{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Exercise: Logistic Regression and neural networks" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "import seaborn as sns\n", "sns.set()\n", "sns.set_context(\"talk\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Examples of classifier functions used in logistic regression and neural networks\n", "\n", "The following code plots the sigmoid and the step function, two common classifier functions used in neural networks (and logistic regression)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "a = np.arange(-2*np.pi, 2*np.pi, .1)\n", "sigma_fn = np.vectorize(lambda a: 1/(1+np.exp(-a)))\n", "sigma = sigma_fn(a)\n", "\n", "fig = plt.figure(figsize=(8,6))\n", "ax = fig.add_subplot(111)\n", "ax.plot(a, sigma, label='sigmoid')\n", "\n", "# Step Function\n", "step_fn = np.vectorize(lambda a: 1.0 if a >= 0.0 else 0.0)\n", "step = step_fn(a)\n", "ax.plot(a, step, '-.', label='step')\n", "\n", "ax.set_ylim([-1.1, 1.1])\n", "ax.set_xlim([-2*np.pi,2*np.pi])\n", "ax.set_ylabel('normalized classifier $y(a)$')\n", "ax.set_xlabel(r'activation $a$')\n", "ax.legend(loc='best');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise\n", "* Add the tanh function. \n", "* Add the ReLU, leaky ReLU, and ELU activation functions (find the functional forms online)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A simple classification problem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`scikit-learn` includes various random [sample generators](https://scikit-learn.org/stable/datasets/index.html#generated-datasets) that can be used to build artificial datasets of controlled size and complexity.\n", "\n", "For example, [`make_moons`](https://scikit-learn.org/stable/modules/generated/sklearn.datasets.make_moons.html#sklearn.datasets.make_moons) generates two overlapping half cricles with optional Gaussian noise." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "from sklearn import datasets, linear_model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Logistic regression using `scikit-learn`" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "np.random.seed(0)\n", "X, y = datasets.make_moons(200, noise=1.20)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(200, 2)" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "X.shape" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(200,)" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "y.shape" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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8IqcFCf7M9XKgEXje5vz78eeZ5AQS2z5JVNfCmG+Or05TqhsmJbOrtRNENbPKuHLdQprrKhNarO00rtbyerpKnTUbS9PoKq3haHk9SwdPho57sFg6eJKlgycpn7OCRdf8TdzjyTQTYiLOO3JakBiG8T3ge9kehyoS2z5J3KU+4qjTlIqchlT5a2BSEK1qqmF/aw+7Dp/h539spay4IKGaXXYa14Gq5pB5ygnNMjlQ1TxFkEyezI8y+gB7DneLiTjPyGlBkm+ky/maj8Rd6iOOOk3JFmlMpK+GG6k0xdhpXIMFpTFDecFv5hooKHU4Ga2h5VKxynB+v7tDTMR5hgiSFJIu52s+Enepjzh3zIkWaYwyuSXpr4HUR+vZaVzlE8NoWLHzQrBCzvapJ6I1tFz2Qajm58wEE3G+IIIkhaTL+Zopws09nYMDFFV7Kb14Q0LmnrhLfSRQpyneIo0Qf18NFRNYqqP1NI+H+k/ezLHPfApr1L9Yruxr5WBVU8y/szQPK/taXTW0XA9TV00UTbegy1WNLRcRQZJi8jW23cncwwsvJmTuUXKIB8lgnSbftheVxtO3fRulS5qUTGDpiNYbaT8WEiKAe14I0FBXyevespmBHdtjamjpClNP1cL7FxfVKyWKptNEnMsaWy4igiQN5FtsezrMPXbmGadkuuXzimL6NFLFuM/HwL597m+0LMZ9vcpzko5ovUgfk21eSCCPxNI81I2e5SNLS6hafQnetetiXjsdgi+VC++6ZbVZNRHnusaWi4ggmUE4mWkwrZS3UY10iA8UlrFl/uunLoIaHKxqorGuklsKSklnTFFQWFojaiUzzNExpTk58cB9FFgXoDHHta5VPDtYOx9TZF7IQEEpFQFh3DTYweD3LNp+9wyLbv6nmNpjqgVfqhfegiybiCWxOH5EkMwQYkUqecor0tJGNegQ79u/jy8/00H3hL9A4GQynZ/27v607/DiDUcePXlcycczdNjgwvJ+WhTqWsVjinHyMYXnhdiOu72N9nu+yJK77sZTaP/zVg1TLx8doPORb9j6hsI3Ja+e12gzlzleK7jwfvmJVyjweJRMXkET8b7WMzy94zinegYAjfk1Zbx5QwOVZUXOg08SSSyOHxEkMwA305U5OKBwkcTaqGoeD0crFtExcTbWpdO+w4s3HNkaUS9C6Oa/ACgtLuCF/Z1YFko+g7h8TBGMn+6m7fOfYfFtt9tqJqph6s0v/4q