV3QwbRdD\nERRsm/3DaSYyFoqQXL21rbIKfGYoiWm5bOmI8tTxaQK6SlfMj2W7NIcM1sWDjKVN2qtSjlb7luZb\nVdaet9z4pXO7uGxTKz95ZpTpnMUFG5o5/zSQaVgI121v56U7OvhkiR21qc1zHBcsh6l8kc5ogFR2\nZoT1gZE0QhXYNmRMC5+q0BrRyZgW6+NBdnRHKxN7/2T2BaUVdKpoqIaEEK8AzsGjhwIgpby59N8v\n400GI4AJCO+w3LXEZeXYZK4y6B9P5shZkqLjYDku0bCOTEiKlsuGuJ+mkME9B8cxiw4+RdAc0rEd\nF9uV+H0KWkFBUwWu9AqcK9pMZUwsV+JTVYQQDEzZrI+HCOgqrpQowkt3mSu+MFYYS+0fqR5EHz82\nje1IOpoCFJ0MRUuQNm2aAzqdUT8PHU7gIihaNutbg+xe10T/RJZYUMfwKSC9d1l0XIq2y1AyTzzk\npyVk0BrRcYH/v733DpPjKBO4f29PTpuTVlplr2U5SLLlKGPjSDpsbGw4gg+TjnCAOY7jCB93wBHu\n4DN3hAM+bA4bY/JhcMCAwQbnJNsKlpUs7WqlzXlyrO+P7h71jmZ3Z3dmZ3el+T3PPjvT011dXVXd\n/Va96eBgEI/Txjkr6/C6HPicGj6XLbvsNBiMs76V7PVZZwqQX6rMDUhWDqo9Dq49c1l5TlYmRIQv\nXnMaV3z9YT7xq+384n3nY9MEh01DE42hcILc5g3GU0RTCr/bTjiZwo+d8WgSp01jbWOApsDR1Kgn\nWqygYikkH8H3AC9wCXArcB3wtGWXH6Cbiu7gqI6g5EQSKY6MRkimMng8djJK4XbYqPbYqfe6GI8m\nqA+4OG91Aw/t7cfnsnPGsmr8Do2UUtT7XKQzGVqrXYhNo63Oy9mr6mj2u1jV6GdJjRun3c5gKMrA\neALd9UHhcdrYvLLO0EGMc3AwTOdQ+IRYd8yVfoudYlsfotVuO3abMB5N4Hc6eMsr2tA0jfamAIOh\nOCPRJFUuB6FEmnAszVA4zuomPxe11xOKp4nEU/SOx6j2OonG09R6nSRTaV4eCFHjcXLTZSfRH4qz\nos5Lvd+VfShYr6l7LMLj+4eoMpSM1kTkkF+qzJejocLsaAq4+bfXr+djv9jG9x8+wAdeuQaP08ab\nzlpGx1AYp5Zha9fRnMdtdV6OjMZw2jR8TgcXtTewqjGA2yHU+CYuk5lh0ysURiEtdYFS6gwR2a6U\n+ryI3Azcb/l9QCl19xzVD4CMUjzbMUw4nkJEQwSaAh5cdsHjsHPa0ipGokmGQ3Ecdo1L2htprfXS\nGHAxEIpTs70bu01DgFed1oLTbiPgsuNy2CZYrGQUeB0aTQEPGQVLazw0GssHHmcKh912Qq07ljoc\nr/UhuqbRx5HxKMPhBHU+Jxesbcwq6DM94zT6nNhsGi6Hi/NX19Na68HvsnP+mnr6g3HsIvzmhSME\nY0kCbgdrmwLs7gmiq6+EZXVe2luqJpzbxLymeDKDy65l+9RMRG4ymVRZeciUjms2LeVPL/Xxhxd7\nee8rVgGwtNZLjc+JXRN294XIKLCLcMm6Zg6NRBgJJ/C77Zy5vBa/x1lZ/ikBhbSeacgcEZFWYAhY\nYvn9eRH5CXAP+tIQUFrzUTMRyqqGAJedAnV+FyvqvLgcNqKJNAcHw7S3VNM9FqGtzsvKel/2Rq33\nuxgKxgknMvqaf3NV3ps4XyYu6wPgRIxRPhfheM2HaH8wxuYVdXl1L8vrvVyxvoWRaJJaj4P2lsCE\n/MjmC+NdFzqza/0ZBQ67xprqwJQvaus1maalk/Vp5YE/94gIX71uA06bht2mTejHUCzFpuX1oBQu\nh42zV9XzmjOWTNDvVJZ/SkMhrXeviNQAXwOeQxe5brX87kF/AVxp2VZS81Hr+m2N18mZy2snWHGY\nU3iPwzbhJQD6zbzlpMaCEqvnHpf7+4m47jhXD0O/y57VvXictgkPYa/TzqXrm6dt6wa/e4K/R6Ev\naus1bV5ZeZjMN9a+st7rzVUu3rCplWgiQ63HwfJ67wRBAI69TyvMDlFqajMYEXEppeLmZ3SFcczc\nVg4aGhrUypUry3W6oskoRSSeNhYpwOuyoYnMeJ/Z7FsIHR0dLJb2TGUUw+EEKAUi1BlLBrmUuo0K\nZTG15VyQ2+5up41IPEUslQEUbrsNv9tecF+c6O1ZarZu3aqUUtNGkCjkdfoEcCaA8fCPi8hz5jYR\nuR24yQw1ISK1wM1KqXfNtvK5rFy5kmeffbZUxc2aQk0p+4Mxnu8cyS57bFpRO2Ht2bqP22kjlkyz\nafmx+1j33dU9nl3LXt9aNem+hbB58+aytedsnLSs++3qGeOBF/tYXuejayTMhWsbWFbnPWa/UrdR\noZSzLeeLyfpmMBRjd2+QoVCc1Q36klxTlYu9vSFGwrrBRa3Pyflr6gvui8XYnkopnjgwxOP7h4gk\n0qxp8nHl+hYaA675rhrGs3papvIsbgGWAh4R2QRZa64qdCsikzOs8YaUUiPG/scVMzGlNJ3QzJAV\nZ6081gltJo5qi1U/UWibTbVfU8CFXRO6RsKk0xm6R6KMx1LH7LdY22ihM1nfmGFZosk0vWNREKHW\n46Ap4OLIcISukRSgWFrjOa77omcsyk0/e4GnDw5j1wSnXSOSSPP5u3fx1nOX809XthNwO+a7mtMy\nVQ+9CrgRWAZ83bJ9HPi05bsmIrVKqRHIJqM57nq+UFNKPShWnLY6D9VeJ6NRPWRF7lp7RkFbnQeU\nEE+nsvuYxzcFXNm10JnqJwZDsWPKmGvySY3TtZlZTw3dP8PjsBM1yhkKxekcjrCizsubz2nL7tc5\nFDb2T00o70TV4cw1phe4htAXjOJ321le52V3b5BoMs2axgCpTAabYX7rddppb6miMeAmo1R2XX8q\nyhGyYy7oGo7wxu8+Tjie4kvXnMa1m5bhdmjs6w/xw8c6uP2JDv74Yi/fu+Eszli2sJ0Ap/Isvh24\nXUTeqJT6vynKuBndoeyXxvfrgS+VsI4LgkIkTlN6iibSdA3rxlaHh6O4bRqDwfgECVYT6BqOEkuk\n6RmP4rLbeLk/xP6+EJomxwS/K1RpO1UAvbliMqlxqjaz1jOeTAGCy2HDrgkt1W7ueKIjew03Xd7O\n+iXVDIZi/PmlvklnWhUrn9JjWlZ1DIQZjMToGArjc9pZWuuldyxKKpNhMBgnk1E83zkCCBml2N8f\nYm2Tn1A8xeaVk/dLOUN2lJJQPMU7fvg0sWSaX33gAk5ZctRUub05wFeuPZ03bV7Gh37yPNd97wlu\nvn4Dr9/QOo81nppC7prHROQHQKtS6jUish443wwxrZT6kYg8C1xq7H9tOcJNlJtCJE5TAm6t8YKA\nz3jwmZLuQDCOx6kfn1GwtsmvK9UEajwuOoZDRJNpTllSTddIeELwu0LpD8aJJdLUV7kYCsVnVcZM\nmUzy9zrtrG+tOiacQ249Dw0laa1xcVJzgFgyTddIhFRGsbohwMHBIJ3DEdrqfNk2M/UqhYb7qCQw\nmT0ZBUtrPXr0VpcNu2YjmszQXO3m3NX1JNMZ1jT6WFLjYXdPEKddo6XaTVopPA7d8TPf7Nkac6qc\nITtKxZd/9xIHB8P85D3nTXgJWNm0vJZ7Pnwh779jKx/52fOE4qlJ80vMN4XcFT80/j5jfN8L/FxE\nfq6UCgEYD/5jHv4i4jf3OR6YTuK0SsAeh40VdV62HRrlYCZCJqNIptJZB5j1rVV4nDYQcDtsRJMp\nar1OhoIJukbC2ERomoWyKeCy0zMe5fBoBJsmBMow3Z5M8o8kUhPCOVglQ2s9M0pY3xpAKfA4bKyq\n9/GX3f0cHAxi04QVdd7seXSTU32/QpYSKmHEi8PvslPrdeCya6TSGUQUHrumL3mO60ugL/eHjRmw\nICjcThs2EaLJ1DGmwXBs5FmQsobsKJanDgzxk6cO8fcXreb8NfVT7lvnc/Kjd5/D+3+8lU/9egeR\nRJp3X7iqTDUtnELuiAal1C9E5FMASqmUiKSB34rIC8Bvga1KqTCAiKxGD0fxJuAW9ExmJwS5s4ZQ\nPJWVYHvHYqSUTPBiNfc9a0VtNrSB6Tk72/V9l8PGRe2NoAREd8SZayabLU2lI8it54a22uxDw+u0\nc9Pl7VkdQVudb8rzTEWpw2ScaJh+OO0tVfqD3WHH57LRH4zjtunhwaPJDPFkhlOWVDEcjtNW72XL\nmvrsmM5t79w+WdXgy/vCAMhkFN97+GXu3dbDinovn3zNOlbU+8p1+ceglOLL9+9mSbWbj13RXtAx\nboeN79+wmY/89Hn+/d5deBw23nruwpoZFHJHhEWkHt1JDBE5DxhTSl0mIq8F3gdsMZTESWAPcB/w\njtyk9ScCubMGTYTRSBKv04bbrk1r1aI7zBx1lJnJsoaZmMfjsOOwa2W1nsk3W/K77CRTGQ4MhvDm\nSPDmb33BOM0BFz6XbcJST1udL/sCyG2DmTzIK9ZExeN12llRf7TddOe9OIOhOKPRJHYNNKfGcDiO\nJoLPOXU/aaLnmYin0ngctmwYl3x89rc7ufOpQ2xeUcuj+wd543cf564PbqGtbn6yst2/s5dtXaN8\n9bozcM9AyHLaNb75lk28745n+cxvduBz2bh649I5rOnMKOSu+BhwN7BGRB4DGtEDz6GU+h3wu5me\nVETOBf4LPUjdM0qpf5xpGYsHhVLgdmhsskj+QFaxbCrW9KmxZB/i61ursksr0y1rWKfboFjV4Jvy\nBisf+vUbckSWoVCch/cNEk/pFicI1PvdJc9NW7EmKi2RRIrH9g2y4/AoncNRqt02/G4H65YEGI8l\n8di1KQMzmsuFLrtGPJnhrBW1k/bJn3b1caexBPPp157C/v4Q137nMf7pl9v42XvPK3tSHqUU3/nL\nflY3+njjLKLBOu0a3337Wdz4w6f52C+24XHYuPLUljmo6cyZ1uNMKfUccDFwAbr0f6pSanuR5+0E\nLlVKXQg0icjpRZY3J5j5UXUzx5nnQw3F9UB1axr9OOw2BoMJBkPxrISbUbonpqlYCycyhBOpbL7l\n/uDRbFq5+Zfzncu6bzinrqXO01tIeaF4ikhSzysbSWUm1L9zOEI6k2FFnY9EOkPPeHzCdVpz0xba\nBhVKhxm6pXMozGAolv08EIwTTujj2uey4XU5SKsMNR4XTrstu/yZ21e5/VlnjtN4Ou/5MxnFV+5/\niZOa/Hz8ypMB3VDgM687hacPDnPfjp6ytIOVpw8Os/PIOO+5cDW2Wb6E3A4bt77jbE5bWs2Hfvo8\nWzuHS1zL2VFIGGo38EHgQnSx7hER+Z5S6tgs7wWSs2SUBPKPhnnEagpqSuxmSOpCpUrrskQomuT+\nzmE0TcOuCVdtbEUzEm+bijWfU8OqOGsKuBgMxgta1jDP1T0aYX+/rp83TVaBkproFSqlx5NpHtk7\nQDqjsGnCmZaEKk1+F6ORJEOhEQDqvI7sdWrCpMrEmS7tVJTFM8eU+nf3jpNMZ0ilFXabnitgZYMP\nuwipdJp4Ko0mdhw23YPe67ABasrsb8lUhngyxY4jY6AUPmf+paE/vNjLywNhvvWWTTjtR+XV689q\n45ZHDvI/D+3ndacvKeus4NZHD1LrdXDtmcUt6fhddn5449lc+53HeM/tz/LrD25hVcP86T2gsKWh\nHwFB4FvG97cCd6D7CxSFkfS+MZ+5qYj8PfD3AMuXl1+xkk9iH43Eee7QCOtaAtMqck2pf1WDj2A8\nhdOmoQ2Gs6ESgvFUXmWxeW5zGWOqoGi5a+ebV9bRMRQGdBNWUzkKE5OslKJtch3ArHUz8wUnUmnq\n/S4CLgehRJKgRUKs8Tm5auNS4ukMbrvGOavqswrDqZSJM32IV5TFMycUTxFOpHDZbYQTKXpGo1R5\nnNT5HIxEEpyzqo7T22r0MeC0ZfU71vGrydEZQW4f1Pu9pAyz1HA8fx7w25/oYHmdl9eevmTCdk0T\nPvjKNXzsF9t4eN8Arzy5qSxt0jMW5U8v9fGhS9bOSDcwGXU+J7e98xyu/e7jvPOHT/PrD26hzjd/\nqUcLuSNOy8lJ/JCITHhwi4gNaLaWp5Q6NFWhhnL52+jWRceglPo+8H2AzZs3lz1BpClhmxJ7XzDC\nUweGWVLlYduh0SkdtfLNJpKpDJlMZoJp6GQKtUJi308m6a6s9+WdRZQyq9ZUITS6hsN84097SWUU\nsaQ+0fM4bMeYsvpddlqq3dn650qF1voWo+uoKItnjt9lxy7Cnr5xQvEUBwfC+Nx24ok056+tZ0mV\nmy0nNU7ZJ9axub61akIfLK/36i+beDpvnxweifDkgWE+dkV73iWY152xhC/e9xI/f6arbC+C+7b3\noBSz0g1MxsoGH7f83WbeesuTvOf2Z/jJe88ryUtmNhRyVzwnIucppZ6ErKI3GxVKRD4M/BvQx9EM\nZQqYNFWliNiBHwMfX6iWRVYl41kratndG2RJVZTVTQH29I3x5IEhzltdn42JrsnRlIf9wTi9YzHi\n6QzD4TjxpBeXQ+OSdc2EEilW1Hlp8LtnbBFkPU+uI47ViSufcrSUWbUyCpbVeQABoz4mncMRYqkM\nS6u9HBwMsbLBS1u9D7ddw+WwTQh/Ue1x8GL3GKe2VgN64DizzqsafFnz0WIk+IqyeOYMheIMhRNU\nuRysqPOilKLB56J3LMbJLVU47DYODUWyKVuX1+sWPGYbDwTjDIcTWYk/HE9nTT7Nl/pUM927njsC\n6Elr8uGy27hm01J+9EQHQ6E49f65D+52z7ZuzlhWzcoSL+GctaKW/37zRj5w53N89jc7+ep1ZyBl\niJqbSyF3xVnA4yJiSvjLgT0isgP9ge8FTlZKDc3gvNcDZwNfNS76U0qpJ2ZwfFmwSuPrWmDboVH2\n9I2x87C+vrmvN8hJTQEcdo39/SHa6jx0DUep9tr5/Y5evA47R8aigMLvcpBMZfB7HBwcDONx2mZs\nEZTPwiifpJtvFlHK8Aua6KEzzIB5msWppsnvYjScYCgYJ53JkEi7GQknsIkwGk7wwC49RMRIOM6u\nniCawD0v9PA3G5ewtMaLJrCqwcfdL3STyqhpZ1+FUAk9UThdw2H+8/6X2Nune7mvbPAST2awiUYi\nnUFQhKIJ7j44RM9oFE0TLlhdR5XHhcOukUyliSczdI1E6RqJsLLex97ecRx2W3Z2B1P3yfNdo5y3\num5KE9E3bW7jB48e5J5t3dy4ZW4dtDqHwmw7PMZnXnvKnJT/mtOX8JFL1/LNB/ezcXkNbzt3xZyc\nZyoKuTtePc3vtwFjMzmpUuqnwE9ncsxsKGVogQa/mzef08aTB4ZAKU5uqWF37xjDkQQrGnyklUIh\n+n8l1HodLKv1YbPDysYATptGyiLB9wfjRBNp3E4b0WT+dVKTfPqKjGEiOtu182IwA+Ypw5PUOiOo\n8Tm5alMr8aSeWN7vsrGkyks0maI/FCeVUSyv87Gvb5xwLEX7kgAdg2EOj0Q5Y2ktQ2E92Jy532xD\nbVQoHOt90jkcIZRIU+/T8zwrBWevrKW9pZpEKs2pS6uJJdJsPzJGY8BNOJGidzyBzWZjTXWAlwdC\ngOK8VfUcGY2ytNbDeDQ1Ix3ND96xmfHo1NZhJ7cEaG/287udvXP+IrhnWzegL0nNFTdd3s72I2N8\n7u4XOWVJFWcunzwa8Vww7dNDKdWZb7uIfMz4eAD4i4jcx8RUlV/Pd1y5mAtrkQa/m/NW19M5GKFr\nJIzbrlHndRIz9AiCLiG7nPoyiBKFz2mnyuPAa59oURFw2WcchtpqYeSZxNqiHJgB88y6X7B2Yl1b\nqjwTLH4y6FnIzJAbXSNhqj0OUpkML3WPAUJzwJVtG+t+sw21UaEwcu+Tlio3fqeN3tEo4USapmpX\n1g+m1utgZb2PSEL3MD40EkYToaXKic9pZygcz1q+hRMp6nwOltd5p0wHmg8Rodo7fejm15y2hG8+\nuI/+YGxOc0/cs62Hs1fW0lrjmbNz2DThv9+8kdd/+1H+4c7n+P1NFxXUBqWimKdIwPh/yPhzGn+Q\n6z00D8yVtYg5MzDXuaOJNJ3DEa5Y30yNz8kFa3WJeePSGvpDcZr8Lmp8zmMsgszwE/ly9uZiDd62\nfkkVLkf5ZwFWzOBv+eqeL9CcdVZmDSm9tsnPYDBBQ8DJJeuaJ8xurG3sddqz+gM4Np90hdljWoC5\nnTZGokkaAi4+clk7Ww8N0z8W58wVdYxE4vhcdtYZuaO9Tjs3XLCCQ0ORrI7AGj49t8/nKh3o685Y\nwjf+vI8/vNjHDefNzXLKnt4ge/qCfOHqU+ekfCs1XifffsuZvPG7j/PZ3+7km28pX1qXWfeKUurz\nACJyvVLql9bfRKRo09JimUtrETNX7mAoll3LtoZ8jiRS7O7R1/97x2Mssyg8rTfCZDl7c5kQvE3i\n824LP1W+4WMDzdVNkNasbRdJZHA6bEQSGXwu24TlH3O/fAHKTM/r+W6H4wHTAiyWTNMzFkWUosbr\n5Ir1LezqHieSSNE1rIdJ39U9ng0cmJsveqo+nysdzUlNftY0+rh/R8+cvQju3d6NJvrsoxxsaKvh\npstO4uYH9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fXHf59Uex2cv6ae+7b38IlXnZw3Dlo+7tvRQzqjuGbTwl0WsvKeV6zihh88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\nfrpt5UZEeoE/ApcCJymlosb2o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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1176166a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "from pandas.tools.plotting import scatter_matrix\n",