+oY4o39D8D/8Dp7777dCm5JXaK9AqY+e4ABw+7i+Rp2ry6h8aY+vzx6ZoJX1Doxw+vj+tfgpJLI6fXO+QKKSA0G48gbLkIZJIaAvu8Fwuz7YDXQldX4V4w5FNNI6UL2Rr3SaeqH8jW+s2caR8IaaN+Srov6gd8QtLzTKj3jM8OsEu4zQPPbmPux7b5boIBX1MrhPnwFh3t9+UZ0aPJRim7nRpzbKoG+6habBjcrNhwZHyhWwZXsy93/4DW4YX++fDUstxCSfS5GXXQTId3SdVCWpssZgpicWqiEaSRlKZPZ0MqeoD7hae6xS143Pp1Be4fFp3ePGEI8dTHDFIuP+ipaqZVm8DI1bBlPfE4zOISrpMACe/VlSYumVhQchxXztylus6nw3V7LKdj5LJ+fCOD7jmuNgRqYlapsn5l1+h5/nn2XvaVDKXpUOLlcTi+BFBkibSkT2dzFiS1UbcwnNjRe2Ul6o9ZmUl6XscVU1FiRRHDBL0X1gQM+dDdREMT7o89/RTDB02XMc/hRh+LW9FMbe/fz2/vffr7BmqjHLcBz+bynyMeIpczVoxhsi2A12smFc85feiYi5Ll59CEovjR0xbaUA1nNbO7JAOQrtxFzzlgTapwfcGXt1KjriZIQaHx5XGeezISXx7d6dlXlRNRcHiiE6+jvDiiE4cqGpGI7bgVjXlBZMuF/3zv/rHHw8ufq2hV/fTcGw313Q9z3s7fsM1Xc+zdPDkFAGpMh/ni73MHvWhJbBZ8WuiI1G/F6WSMGnSYoMaW0NtFRD1c8j5xOJsIBpJGog3ezrdqO7G6z78UTSPh77t29CG+in0Vgcy251LjoB7uKQqZ81iXvivJ1kxb2vKNTZVU1HSxRFRrIsV5yIYGv+DX1GrqAyufi0Vk6fqfMwbPUexOTbF/KWyefFHhw1GfSdKJWHS6KfI18TibCGCJA2kqoNfqlCtllu5Zm1oBxxPy06VcEkVQgt0+x/jToCMxMk/tfjTtzP46gF/o62DB7CGw3wdmpZ8cURNw1um1oI33kWw0Oul4fYv0LdzB12PP+oeWebi11IxearOx4inOCrHhdIy2jyz3IY4taxLAKWSMGn2U+RbYnE2EUGSBlLVwS9VJFst1y1oQCVcUoXQAp2kxqbin5qsozW16OOckkbaO0djGqZsiyOGzeVbNl/F/idfjf1ZE1wENY8H7+UbqbzkUto+/xnGuh2cwgp+LZUAhHiKRUbmuJhoPLH+g5zom4jpa2g608lIxBtmQqvg6YQIkjSQyg5+qRxTItVy3Rbl+k/eTNloYlE7kUxZoBPU2OIt9xJe9NE3MMqJx1928W74Hc4r+1spqq2lpLEJs79vylxWVZfTvO0ERzt8aXPWegoLWXzb7QlvDkDN5BlXscjIMWrwd57D/KB2XcwM9YHv72Ik4vdi3ypYQ9O0hLLbpQBjehFBkgZS3cEvVcRbLdeacFmU245x7DOforlwHq+4ZHYr3S98QUpQY0vUPxUMGDh93sWUZ1nUjZzlwrlFLL7pX239OAUejds/uIF/+86OtJb4SHRzEKR8xSqKamudtRrgAs6zgAFOUW67UdAsi9qRs/6ck0gsi7KBc3zu+ti+Bo/D7yWyJMz4kmXMrpsTt59CCjCmHxEkaSAVHfxygd49e1xzGKzRUZpH1cwQlmVx/HS//ZRELkgJamyqOTO9z/9hiiBRDRiYUzDGjW+7gPkXvyvmQl1dWaLkrLVMk4F9ezn3zK8YPXUKLCheMJ9Zb3ozlWvWuQqDRErpw6SmGUuIBM2A/1pQGr0QBzTQyJyTqYPT8FRWMdiyl3nbt/HWoFl05UYqmuagBeYg1u/Fg8XSoQ5WzCui4SMfittnJgUYM4MIkjSQrE8iV+h5/nmlRdmtMm1wBw6EJcFNfU/UgpSgxqaaMzN48ACWaYa+A9WAgQv0RSy4dJXSWNycteM+Hye+ej+jJ45POT7U52Po8GGKFy1m0a3/kvJ8oyjznw2FtbUs/vTteAoL8UKUUCwfHaD55V9NyTmJvpHFSNtROl7aETOXKp2/FynAmBlEkKSJZM0OucBYr3oio1Nl2ksWFHPlB/4utNv73AcuYf+fz/Dsj56lb3jCNgkuGY1NNYPdGh6eYt5SDRjoGxyLe0y29zdNTj74lSghEs7oieOcePArNN7+BSy0lNn4VQpYjnd3M/jqgdD8aFg0D5xg3il/wEVBVRXDFWOMDzpPmlZczNjp04EPHNtXFfy9cPQwPX94nuGz51Lye5ECjJlBBEkaSdTskCsUVcfX5dCuMm35nBVTFjqPR2Pta+ax8hNv9e9AO44F8g1SswONp9hhuDNftSJuqmzpAy37lPJBRtvbOPXyXh5pGU+ZjT/e8HTHpmeWhVZc7G/AFXG8cF4t46djlBmx8VVpHg/V6y9i1vqLlMLOlT6rFGDMCCJIFMiVmlmpQvXz1GzaxNkXFDoKOhHDz5Euja1i1Rq0klKlviPhzvxM11fq275N6X0mGv/xu046zdLQGMJfY9n4nb7nsd5e5fB0tyg4a2zMNnrNt+0F+s+cznouVaY3CDMVESQu5FLNrFQQz+epXrcudtCAGy5+jkQ1NjdBWL5iBQO7X4l9kQghl+n6SuM+tYi01vJ6OiYckh9xtvHbfc+m5mF3ywlenfUaBuoXhzpUNtv5OQLzM9Cyj6G2NtvOls2DHXgsi7Hubua9531TvsdzzzydE7lUUoAxM4ggiUE6WtBmk3g+D4BWENsJqhUXY42NZTQyTUUQVm+6MkqQ2LX5vbJ5DXWm5Q9BzXBXPtXNR7Bul1uOzlPb23mxJeA/KStiactzLG5v9xfTs6z4KxoHNgGdL+7gsUVvjf135kiUZuGp8nKkYhEHKpuihU+YLyzduVRSgDEzFNxxxx3ZHkMmuc2yKB0aUrOHDuzfy/lnno75none85Q2NVNcNz8V40sr8Xweb+MiAMYooHrTlZQ2Nftt314vpU1Lmfuuzcx952aGjENM9J6PLvQYWNQLSp13005YpsnA/r30bP0J53/7HIMt+9GKiiismcuJB+5z9C1M+HoZPHSQue98NwP79zHh8zdSGigo5QcL/4qXZq+kp7ia80VV9BTPYlfnKHuP9LB+2TxKigsoKS7gyrX1NNd7sSzwlhfTXF/N5quWsvmqCyhVrE5cWurv3jcy4lysUisqom/Hdtdr7a7WOV9U5fq+Ht8wHT0DnD4/TMeZAfZ7ajlSvpBlA8cptCb4wcK/8lfw1bSp/wGDBWUcK1vAWt8Rv7jSNEoal1Dzzs187blTdBV4Xf7uTxR5vXhf+zrA72/4+u4RthcvCZvval71LuVI+SKWDRyn2PLPzdx3bZ7y21GZu3jQNI31y+Zx8Ng5egdGowowBn1Mqt9trpPq+QtSXl6MpmkjwL1256fH7KWJXKiZlUr/TDyfh02XTx4KmKDKV62ZjBw6MEbV0RNc/p6P0zx4koEd21Pi54ilcag6cNu/+G8UzZuHOTTISPdphzLofiJ9DJmqr1Sxag0lDY2uDvfKEve6XUFCCmbg38GS91ec3UNXqfOOO1TRuKKepQMnQ8EOLcfO0UkFTspQ+N+tC2gWwbyNE30Tgfc4lOE/+SvKGhoykkslBRjTjwiSGMRTMysdDvlU+2eSqQHmmh38vg8n7bB0M73FFCJhjJ44zujJE2BZtNWvjL2IZimPQPN4WHjzP9nmkQQpXrSYv/yb13LgqSMJ3SO40O+ctdK9gi8WRuOlbHrDdaFNwLbfthCIp3P+O8vkQGUzmy6/BFDI2wiM6UTjWq66Mf4Ew0SRAozpRQRJDFRrZmmlZbR/6U7XBT8eYZMO/0yiNcAylR2skt+gTGBw+ybm+DsAxihpnq08gkKvl8bP/xsD+/dx7te/YvRUJwDF8xcEMtvX0oBG48tdjjZ+NzTLpKe4WqmC79nqespXrQllnPcNjrnXHUNjqGJWSLNQytsA/rz6at6QhiAVqamVHUSQxEC1ZtbIyeOMuyRe1X/yZjr+/UFl7UK1ZtSJB+5j9pvfoqT5JFoDLFPZwSlpCRyBvwx6bLKZR6B5PFSuXUfl2nX25yFmEIAbQQGi4rA/cbqfux7bFcpLUQqdBebpS0PPnlLeBuBLUWJnOFJTK3vkfqhRFnHtqqdpFNXWMt7d7fxrCy74X747ro6JoUXVhaHDBh0PP0j7l+50DSlV+TwljUui7NbBXWYsgrv6ZEi6JbANwTLoscj1PIKgjf/mzWvYsLyO5Y2z2bC8jmWLq1UeEQDlVrhB7dI0LTaunO8uFDSN165bFPp3UPjEQsOisP0InY98g/59e1LSEVNVazbN1D5fgh8RJDEI1gAqaWgMHIiITGpopHjhIqUFf0xB2Ay07A8dindRVWnfq/J57DLKM5UdrNoSOB5W9rW6LqL5kEcQtPHfcM1K/uW9F3HDNSt5y2WN7o+I5m/WBSg9T+HaZTB0Nsa+g8a6qaGzSsIHjQtP7qHvpZ3KmyA3glpzjJ9Y6HMJqUcEiQvBDOz6G2+h6tLLKF++gqpLL6P+xlto+OznMYeGUrOLDkZLhd03rkXVRhjZ4fZ57Jz3SrvMFOzqqy7fqDSXRbW1kzd1IdggyamfuEb0YpgvuC30ISLf4DLHQe0ykd7lrsLHsqgb7vFXeY6hkcdLprRmwR7xkSgQKwNbtUigKxHRUvHUjJocqFoocrwZ5ZnKDlYtvx9sl9u3fRsjnScZPe5c+NCtMvGCgmFuue6KvHTERiZRuqK4MQnXLuMNnXVM7AxEjdmWnQ/bBM0KCzuPB6mplV1EkCSJ8oIfZ7SU66JqR5pKTmQqO1i1nLinsDAkCC3T9EfMxZgnp8rEK/taWdlQjbfirUmNO5uEL/SP/9qgx+fex92NSO0y3tDZSFLM5C8AACAASURBVOFz5nArJee6o6s8R9w0Mn8pHqSmVnYRQZIkKrvowrnz3HMgIqKlohZVFdJUcsKtfMgCzzDXndlN13d2JZ07E28xR0fhE/kZbCoTo2kUeRcnNM5ESUd4anChr5193F2QaKH/cSQV2mW48Dn+wC8Y6joY+w+S3ARJTa3sIoIkSVR20aHQ3zg7JoYvqueefoqhw0bswbgUSUyGyF1mr2+QwvY/s/zUfpqGOvFYJn0pKmYZr+nNTvhYExNZnS870h2eqrYr1ygrKWRoZDxjtacSzV+KB1WtecK0+ObWFskxSTGalaBtX9f1zcDrgL3A44ZhjIed+6VhGG9LzRBTynnTtKp7evpTfmF/sqHzLjpWTweVhdfVhBMQRqkqIFldXQZg2xci02NJhGyMMZhwOvzyTn9TsPKKkIZmoXHXY7tcF7pkkjr3HjnDQ0/uc33f9X+zgl/vPG6rXaYj36J/3x46Hn7Q9X31N97CwoBpK5F+JE6C2rJg0bwKAE6cHsjIZ84WsX63yVBTU4nHo/UCs+zOJyRIdF2/Cfg08EvgCuA88BbDMM4GzvsMw8jF2uppEyQquAkbN5IVRvEQ64GMZ2HIZlOvTM6X27163v5hvq5Q6uTmzWsSTuo0TUtZWAEZqz0Vj1CfNdu/4Ce6EJqmFfW5Lltex0+fb+X46f60CfFcId8EiQFcZxjGXl3XC4B/B14LvN4wjLO6rvcZhuFesjTzZFWQpIJkhZEqsR7Izke+Qd9LO11NFVWXXsaC6/8xZWNKhEzMl4rD/2f1V3GwbHHsUi2WxYYVddzwdrWe8HbE2pVnc+etKtTTsRCqamrJCPFcIVuCJFEfyQLDMPYCGIYxAXxM1/WvAL/Vdf314FqVQkiQXGjfm0zxx0RIxkGdiflSqRE2QJFC3So4130uqbF4K4r57Psv5hfbjvHH/Z0Mj05QWlzAaxZWY5oW3/rZgaz4BtLVEVMF6duefhIVJKd1XW8yDONo8IBhGP+k6/qDwG+TuK6QB2TCeRokU/WTkqnerFIjLFiqJVa9Kw2L0r7kMq/t5mtweJwdvsmIpmzVn8rWJkhyTNJPotuAZ4EPRh40DONm4HdA/N2MhLxBKQM9BRFRmaqfNO7z0f6lO+l4+EH6XtrJ0KGDcZXvUNHQlEq1aB7WTCSeee00X1H3mWH1pzJVmWEmk6jm8AmnvzUM40Zd1x9IfEhCrqOagZ5s06JMVB2Ot1y/nZlNL13AAs3AYzmX+AiWaukumWPrJ9Esi9qRs7xm7uSuOF4tyW2+oj57iqo25zrpzDGRsvV+lASJruvXGYaxJfhvwzBGAUc90DCM9hSMLfz+7wVuB5qBY8A9hmF8L5X3ENRRzUB3Mwm5/QgzYdtWLdc/0LIfc+lyezObtYi6hW+J7nsehluplmDpkLFRf9+aif7+uJuaqcxXJNPNN2D3TF22oo6G2krau+2DbBLNnZGy9ZOoaiQ/0HV9tmEY30rraGwI5Kt8H3gIeBq4FnhM1/VBwzCezPR4BD/JOk9VfoSZsG2rth/u3baN77w86mhmC7WQPfGUfQkQYpdqCZYOGe8epn/fXs7+fGvcTc1U5iuSROZPVVPK9G491jNVVOj8PC6cWxFVfNKNoBkxqAFGmV27fHz5P/+XT71pAVWr12Y0n2rCtNh75ExGtSRVQfIo8J+6rs81DONLkSd1Xd8IfNkwjE2pHFyAe4AthmHcEvj3r3VdnwPcBYggySKJOk9VfR+1s0vTXj9JNQLtkE+jbcK9hezR8vqpZVgisC3VEo6mcf6Zp5W1pPC5V8lsj7odUNTZxvEHnqHQ66Vyw2VoaPTt3G4rJFTbP2d6t+72TI2NO5sdCzweKsuK4rrfjle7Yptd0eiYKOWF/3qSFfO2pjRnKRa9/SN88dGdtJ70ZVRLUhKThmF8FPgycJeu618LHtf9/Bj4I3BRqgen63ozsBT4n4hTTwIX6rrelOp7CulHtXfEgpoKJY0kmfpJSuX6NY39BXVKDtvWi99CQUVFwuPBsvwtdxVuFt52ANR6gUTdDtDbXvIHGOzcQefXH6bj6w/ZBh2MnT/PyQe/MinkHDSlifGJjDeZcnumYhFvnxLTtPj+bw67vk+zTA5UNaekTL7quL746E6OdviDQzIx70GUne2GYXxa1/Uu4Cu6rs8D+oEP438WvwXcmfLRwYXB20ccD6YI68BR4kDTJpN2BGcKCwuA9MzVrsNnlDSNnr4Rmhd6Odrhc8xIbqr38tp1iyhQUNmtCZPePXvoef55xnp9FFV7qWpYrNR+eHTWXKzu2CYgy4LR8iou+vrDHPzilxj4c2uU/8gVTUNTea9loQ31T/l+XnfRIn6+7ZjjfEXdKuDgbxrosP8wYa8j7W2cvO9LjAZbSjuMaaTtGPu371cKkmjt6ufiC2unnEv0uVN5ppzQNP/fb1qvVsDz5UNdDI6Mu77PQmOgoDQ0Lxw9TPX6lO+3p4yr9aRzhGGseXfDbV8Tb9TWt4G3AX+LX4D8EPicYRitcV5HlerAa+TsBJ/SXCzDIrjgGxhR9n3c/sENtqq6ZfmFyO0f3KAkRMZ6ezl89z0Mth6NWty14mKsUQchoWmUNy2hpq4G7XSnq/CrriyhaFY1q++7h56Xd9Pzh+cZ9/VS6K2mtH4BHT9yscZaFqX19fS7mdw0jUJv9ZRDBR5tyny5MXf