    "df = pd.DataFrame(iris.data, columns=iris.feature_names)\n",
    "pltfig = scatter_matrix(df, alpha=0.2,  diagonal='kde')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## K-Nearest Neighbour Classfication (KNN)\n",
    "Is one of the simplest classifiers working on nominal targets $y$. \n",
    "\n",
    "1. **The fitting step** consists of storing every data point `X` and its associated target value `y`. It potentially involves creating index structures for fast lookup.\n",
    "2. **The predicting step** consists of finding the $k$ closest data points in $X$ and selecting the most common target $y$ in those data points.  \n",
    "\n",
    "The following figure shows the decision boundary of the IRIS data on the first two dimensions (original source is available under http://scikit-learn.org/stable/auto_examples/neighbors/plot_classification.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Module created for script run in IPython\n"
     ]
    },
    {
     "data": {
      "image/png": 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n84NTB7BrhwFJ3/YxY6C42C3IGctZZ8G//x1fTvfu/s2ke886nh9+By8OvZfK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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e5a7898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IYSWnHLIrN739Op/8exC1W0vY5YD5XHxSH/Zo2yfh2z56NBQVwfbt8cdOOw3+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\nbGEYo1liHapGq2LjRiAvftVJNETZ2vZ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11eaa3b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1173dd588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run scripts/plot_classification.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted flower classes:\t [1 2 1 0 0 0 2 1 2 0]\n",
      "True flower classes     :\t [1 1 1 0 0 0 2 1 2 0]\n",
      "correct classifciation? :\t [ True False  True  True  True  True  True  True  True  True]\n",
      "classifc. error (in %)  :\t 90.0\n"
     ]
    }
   ],
   "source": [
    "# random split into train & test data\n",
    "np.random.seed(0)\n",
    "indices = np.random.permutation(len(iris.data))\n",
    "iris_X_train = iris.data[indices[:-10]]\n",
    "iris_y_train = iris.target[indices[:-10]]\n",
    "iris_X_test  = iris.data[indices[-10:]]\n",
    "iris_y_test  = iris.target[indices[-10:]]\n",
    "# Create and fit a nearest-neighbor classifier\n",
    "from sklearn.neighbors import KNeighborsClassifier\n",
    "knn = KNeighborsClassifier()\n",
    "knn.fit(iris_X_train, iris_y_train)  \n",
    "print (\"Predicted flower classes:\\t\", knn.predict(iris_X_test))\n",
    "print (\"True flower classes     :\\t\", iris_y_test)\n",
    "print (\"correct classifciation? :\\t\", \\\n",
    "        knn.predict(iris_X_test) == iris_y_test)\n",
    "print (\"classifc. error (in %)  :\\t\", \\\n",
    "        np.sum(knn.predict(iris_X_test) == iris_y_test)\\\n",
    "        *100.0/len(iris_y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Logistic Regression\n",
    "Logistic Regressions applies a non-linear transformation to the linear regression output in order to bring the output in the range $[0:1]$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rWytPjJvHmIOYlRPLnNw4ZufGkR5zEQ+kDSEV7opyAR6Ph26XkzCZQpPXit9m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\nvRAl7gqFQtELUeKuUCgUvZD/D4N34j7LgsdfAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11b9d27f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def sigmoid(x,beta,offset = 0.0):\n",
    "    return 1/(1+np.exp(-beta*x + offset))\n",
    "\n",
    "x = np.arange(-10, 10,0.1)\n",
    "for beta in np.arange(0.1,3.0,0.4):\n",
    "    plt.plot(x, sigmoid (x, beta))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted flower classes:\t [1 2 1 0 0 0 2 1 2 0]\n",
      "True flower classes     :\t [1 1 1 0 0 0 2 1 2 0]\n",
      "correct classifciation? :\t [ True False  True  True  True  True  True  True  True  True]\n",
      "classifc. error (in %)  :\t 90.0\n"
     ]
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "logistic = linear_model.LogisticRegression(C=1e5)\n",
    "logistic.fit(iris_X_train, iris_y_train)\n",
    "\n",
    "print (\"Predicted flower classes:\\t\", logistic.predict(iris_X_test))\n",
    "print (\"True flower classes     :\\t\", iris_y_test)\n",
    "print (\"correct classifciation? :\\t\", logistic.predict(iris_X_test) \n",
    "                                     == iris_y_test)\n",
    "print (\"classifc. error (in %)  :\\t\", \\\n",
    "      np.sum(logistic.predict(iris_X_test) == iris_y_test)*100.0\\\n",
    "      /len(iris_y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Multiclass, Multilabel Classification\n",
    "\n",
    "- **Multiclass-Classifier:** A classifier is capable to select from more than one class, i.e. a flower can be assigned to seritosa, vertigo and virsicolor\n",
    "- **Multilabel-Classifier:** An example is assigned to one or more classes\n",
    "\n",
    "Our original regression problem only predicted one variable ($y$), which translates into a binary classification model, i.e. an example is assigned to a class or not.\n",
    "\n",
    "If possible, Scikit learn automatically extends the estimators to multiclass-labels, according to the following strategies. \n",
    "\n",
    "Multiclass problems can be decomposed into binary classification problems:\n",
    "\n",
    "- \"One vs. All\" approach: One classifier per class trained against all other classes\n",
    "- \"One vs. One\" approach: There are $k$ classifiers for a class (assuming we have $k$ classes). An example is assigned to the class that has won most often. \n",
    "\n",
    "See the [sklearn documentation](http://scikit-learn.org/stable/modules/multiclass.html) for details."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### One vs. All Decision Surfaces for the Logistic Regression on the IRIS Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Module created for script run in IPython\n"
     ]
    },
    {
     "data": {
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6N+HhFakOR6UAHwWzn7iVEc8tdoj/ZKEemygyqkWAw9AaF6BgaII/61LVPNTJ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\nP6XhV8pPafiV8lMafqX81P8BR3/a2mee8/UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11c1221d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x115762eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run scripts/plot_iris_logistic.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Support Vector Machines\n",
    "Support Vector Machines are linear classifiers that find very robust classifiers. In particular, they maximize the margin between the decision boundary and the positive/negative examples.\n",
    "\n",
    "This decision boundary is described by a weighted combination of a set of border examples, the so called Support Vectors.\n",
    "\n",
    "SVMs can be extended to non-linear classifiers using so called Kernel Methods (out of scope here)\n",
    "\n",
    "<p>\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "Support Vector Machines are usually a very good choice for classification tasks due to their robustnes against irrelevant features and noisy examples, especially in high-dimensional input spaces.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pQxZ0CeNany/MotVaUWhji1GlotDGFoPWiiuffsm1Pl/8v/fcvHiWQ1s3MvaD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\nwGWChJ8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x121b396a0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sCcREhPF6JSc+qu+JvVXRVTQ9vraWbASwERDiHmaM5bQtJUkSR4OTWHExCr1J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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x121b397b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12183b198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%run scripts/plot_svm_margin.py "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted flower classes:\t [1 2 1 0 0 0 2 1 2 0]\n",
      "True flower classes     :\t [1 1 1 0 0 0 2 1 2 0]\n",
      "correct classifciation? :\t [ True False  True  True  True  True  True  True  True  True]\n",
      "classifc. error (in %)  :\t 90.0\n"
     ]
    }
   ],
   "source": [
    "from sklearn import svm\n",
    "svc = svm.SVC(kernel='linear')\n",
    "svc.fit(iris_X_train, iris_y_train)  \n",
    "\n",
    "print (\"Predicted flower classes:\\t\", svc.predict(iris_X_test))\n",
    "print (\"True flower classes     :\\t\", iris_y_test)\n",
    "print (\"correct classifciation? :\\t\", svc.predict(iris_X_test) == iris_y_test)\n",
    "print (\"classifc. error (in %)  :\\t\", \\\n",
    "      np.sum(svc.predict(iris_X_test) == iris_y_test)*100.0\\\n",
    "      /len(iris_y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Model Selection and Performance Evaluation\n",
    "**What is a good estimator?** \n",
    "<div class= \"alert alert-warning\">\n",
    "Model Selection refers to the process of tuning parameters and hyper-parameters in order to find a good machine learning estimator. \n",
    "</div>\n",
    "\n",
    "It requires the \n",
    "\n",
    "- Selection of an error measure\n",
    "- Definition of a test procedure that measures the generalisation performance over unseen examples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Error Measures\n",
    "#### Accuracy\n",
    "The most basic measure for a binary classification task is the accuracy, i.e.\n",
    "\n",
    "$$\n",
    " accuracy =\\frac{\\sum_{x_i}y_i == h(x_i)}{|X|}\n",
    "$$\n",
    "\n",
    "where $h(x_i)$ is the estimator for example $x_i$ and $y_i$ is the true label of $x_i$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "`sklearn` provides a `score` method that calculates this error measure"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.90000000000000002"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "svc.score(iris_X_test,iris_y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "The accuracy is often not an ideal measure, due to several reasons\n",
    "\n",
    "- For unbalanced data sets, i.e. more negative (positive) examples than positive (negative) examples, it does not represent the real performance of an estimator.\n",
    "- For multilabel data, it is unclear how to evaluate the equality of the estimator and the true label\n",
    "- It does not provide any insights on whether the estimator makes errors du to accepting too many examples to a concept, or rejecting too many of them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Precision and Recall\n",
    "Precision and Recall are two measures coming from Information Retrieval, which give insights on the quality of error. They are build on the concept of a contingence table. \n",
    "\n",
    "**Precision** defines the **accuracy** of an estimator **wrt. a certain classification decision**\n",
    "\n",
    "**Recall** defines the **completeness** of an estimator **wrt. a certain classification decision**\n",
    "\n",
    "To illustrate that we introduce the concept of a contingence table. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Contigence Table\n",
    "**Formal definitions**\n",
    "\n",
    "- estimator $h(x)$\n",
    "- examples $X={<x_1,Y_1>,\\ldots,<x_n,Y_n>}$, with $Y_n \\subset Y$ and $Y$ being the **set of possible classes** an example \n",
    "\n",
    "For every class $a\\in Y$ we define the contingency table as:\n",
    "\n",
    "|Contingency Table for Class $a$| $y_i == a$ | $y_i \\neq a$|\n",
    "|---|---|---|\n",
    "|$h(x_i)==a$|True Positive (TP)|False Positive (FP)|\n",
    "|$h(x_i)\\neq a$|False Negative (FN)|True Negative (TN)|\n",
    "\n",
    "- `{False|True}` reflects whether the outcome was correct or not\n",
    "- `{Positive|Negative}` reflects whether the decision was to assign it to $a$ (positive) or not (negative)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "\n",
    "**Precision** now estimates the probability that an assignment made by $h$ is correct:\n",
    "\n",
    "$$\n",
    "Precision_a = \\frac{TP_a}{TP_a+FP_a}\n",
    "$$\n",
    "\n",
    "**Recall** now estimates the probability that $h$ has found all correct assignments\n",
    "\n",
    "$$\n",
    "Recall_a = \\frac{TP_a}{TP_a+FN_a}\n",
    "$$\n",
    "\n",
    "**F1** defines a combined measure, which is the harmonic mean between Precision and Recall:\n",
    "\n",
    "$$\n",
    "F1_a = \\frac{2*Precision_a*Recall_a}{Precision_a + Recall_a}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Microaveraging vs. Macroaveraging\n",
    "\n",
    "Precision and Recall define the quality estimators with respect to a specific class $a$.\n",
    "\n",
    "Given multiple classes $a\\in Y$, there are two ways for generating a single estimator:\n",
    "\n",
    "- **Microaveraging** sums over all single decisions, i.e. \n",
    "$$\n",
    "Precision^\\mu = \\frac{\\sum_{a\\in Y}TP_a}{\\sum_{a\\in Y}TP_a+\\sum_{a\\in Y}FP_a}\n",
    "$$\n",
    "- **Macroaveraging** sums over all class estimators, i.e.\n",
    "\n",
    "$$\n",
    "Precision^\\nu = \\frac{1}{|Y|}\\sum_{a\\in Y}Precision_a\n",
    "$$\n",
    "\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "Note that in the case of microaveraging in a single label classification:\n",
    "$Precision^\\mu==Recall^\\mu== Accuracy$.\n",
    "\n",
    "The reason is, that every FN becomes a FP in another class and hence the sum of FN and FP is the same.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Further details can be found under [1] and [2]\n",
    "\n",
    "[1] http://scikit-learn.org/stable/tutorial/statistical_inference/model_selection.html\n",
    "\n",
    "[2] http://scikit-learn.org/stable/auto_examples/plot_precision_recall.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Test Procedure and Parameter Estimation\n",
    "In the examples above we have always used a fraction of the example for the training and the remaining examples for testing.\n",
    "\n",
    "- Why?\n",
    "- What is the impact of a random split?\n",
    "- Can we do better?\n",
    "\n",
    "Note that we want to generalize over our given data. So we need to split the data into a training and a test set to get an unbiased estimator of the model quality on **unseen examples**. \n",
    "\n",
    "A **random split** can be very bad or very good. So we would need more random splits to avoid such a bias.\n",
    "\n",
    "A better, more efficient method is called **cross-validation**.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### k-folded Cross Validation\n",
    "Given our examples $X$, we split them into $k-folds$ of approximate equal size. \n",
    "\n",
    "1. for every fold $i$ in $k we\n",
    "\n",
    "    1. Fit our model on all but the examples in the $k^{th}$ fold\n",
    "    2. Estimate the quality of our model on the examples from the  $k^{th}$ fold\n",
    "    \n",
    "2. Average the obtained quality indicators (e.g. precision/recall) over al the $k-folds$\n",
    "\n",
    "\n",
    "<p>\n",
    "\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "When averaging over quality indicators like accuracy, always investigate the standard deviation in addition to the average value. The standard deviation tells you how robust your estimated quality indicator is wrt. different runs.\n",
    "</div>\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: [2 3 4 5] | test: [0 1]\n",
      "Train: [0 1 4 5] | test: [2 3]\n",
      "Train: [0 1 2 3] | test: [4 5]\n"
     ]
    }
   ],
   "source": [
    "#sklearn provides cv functionality as generator function\n",
    "from sklearn import cross_validation\n",
    "k_fold = cross_validation.KFold(n=6, n_folds=3)\n",
    "for train_indices, test_indices in k_fold:\n",
    "     print('Train: %s | test: %s' % (train_indices, test_indices))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Score: 1.000000\n",
      "Score: 1.000000\n",
      "Score: 1.000000\n",
      "Score: 0.947368\n",
      "Score: 0.947368\n",
      "Score: 0.947368\n",
      "Score: 0.944444\n",
      "Score: 0.888889\n",
      "Average model accuracy 0.959430 +/- 0.036357\n"
     ]
    }
   ],
   "source": [
    "k_fold = cross_validation.KFold(n=iris.data.shape[0], n_folds=8)\n",
    "\n",
    "scores = []\n",
    "for train_indices, test_indices in k_fold:\n",
    "     logistic = linear_model.LogisticRegression(C=1e5)\n",
    "     logistic.fit(iris.data[train_indices], iris.target[train_indices])  \n",
    "     scores.append(\n",
    "                  logistic.score(iris.data[test_indices], \n",
    "                                 iris.target[test_indices])\n",
    "                  )\n",
    "     print ('Score: %f' % (scores[-1]))\n",
    "\n",
    "print (\"Average model accuracy %f +/- %f\" % (np.mean(scores),np.std(scores)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<div class=\"alert alert-success\">\n",
    "Questions:\n",
    "</div>\n",
    "\n",
    "- Run the above code with $n=3$. What is wrong and why?\n",
    "- What is the highest possible $k$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Text Classification"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Naive Bayes\n",
    "#### Data Set\n",
    "The 20 Newsgroups data set is a collection of approximately 20,000 newsgroup documents, partitioned (nearly) evenly across 20 different newsgroups. The data is organized into 20 different newsgroups, each corresponding to a different topic. Some of the newsgroups are very closely related to each other (e.g. comp.sys.ibm.pc.hardware / comp.sys.mac.hardware), while others are highly unrelated (e.g misc.forsale / soc.religion.christian). Here is a list of the 20 newsgroups, partitioned (more or less) according to subject matter:\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "<table border=1>\n",
    "<tr>\n",
    "<td>comp.graphics<br>comp.os.ms-windows.misc<br>comp.sys.ibm.pc.hardware<br>comp.sys.mac.hardware<br>comp.windows.x</td>\n",
    "<td>rec.autos<br>rec.motorcycles<br>rec.sport.baseball<br>rec.sport.hockey</td>\n",
    "<td>sci.crypt<br>sci.electronics<br>sci.med<br>sci.space</td>\n",
    "</tr><tr>\n",
    "<td>misc.forsale</td>\n",
    "<td>talk.politics.misc<br>talk.politics.guns<br>talk.politics.mideast</td>\n",
    "<td>talk.religion.misc<br>alt.atheism<br>soc.religion.christian</td>\n",
    "</tr>\n",
    "</table>\n",
    "\n",
    "The \"bydate\"-option is sorted by date into training(60%) and test(40%) sets, does not include cross-posts (duplicates) and does not include newsgroup-identifying headers (Xref, Newsgroups, Path, Followup-To, Date). \n",
    "\n",
    "<div class=\"alert alert-success\">\n",
    "Implement your own naive bayes classifier and apply it to the 20newsgroups dataset.  \n",
    "</div>\n",
    "* Download the dataset from http://qwone.com/~jason/20Newsgroups/  Take the \"byDate\"-option.\n",
    "* Read the files and tokenize the text to obtain a \"bag of words\"\n",
    "* Implement the naive bayes classifier (pseudocode is given below)\n",
    "* Evaluate your classfier on the training/test set. Which accuracy can you achieve?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Naive Bayes Pseudocode\n",
    "#### TrainMultiNomialNB($\\mathbb C$,$\\mathbb D$)  \n",
    "$V \\leftarrow extractVocabulary(\\mathbb D)$  \n",
    "$N \\leftarrow countDocs(\\mathbb D)$    \n",
    "for $c \\in \\mathbb C$:  \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;$N_c \\leftarrow countDocsInClass(\\mathbb D, c)$  \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;$prior[c] \\leftarrow \\frac{N_c}{N}$  \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;$text_c \\leftarrow concatenateTextOfAllDocsInClass(\\mathbb D, c)$   \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;for $t \\in V$:  \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$T_{ct} \\leftarrow countTokensOfTerm(text_c,t)$  \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;for $t \\in V$:  \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$condprob[t][c] \\leftarrow \\frac{T_{ct} + 1}{\\sum_{t'}(T_{ct'} + 1)}$  \n",
    "return $V,prior,condprob$\n",
    "\n",
    "#### ApplyMultinomialNB($\\mathbb C,V,prior,condprob,d$)\n",
    "$W \\leftarrow extractTokensFromDoc(V,d)$   \n",
    "for $c \\in \\mathbb C$:  \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;$score[c] \\leftarrow log(prior[c])$  \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;for $t \\in W$:  \n",
    "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;$score[c] += log(condprob[t][c])$  \n",
    "return $argmax_{c \\in \\mathbb C} score[c]$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "** Some snippets that might be useful for the implementation: **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['This', 'is', 'test', 'string']"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# tokenization\n",
    "import re\n",
    "def tokenize(doc):\n",
    "    return re.findall(r'\\b\\w\\w+\\b',doc) # return all words with #characters > 1\n",
    "\n",
    "tokenize(\"This is a test string.\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alt.atheism\n",
      "comp.graphics\n",
      "comp.os.ms-windows.misc\n",
      "comp.sys.ibm.pc.hardware\n",
      "comp.sys.mac.hardware\n",
      "comp.windows.x\n",
      "misc.forsale\n",
      "rec.autos\n",
      "rec.motorcycles\n",
      "rec.sport.baseball\n",
      "rec.sport.hockey\n",
      "sci.crypt\n",
      "sci.electronics\n",
      "sci.med\n",
      "sci.space\n",
      "soc.religion.christian\n",
      "talk.politics.guns\n",
      "talk.politics.mideast\n",
      "talk.politics.misc\n",
      "talk.religion.misc\n"
     ]
    }
   ],
   "source": [
    "# list files (or directories)\n",
    "import os\n",
    "for dir in os.listdir('./data/20news-bydate-train/'):\n",
    "    print(dir)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  \"# Supervised Learning\\n\",\n",
      "\n",
      "  \"# Supervised Learning\\n\",\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import codecs\n",
    "# simple file reading\n",
    "with open('./5-Bayes-Learning.ipynb') as f:\n",
    "    doc = f.read()\n",
    "    print(doc[130:159])\n",
    "    \n",
    "# codecs can help if you run into encoding problems\n",
    "with codecs.open('./5-Bayes-Learning.ipynb', encoding='latin1') as f:\n",
    "    doc = f.read()\n",
    "    print(doc[130:159])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['From: mathew <mathew@mantis.co.uk>\\n',\n",
      " 'Subject: Alt.Atheism FAQ: Atheist Resources\\n',\n",
      " 'Summary: Books, addresses, music -- anything related to atheism\\n',\n",
      " 'Keywords: FAQ, atheism, books, music, fiction, addresses, contacts\\n',\n",
      " 'Expires: Thu, 29 Apr 1993 11:57:19 GMT\\n',\n",
      " 'Distribution: world\\n',\n",
      " 'Organization: Mantis Consultants, Cambridge. UK.\\n',\n",
      " 'Supersedes: <19930301143317@mantis.co.uk>\\n',\n",
      " 'Lines: 290\\n',\n",
      " '\\n',\n",
      " 'Archive-name: atheism/resources\\n',\n",
      " 'Alt-atheism-archive-name: resources\\n',\n",
      " 'Last-modified: 11 December 1992\\n',\n",
      " 'Version: 1.0\\n',\n",
      " '\\n',\n",
      " '                              Atheist Resources\\n',\n",
      " '\\n',\n",
      " '                      Addresses of Atheist Organizations\\n',\n",
      " '\\n',\n",
      " '                                     USA\\n',\n",
      " '\\n',\n",
      " 'FREEDOM FROM RELIGION FOUNDATION\\n',\n",
      " '\\n',\n",
      " 'Darwin fish bumper stickers and assorted other atheist paraphernalia are\\n',\n",
      " 'available from the Freedom From Religion Foundation in the US.\\n',\n",
      " '\\n',\n",
      " 'Write to:  FFRF, P.O. Box 750, Madison, WI 53701.\\n',\n",
      " 'Telephone: (608) 256-8900\\n',\n",
      " '\\n',\n",
      " 'EVOLUTION DESIGNS\\n',\n",
      " '\\n',\n",
      " 'Evolution Designs sell the \"Darwin fish\".  It\\'s a fish symbol, like the '\n",
      " 'ones\\n',\n",
      " 'Christians stick on their cars, but with feet and the word \"Darwin\" '\n",
      " 'written\\n',\n",
      " 'inside.  The deluxe moulded 3D plastic fish is $4.95 postpaid in the US.\\n',\n",
      " '\\n',\n",
      " 'Write to:  Evolution Designs, 7119 Laurel Canyon #4, North Hollywood,\\n',\n",
      " '           CA 91605.\\n',\n",
      " '\\n',\n",
      " 'People in the San Francisco Bay area can get Darwin Fish from Lynn Gold --\\n',\n",