0XHRvkBjjiilEwsb1+5fa0LQq17n6w56TcS9oTqg8U05Ylt8kpMrvd9sIXgdCwReaRs8fnmdWGgXJ73d34NEglsKR6nkPohq1VQR8DH99rXnAK8A6oAhw7iqUPMEVInJqgsfj1hUtK/XlA6Yj3soSevfs4dRzv4s7Qc+NsuICJY2kvKQQJkw+876LHetCMWG6fp/+EiZ3OzqvrbGxSWFiE4E2/xO3cEn3KC/s74x9HwsuWTaX8fEJ/2dYeiFzl144ed40Kdm5yzVs2nv1m+g/6F52vfTiDbaf/TPvu5h9rWf49s8PMuS0c7YsLKBsQn0BVcKy8I1aShuFnvNDUeNPtMSHyjPlRPBZC97TLUjgrOrYNI2VfYE9tmUxfPZcWtees71DMYVIYBi28+5GTU1lTK1EVSP5E7AYeBX4iGEYv9R1/Trge8BTuq6/wzCMdBSw6g28RmoeVRHnhRQy7vPx6t1fi9q9p6JEPMQf1x9vY6VIVEJ8rdFR5lxzLWOnTtlGoK2utJJu7qUaNl1QWZlUno7Ho4GFsxAJXONMyRyOlNezLEZwQCxMNFoDEWiDBaWUByLQKgtBG09vkEQkKs+UE+HPmkqQQFW5gmPesig1R/0thSFtvYLCyWZzL1VBUgD8A/CoYRgmgGEYW3RdP4/fEf5bXdffYhjGmRSPL+gbuQAIb0Z+QcR5IUXEm6CXCJnquBhENcR37NQpxyKTbs297PqX26EaNp1sns7TO9VSuX5edyX/2P4Tx/wXJwYKSm1zYg5WNTG3yIM1FttYkGyQRCRuz5QT4c+aajThNVcscRdamsYbT++YNBta6e99k83mXqqC5DWGYUQ9aYZhPKPr+hvwl5N/EViWysEZhnFE1/WjwLuBn4Sdehfwp1QnPgrxJeglWjMpVYuyKqkqMhlv/3IngmHTFatWh/Ixzj3zNH3bXwyZD5PN0znVM6g0ljFPoWv+SyQmGlsWXE13yRyAUOmXYB2xniGT4kIPow4ht7E2CsGAiHhNqm7PVHA8sZ61vUfOKAUJaGixhVYgiGF5f1voA6ei0oMbq5trXINTUt20LIiSILETImHndui6vgn4dcpGNZU7gf+r6/o54BfANcB1wHvSdL8ZjeruvW/7tqSK76VqUQ4Sy64dq8hkuHlmxKpj7taWmMlbyZrZgqjmY6S9yKFi/ks4reX1dJU6L0aWBaPjJrWzyug+P6S0UTBNiz0tx/n9L1/ENzRB+UQxK/t8NA8ZyibVWM/UisY5vNp2NuazplpJYcfBLnuhZVlYmkZdoEqBRwMslCs9JIsnItgi3Ru0cBLukBiJruuLDcNIi+Nd1/UbgH/G76dpxV8i5fEELpX3/UjSzfEH7mPokIujFyhfvoJF//SpDIzIHbceHNevKqDvWw9H/V2UeUbzTPk71eStyEzvsprZ1GzaBM267eKR7u6Npmnx+e/uoOOMmlaiWSbL+9u4put5x/cUNzSCaTJ68gQ/rb2CQ5VLXGNCN1xYy2tXz3fdKPi/vz20dfVHlY6pG+7xl54xR9LedfP+J3ZzsM29jP/yxtn8y3svim6iVV7EuoohFv35Zaz+zJXJD6e6uowJ0+LFPSdS2rQsXf1IokiXEAlc+1v4c1WENJPJEvGpYGJ8gq88to0TvnFAs7VrP9JSyd83LmEsbOF2NM9E2MPduubZaRZDmsbZF1503EWn03wYFKqqQgTC8h0cmHPNtdT89TWh+l89ZrV7YgHQeXbQVXsL+SW6/Ju7SDNZeOmZZE2qbsTrrHbUTt9waVrGp0pBirTmeMhOQ20hZ8lUifhUMO7z8dy9/8Fx34Rjnw+/Xbuf89d+mJKGRv9BTQuZZ5w6Fgbt4bEynlUDEyIzmkPmw1jYZK67EeksjodzRVU8Uf9GttZt4kj5Qkw0v2bUuISav74GzeMJ+W3Gq+cSHZEfzcDwmOt7QhnpDufDS88kMifxoFIZIF3O6nxHGlAJU8hUifhksUyT4w99lT+O61BgxVyYNQ12Hu3j+jDntXGuxm/TjtVoSotdGTdRzSJdHSbjLSMfQtPwFZbjK6wIRV7VDffw/oLDNN/0ySlmGQsNT3ExDLtHefUNjoVMK04o+SUCpUaWDp50nZNkCkVmOppwOiGCRJhCMNfh1Nej80hUQ08zwamX9/DIxEq6ympcF+Vglnx4kcnxJ3ZjudjDg3/nhG/bi0pj9W1/cYogiTQf2uZj9B9lbWV85sNEysiHvttIk1JpDT+qeyOfq6wKvTVoNuvxqYUKj42bIfMgYLvA+wZG3WVq0PQWZlK1Exhrl87l1zvbae/uT6hgYaajCacTIkiEKAq9XpZ/8Yt0/uQndD/7W8zhITylZXivuII5b/0bPIXZfWxM0+I/fncq5N9wMxPZJWHFYw932uVWdcbOdA8y2jm1pEbFmnWh+l6x8jF2TBTwTy47+nCUysiHv0HTHOfOwm8SDDa9mvRlxKfxtHX18Ydf7+R/W3romCgNtRsOLvDlpe7Pkoblz3MJmFRjJQ1Gfsx4fV6pjiacKYggEaIY9/k4GJHZbg4NcfZnWxnYuzdjJbGd2N/qX5RiWKWmYGfXVk3eWru0hrse22W7aM0vvIjNBaddk/nMgUnHt2WanH3maf9xl3yME30TSotfENUy8hUTwxRYE/gKy0OaiB3hpr1EzWaaZbHllbOMeEpAm/xswTEODisUP9Q8rOxvpaRxCWUrVvHFx19xTBp0vIal3g0yVSHeMwlxtgtTCDqQB48eCxxQcyBnkm0HTqEpJs9p+EubRNq1Vy2ZzWJvgeN1/PbwSn6987jjotVVUM2WBVf7HdMxKKgoD/3/gZZ9jAac86oO/5+9cJRvbm3h/id2882tLew9csa2FLhSGXlN463dLzJ7rA83SRxu2vPPefxYwHBBieNndEOzLOqGe7hwbhELb7qVlmPnEi4XHxSMQuoRjUSYQiYy25Olb3AsppMcCKkOi7yFUXbtYMjutSdO2ZiV/JFCDbVVvOnSxXz7F68630Ixma9ofv3k2MMSPg9UNYfyV2LxsxeOKdn8XZ3FgYzrpsEOWqqaQ2YmJ8JNgv45T5DgwGMQrFob+pyBsS0oHOHjb7iA+Re/C83jYdtvWxIuzmhZcPDYWe5/YveM7a2eLkSQCFPIVGZ7MqiacBrN89x+/dspCPS4gKkhuxWWZdv6dl1ZP3/5/k/w7V8ejCuiyAnvxteG/n94xNZgQam7QAyOW8Hm7+YsDvaF92Cxsq+Vg1VNrvcMmgSVChXaobjqmxa8/Yol9PSN0ts/QnlJoa1fIpF2wuH4BsfwtZ2LywkvuCOCRJhCukJTU4lSpVdN45q/vmSKEIFojcup9e3Qqy30DZrqEUUOlDQumRIqHR6xVT4x7KoVON7Xwebv5Cy+fHkt3h/+B2Omv2x882AHdcM9dJfMsTU7RYa6JlJdV7MsSsxRhj1qi/Sps0N86v2XYE2YdLy4g75nf8TJiHpbibQTtiNeJ7wQGxEkwhRyPbPdMk2aBo5TXzBM50SJ7SKsAQ11laxdGd3xLh6Nq6ruCve3ejSqSgtCfzclVDqQ2R4eKl11+cZQxJaKVhALpzwXJ2fxeFhFYY8G13U+G2ba89eJcgp1Xd1cE6qd5Tou/L6R2pGzXHr+AL+Yf6XS5/ENjDo2IAvW29rw9g8nXC7ejnic8IIzIkiEKYQvdI5kKbM9vBzJOwrL+H79X3G+2Bta6TXN7zpvqHOO949H49r4erXIrqs3X0390PJQld7SObOpuXITNC2LyrcJT/h00wrccMtziSSyonB5n49PVPZwYukS9gyU4Rsccwx19Xg0bnvfem771jbHqr4ApcUFrFlaw0UVg1T/0F8O738nRvxaictn9JYX+YVIjECP2Vu/S+Oit9Le3Z+0VhLELfFUcEcEiTCFXM1sD/dtDBSU8uT81weEiEkw+sgCameVctO71zjavOPRuJbPLWKB2ccprdLe/INfaK1eOhePZ17IZxSry19kc6vrTj3Hlvmvn+rw92jKi2S8tv3wpMwgC4HLFP52VlUJ996wkXu//4qtZhLub7BMk/ZtjYy0t7GpZze/qb3c9frrKgb9mogTlsVY2zGuf3MRj7RUJZbFb3/ZuASyEE3BHXfcke0xZJLbLIvSoSF5aJzQNI3Ki9Yz8qdDjJ07P7mLDLwGzTUFpc5+gXQwsH8v5595GhONHyz8K3/uRTChLiyxbnB4nEPt57lybT2a3eJfVETfju2u96t5x7s4/fijNJ3Yy7Gy+QwUlqNZ/p24ht/cssDs458+9FrKSqc6oksD/x5x6FDoKSmhetOVlDY1Uzwxxnqri4Zyi8K585hV46W5vpr1r5nL4ePuDUCvvXQ+9XW2BVnTQmlJIa9fv4jmei8W4C0vZunCajZftZTNV11AaYl/bxp8jvoPHeSXxRcyUFAWUyNprKviqjMvMxaRvBmFplHigbd++Bp2/+lMSgSApkFzfTWX6KntY54N3J69RCkvL0bTtBHgXrvzopEIURR6vay4+2569+7l1LO/i7upUjoI+jZay1x6YRDb5q2qcWnASNsxKsA2smtlXytNgx0UHF0CCUSvRWoGi0yL2YHsed/AKOcUy5D0/OynWKs+mdHvRDVhr9Drpfc9H6f7f/bHfB/AX21YjPmr55TNjh6PxoKack6cTt7EJYUYk0cEiWCLVuBh1vqL0JZemO2hAJO+DZXci1g2b9W+6ad/+P3QMafIrlSFQduV/FBBs0xeGJ3H4cdfZKi4IidzI7a/2qX0mfb+uYfGOAM9kunTHnY5KcSYAkSQCHlB0LehknvhZvNWaWObqTBopz7hKlhoHC+fz4nOESxGczI3QjXvwzcwGnegRzx92lVa7QqJI4JEyAuCi4xK7oVdkcao99g4ncNRcsoDIydP0PnIN5T6ituRcOn3MCLrV+VSbkQ8xTErVi2nvLnJH7WlEOjhmICJ38RZWlzAiiVzuHLtAqVWu0LiiCAR8oKgb2PlmaNxZWQnisru2ETjyHgVB9qKGTxxgKpfHOKqv34tV75uGQWKi1NCpd+DKDTlynZIq2pxzI0r67DQ6L/uBn71o98F+rb7fVHNQ514LNO2hUE81XqlEGP6EEEi5AVB34b50FfjysgGonqqh2dKO2kQbk55p/LvLU8d4ak93dz+oQ1KnyvZkh9OJJIbkUxTKCdUm0U11FZNVln21GKVEyqnX18wzMevWsD8i9fafl9SrTf7aFY6nuLc5bxpWtU9Pf3ZHkfOEysXIptYpsmpl/fyH7/rjOpvYVlE+QfseqpHZp47lcS3/Vv8mshji97qLMyApoVePvO+i10X4G9ubeGlQ91pESbLG2fzL++9SOm9Tj0+7OY0XtyufdO71/DQk/uchQ2woGCYf2A/xdXum4CZTLp+tzU1lXg8Wi9gG2sugkSwJVcFSRDTtGzNGSsbZzNwYB8vP7+f3QNl9A1PUD464DeRDHbgCa9hG7C5N3z2846Lkl+b8TvlBw+9yoTPx5HyhTxZf7XrGG/evMZ1l7z3yBkeenJfXJ9dBU2DDcvruOGala7vNU2Lux7b5ao1JONzcfq+VjXVsL+1R2kONnc8y9KhDqVNwEwlW4JETFtCXmJnzhj3+TDuuZfHJ5bRVbrIb3Iq1tCK54b6kF/X+exkIyqFkvjhTvnjD9zHkM+XdAhyOPFEHsVDPH4iN4d/KnwuscxP8fZth8m+OLE2AULmkG9AmBZYpsnxh77K4xPLpnYc1LTQgt9dMie6EVUgF0SFVIYgBwlGHjXUVgWHE30hpxs4nNM0bJt5ORFcyGORzqZQKn6iqCrLYZsAIfuIIBGmBQMt+zh4eix2x8GwRlSTB9VzQaou3zil/HssVEKQgwQjj27evIYNy+tY3jiby1bU8fdry6kbOeu/nmWCZYXKtMwbPce8kXP+c2H3hPhzI5QW8jTWowqGCMci1Ld9ykH1TYCQXsS0JUwL+rZvUzM5RTaiiqMkfjpDkO1MP52PfIP5J1/iaNkC2/IsAEcr6jEaL2VsQWPCuRFKuR5YFLYfofOR7Sl3diuFCGseVva1RhzMbl8cYRIRJELaSEc4qRPjPh+DBYvcTU42JhLVkvjxhCA31XuTLrsx7vPhsUz78iwBlg6cZLVVzaL3XpvwfZQWcjQuPLmHviMdod4gqXJ2x9MieOqJ7PXFEaYipi0hLfgGRrnrsV089OQ+XjrUzcG2c7x0qJuHntzHXY/tSrmZpNDrVTM5hZtINC2qg6HKfZZ89vPc+LYLWFA4Erpm4HKAX4jc/sENSQvLUHZ9LFKwmAYXcsdbWBZ1wz3+hTysN8jJh76KZTr3JomHN126mLKSqfvaoBkvvEXwFLLUF0eIRjQSIeU41Y9KZwmPqss3srLlR+4mpzATSfHCRVGZ0ipoHg8LLr2IOy9eZxvS+tp1iyjwaEmHYGaqyVj/0BgTMQTC3NFz0Qu5QsSbCuE5JpGUMMEbu15ged+xaCGSpb44gj0iSLJAJk0+2SAT4aSRVKxaw/J5P41tcppiItHQPB4KKisTvqdTSKtqeRQ3MtFkLCj0T54ZsH+DZaFZFmUTI7b3T6b6ceSGI5IRrYhd89axvO+YY5VmCf3NDUSQZBinLN9cq9qaDEp5ASlub6p5PCy+6Vbe/9C/8/jIsqjSJZbmiTKRjLS3Jb2jTieqJe+TWUxdi0ZqGt2BSLcoP02Szm7XDQfQ6ami9z0fo6H15ZzoiyPYI4Ikg2TD5JMNshVOWuj1svyzn+bT+/exfcvT7GNeVKRTZGZ7KvqJpBOVkvfJkEgy4OSJ5PwzqgUrdw+Ucdn1/5jwfYT0I4Ikg2TD5JMN4ikdnmo0jwfv2nUs/82vWXLo+dhvzpPwUbeS98mQUDJg6IS9f0bVdKtasHLfn3tCPighNxFBkkGyYfLJBvGUDk8XSv1ENI3Rri6OP3CfUkXg6YhqDoldMqCdfyYe063KvQGGRyemhaY+nZk5v5gcINsZxJkiGE7qFLkabwmPRAhmocfEshg/28PQoYP0vbSTjocfpP1Ld/q7I6YJ07TYe+QM39zawv1P7OabW1vYe+QMppmd4qkbV853nybNw8r+QDJg4Eu188+omm6Dn1Xl3kGCmrqQm4hGkkGyafLJJI6d6zLY3tQ14imSiPyIdBQDzMVAC9dkQGCRt4A1sxdj9VfH9M/Ea7oN3lulQ+R00NQTIV8iPAvuuOOObI8hk9xmWZQODWVnx19U6GH7q+6F7zZftZS6OeUZGJEzpaVFAIyMjCf09yXFBVy5tp7mei+WBd7yYprrq9l81VI2X3UBpSXp3cNomkblResZPHSQid7zk4l9bgl+wETveUqbmimum5/Qve3mzjQt7vvBbsdQV9/gKAePnePKtfVoCmNMFZqmsX7ZPA4eO0fvwGjUNDXWVXHr+y5h3sbL8L72dVRdfAnFdfNtx/jT51vp6HEIIw7dzy9QLtFrQ/f+3Z6TjE+4C3tveTGvW70g7s+Yr/gGRrnvB7v59UvH6egZ4PT5YTp6Btj+ahd7j/Swftk8SooLpvxNsr9bJ8rLi9E0bQS41+68aCQZRLVbXDpNPpkk253r7CKeRru6GD/rYiJJQzRXLgdaxNOuNhaJmG69FcWsaa7xN/eK8XfTQVOPh3yL8BRBkkFyweQz04iMeDr+wH3ugiQN0Vy5HmiRCqGfqOl246r57DyU3eCMXCOXNx52iCDJMKna/QmJoRrNlepigDMh0CLRaL2ZpqmrkOsbj0hEkGSBbJt8ZjJO9atMNFrL6zlQ1cxgQSk1JY1sOnImZU7NmRBokahAEE09mnzbeIggEWYUdtFcAwWlbFlw9ZSyKu2nRnnlyX0pi6bKhdyadJOMQAhq6q1d/fxhz0l6zg/NaE093zYeIkiEGUVk/SpT87BlwdVT2/OSeqfmTDHfJGO69Xg0Lr6wlosvrFWqnJwvobGJkG8bj5wXJLquzwfuAt4EzAEM4D7DMH6U1YEJeUt4NNdLf9hHV7/z4p0qp2aiu/V8XCwzYbrNxZycVJJvGw/NUk0tzQK6rpcAO4BZwBeADuDdwPXA3xqG8USclzxvmlZ1T09/agc6DamuLgNIuqdGrvPNrS3+0FMXE8KG5XXccM1KpWvGmjvTtJR3606LpWUxLRZLO1SeO9O0uOuxXa6LbK6ExiZKIt9/un63NTWVeDxaL/61OIpc10jeAqwFNhiG8VLg2G90XW8A/hWIV5AIwhQy7dSMtVsP1z58A6O0d/czODwezO20OAAADKlJREFUGkP4a67lEWSSXAuNTZfWmE8RnrkuSHzAI8CuiOOHgCsyPxxhupErTk273Wcsci2PIJPkUmhsuk1s+RLhmdOCxDCM54Dnwo/pul4EvA04kMg1NW1S/ROcKSz0l16Y7nP1hg0NSk7Nqy9tUJ6LeOduwrT44uO7orKY3dA02HX4DJvWL1b7gzxAZe6GRieUBO3gyHhan1+n7y1ca3z4x/u492NXpKxrphvp+t26Ve3JmiDRdb0QeE+Mt3QZhvEbm+P3Aa8Brk3LwIQZxbpltTQv9HK0w+dob2+q97Ju2by0jWHP4W5aT8afSW9Z0Ntv0wJ3muOtKFHSSKorS9I6DrfvzbKg9aSPPYdPc/GFtWkdS7bJpkZSCjwe4/zvgZAg0XVdwy9EbgHuNwxjayI3tazp70BOBTPF2Q5w4zvXxIymuvGda+jvG3a/UIB45+5/d7YrmbMi0TQoLymcVt+RytxdsmwuL+zriHkdy/K/L51zo/K9aRo8+1I7FyyoSts4wkmnsz2WVpI1QWIYRj/+KtWuBKK3HsWvwdxvGMan0jg0YYaRbaemaqfASHIpjyCT5EpobL5ln6eTnPaRAOi67gV+AbwOuNkwjIeyPCRhGpJNp6Zqp8Bwci2PIJPkSkmVXAnUyAVyWpDoul4AbAUuB94jSYjCdEQliznIdKo/ZRc2+4YNDaxb5u5PyLYWCfmXfZ5OclqQAP8IXAV8Cziu6/rlYecswzCiq+8JQp7hZqoBKC8tpLGuKmfzCOIlVths80IvN75zjetOPtuhsbliYssFcj2z/TngLx1OTxiGEa8glMx2RWaSsz3VJDJ3uZ7Fnsqku+mUmZ5r31u2MttzWpCkAREkioggSZxE5y6e8imZJNWL5d4jZ3joyX2u77t585qcT8SD3PrepESKMG2xTJOBln30bd/GuM9HoddL1eUbqVi1Bs3jyfbwcoZsm2rsSEfL11zKTE8Fufi9ZRoRJEJaGff5QiXbw7ezfTt3UNK4hIU33ervWijkJOmoayVhs9MP2Q4KacEyTfr2vMKx22/zCxGI2s6OtLdx8qGvYplmdgYpuBLUHmIR1B5UCYbNul1zJoTNThdEIxFSzhQtJBaWxUjbMQZa9lO5Zm1GxibERzq0BwmbnX6IRiKkFMs0/UKkvU3tDzSNvu3b0jsoIWHSoT0Ew2adrqtpfif+TAibnS6IIBFSykDLPr8mohoNaFlM9MVfsFDIDBtXzlfSSOLRHoKZ6Q21/vpTQYESfG2q9+Z9suVMQ0xbQkrp274N15CccDSNgipxtucq6Uq6c8pMv/rSBtYtmxdXkUwh+4ggEVLKuM8XX9Eoy6Lq8o3pG5CQFOmsa2UXNjvd+99MV0SQCCml0OtV10g0jZKGRipWrU7/wISEyYW6VkJuI4JESClVl2+kb6daCbSShkYW3nSrJCXmAZJ0J8RCBImQUipWraGkcYk/astBK/GUVzD/I/9AxWrJbBeE6YD8ioWUonk8LLzpVkoaGgMHpobklDQuYckX76Fy7ToRIoIwTRCNREg5hV4vDZ/9PAMt++nbvo2JPh8FVcH6WqtFgAjCNEMEiZAWNI+HyjVrJWNdEGYAIkgEQUgJdj1LLl9RhwXseLUr6T4mQu4igkQQhKSJ1fEwnOCxXGjWJaQOMVYLgpAUbj1LwonsY2KaM6qx3rRFBIkgCEkR7FkSZ0GDUB8TIf8RQSIIQlKo9CyxI94+JkLuIoJEEISkUOlZYod0QZw+iCARBCEpVHqW2CFdEKcPIkgEQUgKlZ4ldkgXxOmDhP8KgpAUbj1L7HDrY2KXkyL5J7mLCBJBEJLCrWdJOCp9THr7R7jrsV22OSmSf5KbaFYiOmn+ct40reqenv5sjyPnCTYY6u0dyvJI8o+ZOnemaUX1LLlseR1oFjte7VbqY1JZVcpt//lHjnb4YnZk/NwHLhHNxIZ0PXs1NZV4PFovMMvuvGgkgiCkhFg9S9ZdME/pGnsOd9N60ud4Pjz/RHqj5A7ibBcEIWf4/e4O1wgwyT/JPUSQCIKQM/gGRlwd9pJ/knuIIBEEIWfwVpQoaSTibM8tRJAIgpAz/MVF9UoaieSf5BYiSARByBnWLauleaHXUSvRNGisc84/EbKDCBJBEHKGAo/G7R/cQENtFUBIoARfY+WfCNlDwn8FQcgpqitL+NwHLonKSYmVfyJkFxEkgiDkHLFyUoTcQ0xbgiAIQlKIIBEEQRCSQgSJIAiCkBQiSARBEISkEEEiCIIgJIUIEkEQBCEpZlo/EtOyLG1mfeTECCaAyVzFj8xd4sjcJUe65k/TQNM0CwflY6YJknH8E+Hc8EAQBEGIxAuYOOQezjRBIgiCIKQY8ZEIgiAISSGCRBAEQUgKESSCIAhCUoggEQRBEJJCBIkgCIKQFCJIBEEQhKQQQSIIgiAkhQgSQRAEISlEkAiCIAhJIYJEEARBSAoRJIIgCEJS2BbgEoQguq7PB+4C3gTMAQzgPsMwfpTVgeUouq6/F7gdaAaOAfcYhvG9rA4qD9B13QNcD3wM/9x1AVuBLxiG0ZfNseUbuq7/GFhjGMYFmbqnaCSCI7qulwBPA28EPg+8E3gZ2BJYMIUwdF3fDHwfeAa4Fvgd8Jiu6+/O5rjyhE8BXwd+iX/uvgJ8AJANSxzouv53wDsyfV+p/is4ouv6tcBPgA2GYbwUdvxXwALDMNZlbXA5iK7rR4BdhmG8J+zYf+PfHS7P3shyG13XNaAHeMIwjI+HHf8/wA+BiwzD2JOt8eULuq7XAy3AADAiGomQK/iAR4BdEccPAUszP5zcRdf1Zvxz8j8Rp54ELtR1vSnzo8obqoD/B/wg4vihwKs8a2p8B782/Gymbyw+EsERwzCeA54LP6brehHwNuBAVgaVu1wYeDUijh8JvOrA0cwNJ38wDMMH3Ghz6trAqzxrLui6/lHgYmAl8ECm7y+CZIai63oh8J4Yb+kyDOM3NsfvA17D5I9c8FMdeI3svhl0FHszOJa8R9f1y4DbgJ8ahnHI7f0zGV3XG4GvAh8yDOOMrusZH4MIkplLKfB4jPO/B0KCJGDHvg+4BbjfMIyt6R1e3hHolk2k0zF43MzgWPIaXddfB/wCvwb30SwPJ6cJ/C6