      " 'try mailing <figmo@netcom.com>.  For net people who go to Lynn directly, '\n",
      " 'the\\n',\n",
      " 'price is $4.95 per fish.\\n',\n",
      " '\\n',\n",
      " 'AMERICAN ATHEIST PRESS\\n',\n",
      " '\\n',\n",
      " 'AAP publish various atheist books -- critiques of the Bible, lists of\\n',\n",
      " 'Biblical contradictions, and so on.  One such book is:\\n',\n",
      " '\\n',\n",
      " '\"The Bible Handbook\" by W.P. Ball and G.W. Foote.  American Atheist Press.\\n',\n",
      " '372 pp.  ISBN 0-910309-26-4, 2nd edition, 1986.  Bible contradictions,\\n',\n",
      " 'absurdities, atrocities, immoralities... contains Ball, Foote: \"The Bible\\n',\n",
      " 'Contradicts Itself\", AAP.  Based on the King James version of the Bible.\\n',\n",
      " '\\n',\n",
      " 'Write to:  American Atheist Press, P.O. Box 140195, Austin, TX 78714-0195.\\n',\n",
      " '      or:  7215 Cameron Road, Austin, TX 78752-2973.\\n',\n",
      " 'Telephone: (512) 458-1244\\n',\n",
      " 'Fax:       (512) 467-9525\\n',\n",
      " '\\n',\n",
      " 'PROMETHEUS BOOKS\\n',\n",
      " '\\n',\n",
      " 'Sell books including Haught\\'s \"Holy Horrors\" (see below).\\n',\n",
      " '\\n',\n",
      " 'Write to:  700 East Amherst Street, Buffalo, New York 14215.\\n',\n",
      " 'Telephone: (716) 837-2475.\\n',\n",
      " '\\n',\n",
      " 'An alternate address (which may be newer or older) is:\\n',\n",
      " 'Prometheus Books, 59 Glenn Drive, Buffalo, NY 14228-2197.\\n',\n",
      " '\\n',\n",
      " 'AFRICAN-AMERICANS FOR HUMANISM\\n',\n",
      " '\\n',\n",
      " 'An organization promoting black secular humanism and uncovering the history '\n",
      " 'of\\n',\n",
      " 'black freethought.  They publish a quarterly newsletter, AAH EXAMINER.\\n',\n",
      " '\\n',\n",
      " 'Write to:  Norm R. Allen, Jr., African Americans for Humanism, P.O. Box '\n",
      " '664,\\n',\n",
      " '           Buffalo, NY 14226.\\n',\n",
      " '\\n',\n",
      " '                                United Kingdom\\n',\n",
      " '\\n',\n",
      " 'Rationalist Press Association          National Secular Society\\n',\n",
      " '88 Islington High Street               702 Holloway Road\\n',\n",
      " 'London N1 8EW                          London N19 3NL\\n',\n",
      " '071 226 7251                           071 272 1266\\n',\n",
      " '\\n',\n",
      " 'British Humanist Association           South Place Ethical Society\\n',\n",
      " \"14 Lamb's Conduit Passage              Conway Hall\\n\",\n",
      " 'London WC1R 4RH                        Red Lion Square\\n',\n",
      " '071 430 0908                           London WC1R 4RL\\n',\n",
      " 'fax 071 430 1271                       071 831 7723\\n',\n",
      " '\\n',\n",
      " 'The National Secular Society publish \"The Freethinker\", a monthly magazine\\n',\n",
      " 'founded in 1881.\\n',\n",
      " '\\n',\n",
      " '                                   Germany\\n',\n",
      " '\\n',\n",
      " 'IBKA e.V.\\n',\n",
      " 'Internationaler Bund der Konfessionslosen und Atheisten\\n',\n",
      " 'Postfach 880, D-1000 Berlin 41. Germany.\\n',\n",
      " '\\n',\n",
      " 'IBKA publish a journal:\\n',\n",
      " 'MIZ. (Materialien und Informationen zur Zeit. Politisches\\n',\n",
      " 'Journal der Konfessionslosesn und Atheisten. Hrsg. IBKA e.V.)\\n',\n",
      " 'MIZ-Vertrieb, Postfach 880, D-1000 Berlin 41. Germany.\\n',\n",
      " '\\n',\n",
      " 'For atheist books, write to:\\n',\n",
      " '\\n',\n",
      " 'IBDK, Internationaler B\"ucherdienst der Konfessionslosen\\n',\n",
      " 'Postfach 3005, D-3000 Hannover 1. Germany.\\n',\n",
      " 'Telephone: 0511/211216\\n',\n",
      " '\\n',\n",
      " '\\n',\n",
      " '                               Books -- Fiction\\n',\n",
      " '\\n',\n",
      " 'THOMAS M. DISCH\\n',\n",
      " '\\n',\n",
      " '\"The Santa Claus Compromise\"\\n',\n",
      " 'Short story.  The ultimate proof that Santa exists.  All characters and \\n',\n",
      " 'events are fictitious.  Any similarity to living or dead gods -- uh, '\n",
      " 'well...\\n',\n",
      " '\\n',\n",
      " 'WALTER M. MILLER, JR\\n',\n",
      " '\\n',\n",
      " '\"A Canticle for Leibowitz\"\\n',\n",
      " 'One gem in this post atomic doomsday novel is the monks who spent their '\n",
      " 'lives\\n',\n",
      " 'copying blueprints from \"Saint Leibowitz\", filling the sheets of paper '\n",
      " 'with\\n',\n",
      " 'ink and leaving white lines and letters.\\n',\n",
      " '\\n',\n",
      " 'EDGAR PANGBORN\\n',\n",
      " '\\n',\n",
      " '\"Davy\"\\n',\n",
      " 'Post atomic doomsday novel set in clerical states.  The church, for '\n",
      " 'example,\\n',\n",
      " 'forbids that anyone \"produce, describe or use any substance containing...\\n',\n",
      " 'atoms\". \\n',\n",
      " '\\n',\n",
      " 'PHILIP K. DICK\\n',\n",
      " '\\n',\n",
      " 'Philip K. Dick Dick wrote many philosophical and thought-provoking short \\n',\n",
      " 'stories and novels.  His stories are bizarre at times, but very '\n",
      " 'approachable.\\n',\n",
      " 'He wrote mainly SF, but he wrote about people, truth and religion rather '\n",
      " 'than\\n',\n",
      " 'technology.  Although he often believed that he had met some sort of God, '\n",
      " 'he\\n',\n",
      " 'remained sceptical.  Amongst his novels, the following are of some '\n",
      " 'relevance:\\n',\n",
      " '\\n',\n",
      " '\"Galactic Pot-Healer\"\\n',\n",
      " 'A fallible alien deity summons a group of Earth craftsmen and women to a\\n',\n",
      " 'remote planet to raise a giant cathedral from beneath the oceans.  When '\n",
      " 'the\\n',\n",
      " 'deity begins to demand faith from the earthers, pot-healer Joe Fernwright '\n",
      " 'is\\n',\n",
      " 'unable to comply.  A polished, ironic and amusing novel.\\n',\n",
      " '\\n',\n",
      " '\"A Maze of Death\"\\n',\n",
      " 'Noteworthy for its description of a technology-based religion.\\n',\n",
      " '\\n',\n",
      " '\"VALIS\"\\n',\n",
      " 'The schizophrenic hero searches for the hidden mysteries of Gnostic\\n',\n",
      " 'Christianity after reality is fired into his brain by a pink laser beam of\\n',\n",
      " 'unknown but possibly divine origin.  He is accompanied by his dogmatic and\\n',\n",
      " 'dismissively atheist friend and assorted other odd characters.\\n',\n",
      " '\\n',\n",
      " '\"The Divine Invasion\"\\n',\n",
      " 'God invades Earth by making a young woman pregnant as she returns from\\n',\n",
      " 'another star system.  Unfortunately she is terminally ill, and must be\\n',\n",
      " 'assisted by a dead man whose brain is wired to 24-hour easy listening '\n",
      " 'music.\\n',\n",
      " '\\n',\n",
      " 'MARGARET ATWOOD\\n',\n",
      " '\\n',\n",
      " '\"The Handmaid\\'s Tale\"\\n',\n",
      " 'A story based on the premise that the US Congress is mysteriously\\n',\n",
      " 'assassinated, and fundamentalists quickly take charge of the nation to set '\n",
      " 'it\\n',\n",
      " '\"right\" again.  The book is the diary of a woman\\'s life as she tries to '\n",
      " 'live\\n',\n",
      " \"under the new Christian theocracy.  Women's right to own property is \"\n",
      " 'revoked,\\n',\n",
      " 'and their bank accounts are closed; sinful luxuries are outlawed, and the\\n',\n",
      " 'radio is only used for readings from the Bible.  Crimes are punished\\n',\n",
      " 'retroactively: doctors who performed legal abortions in the \"old world\" '\n",
      " 'are\\n',\n",
      " \"hunted down and hanged.  Atwood's writing style is difficult to get used \"\n",
      " 'to\\n',\n",
      " 'at first, but the tale grows more and more chilling as it goes on.\\n',\n",
      " '\\n',\n",
      " 'VARIOUS AUTHORS\\n',\n",
      " '\\n',\n",
      " '\"The Bible\"\\n',\n",
      " 'This somewhat dull and rambling work has often been criticized.  However, '\n",
      " 'it\\n',\n",
      " \"is probably worth reading, if only so that you'll know what all the fuss \"\n",
      " 'is\\n',\n",
      " 'about.  It exists in many different versions, so make sure you get the one\\n',\n",
      " 'true version.\\n',\n",
      " '\\n',\n",
      " '                             Books -- Non-fiction\\n',\n",