/CzxlGEakWTVjiCCZoRiG0c/kIheTQPTWo/g1mPsNw/hUGoeWr/QGXiM1j6qI80IMAg72R4HDwJsNw+jJ7ohyno8Da4DVASsDBH7XgX9PGIaR9ogqcbYLMdF13YtfM7kOuFmEiCNB30hkpMwFEecFB3RdvxV4AtgGXGkYRmeWh5QPvBuYC3QCY4H//h5/gMIY/hDqtCOCRHBE1/UC/ElhlwPvMQzjoSwPKWcxDOMIflNMZM7Iu4A/GYbRnvlR5Q+6rn8Ef+7IFvyaiGhwatwAXBrx3y+AE4H///NMDEJMW0Is/hG4CvgWcFzX9cvDzlmGYezIyqhylzuB/6vr+jn8P+Zr8GtysYIaZjy6rtcCDwNt+JMS10c4jI8YhnEmG2PLdQzDiNJ0dV3vwZ9HEhm2nzZEkAixeFfg9YbAf+FMIM/PFAzDeDTgT/pn/E7iVuDvDcP47+yOLOd5M1AONALP25x/P/48EyFHkcx2QRAEISnERyIIgiAkhQgSQRAEISlEkAiCIAhJIYJEEARBSAoRJIIgCEJSiCARBEEQkkIEiSAIgpAUIkgEQRCEpBBBIgiCICSFlLgQhAyi63oZ8Cf8/UleYxjGSNi57wAfAt5nGMYPszREQYgb0UgEIYMYhjEEfAFYDHwseFzX9XuAjwCfFCEi5BtSa0sQMkygPP9eoBZoxl/g8WvAFwzDuDObYxOERBBBIghZQNf1v8bfK+JZ4PXA1w3DuDG7oxKExBBBIghZQtf1l4H1wA+Bv41siarr+sfxd7hbA2w3DOOqjA9SEBQQZ7sgZAFd168D1gX+2efQV7sTuBd/p7uNmRqbIMSLONsFIcPouv4m4HHgJ/i1kQ/rur488n2GYfzYMIwfA10ZHqIgxIUIEkHIILquXwb8GHgBeB9wO/5Q4HuyOS5BSAYRJIKQIQJaxy+Bw8C1hmGMGIbxZ+C/gLfruv66rA5QEBJEBIkgZABd1xuAZ4Be4C2GYfjCTt8JDAFfzsbYBCFZxNkuCBnAMIx2/EmIduc6gfLMjkgQUocIEkHIUXRdL8T/Gy0EPLqulwKmYRij2R2ZIExFBIkg5C634y+nEmQI+D1wVVZGIwgOSEKiIAiCkBTibBcEQRCSQgSJIAiCkBQiSARBEISkEEEiCIIgJIUIEkEQBCEpRJAIgiAISSGCRBAEQUgKESSCIAhCUvx/SQIFEHhbszsAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax=plt.subplots(1,1)\n", "ax.scatter(X[y==0,0],X[y==0,1],c='r')\n", "ax.scatter(X[y==1,0],X[y==1,1],c='b')\n", "ax.set_xlabel(r'$x_1$')\n", "ax.set_ylabel(r'$x_2$');" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "LogisticRegressionCV(Cs=10, class_weight=None, cv=5, dual=False,\n", " fit_intercept=True, intercept_scaling=1.0, l1_ratios=None,\n", " max_iter=100, multi_class='auto', n_jobs=None,\n", " penalty='l2', random_state=None, refit=True, scoring=None,\n", " solver='lbfgs', tol=0.0001, verbose=0)" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clf = linear_model.LogisticRegressionCV(cv=5,penalty='l2')\n", "clf.fit(X, y)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0.18505795, -0.14192397]])" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clf.coef_" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-0.03432889])" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "clf.intercept_" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "# Helper functions to visualize the data and the decision boundary\n", "#\n", "def visualize(X, y, clf,ax=[]):\n", " plot_decision_boundary(lambda x: clf.predict(x), X, y, ax=ax)\n", "\n", "def plot_decision_boundary(pred_func, X, y,ax=[]):\n", " # Set min and max values and give it some padding\n", " x0_min, x0_max = X[:, 0].min() - .5, X[:, 0].max() + .5\n", " x1_min, x1_max = X[:, 1].min() - .5, X[:, 1].max() + .5\n", " h = 0.01\n", " # Generate a grid of points with distance h between them\n", " xx0, xx1 = np.meshgrid(np.arange(x0_min, x0_max, h), np.arange(x1_min, x1_max, h))\n", " # Predict the function value for the whole gid\n", " Z = pred_func(np.c_[xx0.ravel(), xx1.ravel()])\n", " Z = Z.reshape(xx0.shape)\n", " # Plot the contour and training examples\n", " if ax:\n", " ax.contourf(xx0, xx1, Z, cmap=plt.cm.RdBu, alpha=0.2)\n", " ax.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdBu)\n", " else:\n", " plt.contourf(xx0, xx1, Z, cmap=plt.cm.RdBu, alpha=0.2)\n", " plt.scatter(X[:, 0], X[:, 1], c=y, cmap=plt.cm.RdBu)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig,ax = plt.subplots(figsize=(8,8))\n", "visualize(X, y, clf,ax)\n", "ax.set_xlabel(r'$x_0$')\n", "ax.set_ylabel(r'$x_1$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sub-task\n", "* Generate 200 new samples for use as test data.\n", "* What is the accuracy of your binary classifier on\n", " * The training data\n", " * The test data?