      " '\\n',\n",
      " 'PETER DE ROSA\\n',\n",
      " '\\n',\n",
      " '\"Vicars of Christ\", Bantam Press, 1988\\n',\n",
      " 'Although de Rosa seems to be Christian or even Catholic this is a very\\n',\n",
      " 'enlighting history of papal immoralities, adulteries, fallacies etc.\\n',\n",
      " '(German translation: \"Gottes erste Diener. Die dunkle Seite des '\n",
      " 'Papsttums\",\\n',\n",
      " 'Droemer-Knaur, 1989)\\n',\n",
      " '\\n',\n",
      " 'MICHAEL MARTIN\\n',\n",
      " '\\n',\n",
      " '\"Atheism: A Philosophical Justification\", Temple University Press,\\n',\n",
      " ' Philadelphia, USA.\\n',\n",
      " 'A detailed and scholarly justification of atheism.  Contains an '\n",
      " 'outstanding\\n',\n",
      " 'appendix defining terminology and usage in this (necessarily) tendentious\\n',\n",
      " 'area.  Argues both for \"negative atheism\" (i.e. the \"non-belief in the\\n',\n",
      " 'existence of god(s)\") and also for \"positive atheism\" (\"the belief in the\\n',\n",
      " 'non-existence of god(s)\").  Includes great refutations of the most\\n',\n",
      " 'challenging arguments for god; particular attention is paid to refuting\\n',\n",
      " 'contempory theists such as Platinga and Swinburne.\\n',\n",
      " '541 pages. ISBN 0-87722-642-3 (hardcover; paperback also available)\\n',\n",
      " '\\n',\n",
      " '\"The Case Against Christianity\", Temple University Press\\n',\n",
      " 'A comprehensive critique of Christianity, in which he considers\\n',\n",
      " 'the best contemporary defences of Christianity and (ultimately)\\n',\n",
      " 'demonstrates that they are unsupportable and/or incoherent.\\n',\n",
      " '273 pages. ISBN 0-87722-767-5\\n',\n",
      " '\\n',\n",
      " 'JAMES TURNER\\n',\n",
      " '\\n',\n",
      " '\"Without God, Without Creed\", The Johns Hopkins University Press, '\n",
      " 'Baltimore,\\n',\n",
      " ' MD, USA\\n',\n",
      " 'Subtitled \"The Origins of Unbelief in America\".  Examines the way in which\\n',\n",
      " 'unbelief (whether agnostic or atheistic)  became a mainstream alternative\\n',\n",
      " 'world-view.  Focusses on the period 1770-1900, and while considering '\n",
      " 'France\\n',\n",
      " 'and Britain the emphasis is on American, and particularly New England\\n',\n",
      " 'developments.  \"Neither a religious history of secularization or atheism,\\n',\n",
      " 'Without God, Without Creed is, rather, the intellectual history of the '\n",
      " 'fate\\n',\n",
      " 'of a single idea, the belief that God exists.\" \\n',\n",
      " '316 pages. ISBN (hardcover) 0-8018-2494-X (paper) 0-8018-3407-4\\n',\n",
      " '\\n',\n",
      " 'GEORGE SELDES (Editor)\\n',\n",
      " '\\n',\n",
      " '\"The great thoughts\", Ballantine Books, New York, USA\\n',\n",
      " 'A \"dictionary of quotations\" of a different kind, concentrating on '\n",
      " 'statements\\n',\n",
      " \"and writings which, explicitly or implicitly, present the person's \"\n",
      " 'philosophy\\n',\n",
      " 'and world-view.  Includes obscure (and often suppressed) opinions from '\n",
      " 'many\\n',\n",
      " 'people.  For some popular observations, traces the way in which various\\n',\n",
      " 'people expressed and twisted the idea over the centuries.  Quite a number '\n",
      " 'of\\n',\n",
      " 'the quotations are derived from Cardiff\\'s \"What Great Men Think of '\n",
      " 'Religion\"\\n',\n",
      " 'and Noyes\\' \"Views of Religion\".\\n',\n",
      " '490 pages. ISBN (paper) 0-345-29887-X.\\n',\n",
      " '\\n',\n",
      " 'RICHARD SWINBURNE\\n',\n",
      " '\\n',\n",
      " '\"The Existence of God (Revised Edition)\", Clarendon Paperbacks, Oxford\\n',\n",
      " 'This book is the second volume in a trilogy that began with \"The Coherence '\n",
      " 'of\\n',\n",
      " 'Theism\" (1977) and was concluded with \"Faith and Reason\" (1981).  In this\\n',\n",
      " 'work, Swinburne attempts to construct a series of inductive arguments for '\n",
      " 'the\\n',\n",
      " 'existence of God.  His arguments, which are somewhat tendentious and rely\\n',\n",
      " 'upon the imputation of late 20th century western Christian values and\\n',\n",
      " 'aesthetics to a God which is supposedly as simple as can be conceived, '\n",
      " 'were\\n',\n",
      " 'decisively rejected in Mackie\\'s \"The Miracle of Theism\".  In the revised\\n',\n",
      " 'edition of \"The Existence of God\", Swinburne includes an Appendix in which '\n",
      " 'he\\n',\n",
      " 'makes a somewhat incoherent attempt to rebut Mackie.\\n',\n",
      " '\\n',\n",
      " 'J. L. MACKIE\\n',\n",
      " '\\n',\n",
      " '\"The Miracle of Theism\", Oxford\\n',\n",
      " 'This (posthumous) volume contains a comprehensive review of the principal\\n',\n",
      " 'arguments for and against the existence of God.  It ranges from the '\n",
      " 'classical\\n',\n",
      " 'philosophical positions of Descartes, Anselm, Berkeley, Hume et al, '\n",
      " 'through\\n',\n",
      " 'the moral arguments of Newman, Kant and Sidgwick, to the recent '\n",
      " 'restatements\\n',\n",
      " 'of the classical theses by Plantinga and Swinburne.  It also addresses '\n",
      " 'those\\n',\n",
      " 'positions which push the concept of God beyond the realm of the rational,\\n',\n",
      " 'such as those of Kierkegaard, Kung and Philips, as well as \"replacements '\n",
      " 'for\\n',\n",
      " 'God\" such as Lelie\\'s axiarchism.  The book is a delight to read - less\\n',\n",
      " \"formalistic and better written than Martin's works, and refreshingly \"\n",
      " 'direct\\n',\n",
      " 'when compared with the hand-waving of Swinburne.\\n',\n",
      " '\\n',\n",
      " 'JAMES A. HAUGHT\\n',\n",
      " '\\n',\n",
      " '\"Holy Horrors: An Illustrated History of Religious Murder and Madness\",\\n',\n",
      " ' Prometheus Books\\n',\n",
      " 'Looks at religious persecution from ancient times to the present day -- '\n",
      " 'and\\n',\n",
      " 'not only by Christians.\\n',\n",
      " 'Library of Congress Catalog Card Number 89-64079. 1990.\\n',\n",
      " '\\n',\n",
      " 'NORM R. ALLEN, JR.\\n',\n",
      " '\\n',\n",
      " '\"African American Humanism: an Anthology\"\\n',\n",
      " 'See the listing for African Americans for Humanism above.\\n',\n",
      " '\\n',\n",
      " 'GORDON STEIN\\n',\n",
      " '\\n',\n",
      " '\"An Anthology of Atheism and Rationalism\", Prometheus Books\\n',\n",
      " \"An anthology covering a wide range of subjects, including 'The Devil, Evil\\n\",\n",
      " \"and Morality' and 'The History of Freethought'.  Comprehensive \"\n",
      " 'bibliography.\\n',\n",
      " '\\n',\n",
      " 'EDMUND D. COHEN\\n',\n",
      " '\\n',\n",
      " '\"The Mind of The Bible-Believer\", Prometheus Books\\n',\n",
      " 'A study of why people become Christian fundamentalists, and what effect it\\n',\n",
      " 'has on them.\\n',\n",
      " '\\n',\n",
      " '                                Net Resources\\n',\n",
      " '\\n',\n",
      " \"There's a small mail-based archive server at mantis.co.uk which carries\\n\",\n",
      " 'archives of old alt.atheism.moderated articles and assorted other files.  '\n",
      " 'For\\n',\n",
      " 'more information, send mail to archive-server@mantis.co.uk saying\\n',\n",
      " '\\n',\n",
      " '   help\\n',\n",
      " '   send atheism/index\\n',\n",
      " '\\n',\n",
      " 'and it will mail back a reply.\\n',\n",
      " '\\n',\n",
      " '\\n',\n",
      " 'mathew\\n',\n",
      " 'ÿ\\n']\n"
     ]
    }
   ],
   "source": [
    "import pprint\n",
    "with codecs.open('./data/20news-bydate-train/alt.atheism/49960', encoding='latin1') as file:\n",
    "    pprint.pprint(file.readlines())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def tokenize(doc_file):\n",
    "    with codecs.open(doc_file, encoding='latin1') as doc:\n",
    "        doc = doc.read().lower()\n",
    "        _header, _blankline, body = doc.partition('\\n\\n')\n",
    "        return re.findall(r'\\b\\w\\w+\\b',body)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      " 'and',\n",
      " 'noyes',\n",
      " 'views',\n",
      " 'of',\n",
      " 'religion',\n",
      " '490',\n",
      " 'pages',\n",
      " 'isbn',\n",
      " 'paper',\n",
      " '345',\n",
      " '29887',\n",
      " 'richard',\n",
      " 'swinburne',\n",
      " 'the',\n",
      " 'existence',\n",
      " 'of',\n",
      " 'god',\n",
      " 'revised',\n",
      " 'edition',\n",
      " 'clarendon',\n",
      " 'paperbacks',\n",
      " 'oxford',\n",
      " 'this',\n",
      " 'book',\n",
      " 'is',\n",
      " 'the',\n",
      " 'second',\n",
      " 'volume',\n",
      " 'in',\n",
      " 'trilogy',\n",
      " 'that',\n",
      " 'began',\n",
      " 'with',\n",
      " 'the',\n",
      " 'coherence',\n",
      " 'of',\n",
      " 'theism',\n",
      " '1977',\n",
      " 'and',\n",
      " 'was',\n",
      " 'concluded',\n",
      " 'with',\n",
      " 'faith',\n",
      " 'and',\n",
      " 'reason',\n",
      " '1981',\n",
      " 'in',\n",
      " 'this',\n",
      " 'work',\n",
      " 'swinburne',\n",
      " 'attempts',\n",
      " 'to',\n",
      " 'construct',\n",
      " 'series',\n",
      " 'of',\n",
      " 'inductive',\n",
      " 'arguments',\n",
      " 'for',\n",
      " 'the',\n",
      " 'existence',\n",
      " 'of',\n",
      " 'god',\n",
      " 'his',\n",
      " 'arguments',\n",
      " 'which',\n",
      " 'are',\n",
      " 'somewhat',\n",
      " 'tendentious',\n",
      " 'and',\n",
      " 'rely',\n",
      " 'upon',\n",
      " 'the',\n",
      " 'imputation',\n",
      " 'of',\n",
      " 'late',\n",
      " '20th',\n",
      " 'century',\n",
      " 'western',\n",
      " 'christian',\n",
      " 'values',\n",
      " 'and',\n",
      " 'aesthetics',\n",
      " 'to',\n",
      " 'god',\n",
      " 'which',\n",
      " 'is',\n",
      " 'supposedly',\n",
      " 'as',\n",
      " 'simple',\n",
      " 'as',\n",
      " 'can',\n",
      " 'be',\n",
      " 'conceived',\n",
      " 'were',\n",
      " 'decisively',\n",
      " 'rejected',\n",
      " 'in',\n",
      " 'mackie',\n",
      " 'the',\n",
      " 'miracle',\n",
      " 'of',\n",
      " 'theism',\n",
      " 'in',\n",
      " 'the',\n",
      " 'revised',\n",
      " 'edition',\n",
      " 'of',\n",
      " 'the',\n",
      " 'existence',\n",
      " 'of',\n",
      " 'god',\n",
      " 'swinburne',\n",
      " 'includes',\n",
      " 'an',\n",
      " 'appendix',\n",
      " 'in',\n",
      " 'which',\n",
      " 'he',\n",
      " 'makes',\n",
      " 'somewhat',\n",
      " 'incoherent',\n",
      " 'attempt',\n",
      " 'to',\n",
      " 'rebut',\n",
      " 'mackie',\n",
      " 'mackie',\n",
      " 'the',\n",
      " 'miracle',\n",
      " 'of',\n",
      " 'theism',\n",
      " 'oxford',\n",
      " 'this',\n",
      " 'posthumous',\n",
      " 'volume',\n",
      " 'contains',\n",
      " 'comprehensive',\n",
      " 'review',\n",
      " 'of',\n",
      " 'the',\n",
      " 'principal',\n",
      " 'arguments',\n",
      " 'for',\n",
      " 'and',\n",
      " 'against',\n",
      " 'the',\n",
      " 'existence',\n",
      " 'of',\n",
      " 'god',\n",
      " 'it',\n",
      " 'ranges',\n",
      " 'from',\n",
      " 'the',\n",
      " 'classical',\n",
      " 'philosophical',\n",
      " 'positions',\n",
      " 'of',\n",
      " 'descartes',\n",
      " 'anselm',\n",
      " 'berkeley',\n",
      " 'hume',\n",
      " 'et',\n",
      " 'al',\n",
      " 'through',\n",
      " 'the',\n",
      " 'moral',\n",
      " 'arguments',\n",
      " 'of',\n",
      " 'newman',\n",
      " 'kant',\n",
      " 'and',\n",
      " 'sidgwick',\n",
      " 'to',\n",
      " 'the',\n",
      " 'recent',\n",
      " 'restatements',\n",
      " 'of',\n",
      " 'the',\n",
      " 'classical',\n",
      " 'theses',\n",
      " 'by',\n",
      " 'plantinga',\n",
      " 'and',\n",
      " 'swinburne',\n",
      " 'it',\n",
      " 'also',\n",
      " 'addresses',\n",
      " 'those',\n",
      " 'positions',\n",
      " 'which',\n",
      " 'push',\n",
      " 'the',\n",
      " 'concept',\n",
      " 'of',\n",
      " 'god',\n",
      " 'beyond',\n",
      " 'the',\n",
      " 'realm',\n",
      " 'of',\n",
      " 'the',\n",
      " 'rational',\n",
      " 'such',\n",
      " 'as',\n",
      " 'those',\n",
      " 'of',\n",
      " 'kierkegaard',\n",
      " 'kung',\n",
      " 'and',\n",
      " 'philips',\n",
      " 'as',\n",
      " 'well',\n",
      " 'as',\n",
      " 'replacements',\n",
      " 'for',\n",
      " 'god',\n",
      " 'such',\n",
      " 'as',\n",
      " 'lelie',\n",
      " 'axiarchism',\n",
      " 'the',\n",
      " 'book',\n",
      " 'is',\n",
      " 'delight',\n",
      " 'to',\n",
      " 'read',\n",
      " 'less',\n",
      " 'formalistic',\n",
      " 'and',\n",
      " 'better',\n",
      " 'written',\n",
      " 'than',\n",
      " 'martin',\n",
      " 'works',\n",
      " 'and',\n",
      " 'refreshingly',\n",
      " 'direct',\n",
      " 'when',\n",
      " 'compared',\n",
      " 'with',\n",
      " 'the',\n",
      " 'hand',\n",
      " 'waving',\n",
      " 'of',\n",
      " 'swinburne',\n",
      " 'james',\n",
      " 'haught',\n",
      " 'holy',\n",
      " 'horrors',\n",
      " 'an',\n",
      " 'illustrated',\n",
      " 'history',\n",
      " 'of',\n",
      " 'religious',\n",
      " 'murder',\n",
      " 'and',\n",
      " 'madness',\n",
      " 'prometheus',\n",
      " 'books',\n",
      " 'looks',\n",
      " 'at',\n",
      " 'religious',\n",
      " 'persecution',\n",
      " 'from',\n",
      " 'ancient',\n",
      " 'times',\n",
      " 'to',\n",
      " 'the',\n",
      " 'present',\n",
      " 'day',\n",
      " 'and',\n",
      " 'not',\n",
      " 'only',\n",
      " 'by',\n",
      " 'christians',\n",
      " 'library',\n",
      " 'of',\n",
      " 'congress',\n",
      " 'catalog',\n",
      " 'card',\n",
      " 'number',\n",
      " '89',\n",
      " '64079',\n",
      " '1990',\n",
      " 'norm',\n",
      " 'allen',\n",
      " 'jr',\n",
      " 'african',\n",
      " 'american',\n",
      " 'humanism',\n",
      " 'an',\n",
      " 'anthology',\n",
      " 'see',\n",
      " 'the',\n",
      " 'listing',\n",
      " 'for',\n",
      " 'african',\n",
      " 'americans',\n",
      " 'for',\n",
      " 'humanism',\n",
      " 'above',\n",
      " 'gordon',\n",
      " 'stein',\n",
      " 'an',\n",
      " 'anthology',\n",
      " 'of',\n",
      " 'atheism',\n",
      " 'and',\n",
      " 'rationalism',\n",
      " 'prometheus',\n",
      " 'books',\n",
      " 'an',\n",
      " 'anthology',\n",
      " 'covering',\n",
      " 'wide',\n",
      " 'range',\n",
      " 'of',\n",
      " 'subjects',\n",
      " 'including',\n",
      " 'the',\n",
      " 'devil',\n",
      " 'evil',\n",
      " 'and',\n",
      " 'morality',\n",
      " 'and',\n",
      " 'the',\n",
      " 'history',\n",
      " 'of',\n",
      " 'freethought',\n",
      " 'comprehensive',\n",
      " 'bibliography',\n",
      " 'edmund',\n",
      " 'cohen',\n",
      " 'the',\n",
      " 'mind',\n",
      " 'of',\n",
      " 'the',\n",
      " 'bible',\n",
      " 'believer',\n",
      " 'prometheus',\n",
      " 'books',\n",
      " 'study',\n",
      " 'of',\n",
      " 'why',\n",
      " 'people',\n",
      " 'become',\n",
      " 'christian',\n",
      " 'fundamentalists',\n",
      " 'and',\n",
      " 'what',\n",
      " 'effect',\n",
      " 'it',\n",
      " 'has',\n",
      " 'on',\n",
      " 'them',\n",
      " 'net',\n",
      " 'resources',\n",
      " 'there',\n",
      " 'small',\n",
      " 'mail',\n",
      " 'based',\n",
      " 'archive',\n",
      " 'server',\n",
      " 'at',\n",
      " 'mantis',\n",
      " 'co',\n",
      " 'uk',\n",
      " 'which',\n",
      " 'carries',\n",
      " 'archives',\n",
      " 'of',\n",
      " 'old',\n",
      " 'alt',\n",
      " 'atheism',\n",
      " 'moderated',\n",
      " 'articles',\n",
      " 'and',\n",
      " 'assorted',\n",
      " 'other',\n",
      " 'files',\n",
      " 'for',\n",
      " 'more',\n",
      " 'information',\n",
      " 'send',\n",
      " 'mail',\n",
      " 'to',\n",
      " 'archive',\n",
      " 'server',\n",
      " 'mantis',\n",
      " 'co',\n",
      " 'uk',\n",
      " 'saying',\n",
      " 'help',\n",
      " 'send',\n",
      " 'atheism',\n",
      " 'index',\n",
      " 'and',\n",
      " 'it',\n",
      " 'will',\n",
      " 'mail',\n",
      " 'back',\n",
      " 'reply',\n",
      " 'mathew']\n"
     ]
    }
   ],
   "source": [
    "pprint.pprint(tokenize('./data/20news-bydate-train/alt.atheism/49960'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import os\n",
    "import re\n",
    "import math\n",
    "import codecs\n",
    "from sklearn import metrics\n",
    "\n",
    "\n",
    "class NaiveBayesClassifier:\n",
    "    def __init__(self, min_count=1):\n",
    "        self.min_count = min_count\n",
    "        self.vocabulary = {}\n",
    "        self.num_docs = 0\n",
    "        self.classes = {}\n",
    "        self.priors = {}\n",
    "        self.conditionals = {}\n",
    "\n",
    "    def train(self, path):\n",
    "        self.num_docs = 0\n",
    "        for d in os.listdir(path):\n",
    "            self.classes[d] = {'doc_counts':0, 'terms':{}}\n",
    "            print(d)\n",
    "            for f in os.listdir(path + d):\n",
    "                terms = tokenize(path + d + '/' + f)\n",
    "                self.num_docs += 1\n",
    "                self.classes[d]['doc_counts'] += 1\n",
    "                \n",
    "                # build vocabulary and count terms\n",
    "                for term in terms:\n",
    "                    if not term in self.vocabulary:\n",
    "                        self.vocabulary[term] = 1\n",
    "                        self.classes[d]['terms'][term] = 1\n",
    "                    else:\n",
    "                        self.vocabulary[term] += 1\n",
    "                        if not term in self.classes[d]['terms']:\n",
    "                            self.classes[d]['terms'][term] = 1\n",
    "                        else:\n",
    "                            self.classes[d]['terms'][term] += 1\n",
    "                            \n",
    "        # remove terms with frequency < min_count\n",
    "        self.vocabulary = {k:v for k,v in self.vocabulary.items() if v > self.min_count}\n",
    "\n",
    "        for c in self.classes:\n",
    "            # calculate priors\n",
    "            self.priors[c] = math.log(self.classes[c]['doc_counts']) - math.log(self.num_docs)\n",
    "            \n",
    "            # calculate conditionals\n",
    "            self.conditionals[c] = {}\n",
    "            c_len = sum([self.classes[c]['terms'][x] for x in self.classes[c]['terms']])\n",
    "            for term in self.vocabulary:\n",
    "                t_ct = 1\n",
    "                if term in self.classes[c]['terms']:\n",
    "                    t_ct += self.classes[c]['terms'][term]\n",
    "                self.conditionals[c][term] = math.log(t_ct) - math.log(c_len + len(self.vocabulary))\n",
    "\n",
    "    def classify(self, doc):\n",
    "        scores = {}\n",
    "        for c in self.classes:\n",
    "            scores[c] = self.priors[c]\n",
    "            for term in doc:\n",
    "                if term in self.vocabulary:\n",
    "                    scores[c] += self.conditionals[c][term]\n",
    "\n",
    "        return scores, max(scores, key=scores.get)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "alt.atheism\n",
      "comp.graphics\n",
      "comp.os.ms-windows.misc\n",
      "comp.sys.ibm.pc.hardware\n",
      "comp.sys.mac.hardware\n",
      "comp.windows.x\n",
      "misc.forsale\n",
      "rec.autos\n",
      "rec.motorcycles\n",
      "rec.sport.baseball\n",
      "rec.sport.hockey\n",
      "sci.crypt\n",
      "sci.electronics\n",
      "sci.med\n",
      "sci.space\n",
      "soc.religion.christian\n",
      "talk.politics.guns\n",
      "talk.politics.mideast\n",
      "talk.politics.misc\n",
      "talk.religion.misc\n",
      "accuracy 0.757302177377\n"
     ]
    }
   ],
   "source": [
    "clf = NaiveBayesClassifier()\n",
    "\n",
    "clf.train('./data/20news-bydate-train/')\n",
    "\n",
    "\n",
    "test_path = './data/20news-bydate-test/'\n",
    "\n",
    "out_y = []\n",
    "true_y = []\n",
    "for cl in clf.classes:\n",
    "    for f in os.listdir(test_path + cl):\n",
    "        _, result_class = clf.classify(tokenize(test_path+cl+'/'+f))\n",
    "        out_y.append(result_class)\n",
    "        true_y.append(cl)\n",
    "\n",
    "print('accuracy',metrics.accuracy_score(true_y,out_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### compare with sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(11314, 130107)\n",
      "accuracy 0.772835900159\n"
     ]
    }
   ],
   "source": [
    "from sklearn.datasets import load_files\n",
    "from sklearn import feature_extraction\n",
    "from sklearn import metrics\n",
    "from sklearn.naive_bayes import MultinomialNB\n",
    "\n",
    "\n",
    "twenty_train = load_files('./data/20news-bydate-train/', encoding='latin1')\n",
    "twenty_test = load_files('./data/20news-bydate-test/', encoding='latin1')\n",
    "\n",
    "vectorizer = feature_extraction.text.CountVectorizer()\n",
    "train_X = vectorizer.fit_transform(twenty_train.data)\n",
    "print(train_X.shape)\n",
    "\n",
    "clf = MultinomialNB()\n",
    "clf.fit(train_X,twenty_train.target)\n",
    "\n",
    "pred = clf.predict(vectorizer.transform(twenty_test.data))\n",
    "\n",
    "print('accuracy',metrics.accuracy_score(twenty_test.target,pred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Naive Bayes with scikit learn\n",
    "Fetch the 20 Newsgroups data set and load it via the  `sklearn.datasets.fetch_20newsgroups` function. The data set contains 20 newsgroups with 1000 posts in each newsgroup. The data set comes with a test/training split. \n",
    "\n",
    "<div class=\"alert alert-success\">\n",
    "Conduct the following tasks:\n",
    "</div>\n",
    "1. Preprocess the data set using scikit learn vectorizer\n",
    "2. Train the data set using two classifiers of your choice\n",
    "3. Tune the parameters of those classifiers to obtain the best results\n",
    "4. Evaluate the performance on the test set and compare both classifiers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy 0.817843866171\n",
      "clf__alpha 0.1\n",
      "tfidf__use_idf True\n",
      "vect__ngram_range (1, 2)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.pipeline import Pipeline\n",
    "from sklearn.feature_extraction.text import CountVectorizer\n",
    "from sklearn.feature_extraction.text import TfidfTransformer\n",
    "from sklearn.model_selection import GridSearchCV\n",
    "\n",
    "\n",
    "clf = Pipeline([('vect', CountVectorizer()),\n",
    "                ('tfidf', TfidfTransformer()),\n",
    "                ('clf', MultinomialNB()),\n",
    "               ])\n",
    "\n",
    "parameters = {'vect__ngram_range': [(1, 1), (1, 2)],\n",
    "              'tfidf__use_idf': (True, False),\n",
    "              'clf__alpha': (1.0, 0.1),\n",
    "             }\n",
    "\n",
    "gs_clf = GridSearchCV(clf, parameters, n_jobs=-1)\n",
    "gs_clf.fit(twenty_train.data, twenty_train.target)\n",
    "pred = gs_clf.predict(twenty_test.data)\n",
    "print('accuracy',metrics.accuracy_score(twenty_test.target,pred))\n",
    "\n",
    "for param_name in sorted(parameters.keys()):\n",
    "    print(param_name, gs_clf.best_params_[param_name])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy 0.834838024429\n",
      "clf__alpha 0.001\n",
      "tfidf__use_idf True\n",
      "vect__ngram_range (1, 2)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import SGDClassifier\n",
    "\n",
    "\n",
    "clf = Pipeline([('vect', CountVectorizer()),\n",
    "                ('tfidf', TfidfTransformer()),\n",
    "                ('clf', SGDClassifier(loss='hinge', penalty='l2',alpha=1e-3, n_iter=5, random_state=42)),\n",
    "               ])\n",
    "\n",
    "parameters = {'vect__ngram_range': [(1, 1), (1, 2)],\n",
    "              'tfidf__use_idf': (True, False),\n",
    "              'clf__alpha': (1e-2, 1e-3),\n",
    "             }\n",
    "\n",
    "gs_clf = GridSearchCV(clf, parameters, n_jobs=-1)\n",
    "gs_clf.fit(twenty_train.data, twenty_train.target)\n",
    "pred = gs_clf.predict(twenty_test.data)\n",
    "print('accuracy',metrics.accuracy_score(twenty_test.target,pred))\n",
    "\n",
    "for param_name in sorted(parameters.keys()):\n",
    "    print(param_name, gs_clf.best_params_[param_name])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "further details can be found at http://scikit-learn.org/stable/tutorial/text_analytics/working_with_text_data.html"
   ]
  }
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