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Develop your own logistic regression binary classifier" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Implement your own logistic regression binary classifier by modifying the function definitions below\n", "1. Define the sigmoid activation function.\n", "1. Define the feed-forward function that returns the output of the neuron given some input and weights.\n", "1. Define the learning algorithm that:\n", " * use the cross entropy cost function defined in the lecture. Add an L2 regularizer with `alpha=0.1`\n", " * computes gradients of the cross entropy cost function (i.e. back propagation)\n", " * modifies the parameters with a learning rate parameter `eta = 0.01`.\n", " * returns the new weights.\n", "\n", "Then:\n", "1. Train the binary classifier on the data set. Perform rather many iterations.\n", "1. Plot the decision boundary and compare with the `scikit-learn` implementation above." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "def sigmoid(a):\n", " '''\n", " Sigmoid activation function\n", " \n", " Args:\n", " a (array[float]): activation signal\n", " \n", " Returns:\n", " y (float): the output of the neuron\n", " '''\n", " # Add code here (remove the dummy lines)\n", " y = None\n", " return y\n", "\n", "def single_neuron(x, w):\n", " \"\"\"\n", " Single neuron prediction. \n", " \n", " Args:\n", " x (array[float]): input to the neuron\n", " w (array[float]):\n", "\n", " Returns:\n", " y (float): the output of the neuron\n", " \"\"\"\n", " if len(np.array([x1[0],x2[1]]).shape)==1:\n", " x = np.append(1, x)\n", " else:\n", " m = len(x)\n", " x = np.c_[np.ones((m, 1)), x] \n", " assert(len(w)==x.shape[-1])\n", "\n", " a = np.dot(x,w)\n", " return sigmoid(a)\n", "\n", "def single_neuron_binary_classifier(x, t, iters=10000, alpha=0.1, eta0=0.01):\n", " \"\"\"\n", " Makes predictions for a single neuron binary classifier\n", " \n", " Args:\n", " x (array[float]): an array of input data\n", " t (float): target output for each data points\n", " iters (int): number of iterations to apply gradient descent\n", " alpha (float): a rescaling parameter for the weights\n", " eta (float): learning rate\n", " \n", " Return\n", " w (array[float]): the trained weights of the classifier \n", " \"\"\"\n", " # Insert code here (remove the dummy lines)\n", " w = None\n", " return w" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Sub-tasks and follow-up questions\n", "* Plot the decision boundary $p(t=1|x_1,x_2,w_0^*, w_1^*) = 0.5$, where $w^*$ are the optimized weights. \n", "* Why does it correspond to a straight line?\n", "* What is the accuracy for the training set?\n", "* Create a test set. What is the accuracy on that?\n", "* What would be needed to construct a better classifier that could handle the complicated class boundary?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercise: Create a neural net binary classifier" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Import and use tensorflow to create a (non-linear) binary classifier\n", "1. Build a keras sequential model as in the `demo-NeuralNet.ipynb` example. A single hidden layer is sufficient.\n", "1. Print a summary of your model. How many parameters does it have?\n", "1. Train the binary classifier on the training data set. Try with different activation functions and different number of epochs of training.\n", "1. Plot the decision boundary and compare with the Logistic Regression implementations above.\n", "1. What is the accuracy on the test set?" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "# Install TensorFlow by updating the conda environment\n", "# Download the latest version of the environment.yml file\n", "# (with tensorflow on the last line)\n", "# Then run:\n", "# conda env update -f /path/to/environment.yml\n", "\n", "import tensorflow as tf" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }