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}, "metadata": {}, @@ -401,7 +401,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.6" + "version": "3.10.12" }, "vscode": { "interpreter": { diff --git a/datascienceintro/LinearRegression_sklearn.ipynb b/datascienceintro/LinearRegression_sklearn.ipynb new file mode 100644 index 0000000000000000000000000000000000000000..439b9f13e132906397762278f494c4fa81f03fd8 --- /dev/null +++ b/datascienceintro/LinearRegression_sklearn.ipynb @@ -0,0 +1,708 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Linear Regression\n", + "\n", + "In this notebook, we will look at the simplest regression model, the linear regression which can be described as $\\hat{y} = \\sum_i a_i \\cdot x_i$.\n", + "\n", + "For this demo, we will generate some simple artificial dataset and then explore various simple regression methods, such as the \"plain\" simple linear regression, regularised linear regression, and how to handle polynomials fits.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 54, + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import norm\n", + "from sklearn.linear_model import LinearRegression\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "from sklearn.linear_model import Lasso, LassoCV, Ridge, RidgeCV, HuberRegressor\n", + "import numpy as np\n", + "\n", + "import matplotlib.pyplot as plt\n", + "import seaborn as sns" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Generate artificial data\n", + "\n", + "Define a small function which generates test data according to a linear model in the following way:\n", + " * x-axis: Random numbers drawn from a Gaussian (Normal) distribution with default parameters (mean=0, sigma = 1)\n", + " * y-axis: x-value times slope plus a noise term (Gaussian random numbers)\n", + " \n", + "The input parameters to this function are:\n", + " * The number of samples to generate\n", + " * slope\n", + " * noise\n", + "\n", + "The output of the function is:\n", + " * array of x values\n", + " * array of y values" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "def generate_test_data(slope, noise, n_samples):\n", + " x = norm.rvs(size=n_samples)\n", + " y = slope * x + norm.rvs(scale=noise, size=n_samples)\n", + " return x,y" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "true_slope = 1.0\n", + "noise_level = 1\n", + "n_samples = 100\n", + "\n", + "x, y = generate_test_data(true_slope, noise_level, n_samples)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.scatterplot(x=x, y=y)\n", + "plt.xlabel('x', size=15)\n", + "plt.ylabel('y', size=15)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Ordinary Linear Regression (OLS)\n", + "\n", + "We first look at the simplest case for the linear regression, fitting a straight line to the data." + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[array([[1.21497597]]), 0.0]\n" + ] + }, + { + "data": { + "image/png": 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zr6ZtQlosf7p2IAkdwjzYMxHxd6rY+YmQkBC6du1a5ys9Pb1mKHbSpEkcOnSIX/7ylzUVPRFxvoJS23mhDmBNZh4PLduuyp2IuJQqdg0wDIOySrtHnjssKMDpweu9995j0KBB/OIXv+DOO+906mOLSK28Ytt5oa7amsw88optxIQHu7lXItJeKNg1oKzSTt9HPvfIc+9+/DLCg1v20Xz88cdERkbWXJ42bVqd6zt16kRAQABRUVF07drVKf0UkfMVlje+b2NRE9eLiLSFgp2fmDx5Ms8//3zN5YiICG666SYP9kikfYoODWr0+qgmrhcRaQsFuwaEBQWw+/HLPPbcLRUREUFqaqoLeiMiLREbGcyEtFjW1DMcOyEtlthIDcOKiOso2DXAYrG0eDjU2wUHB2O3e2beoEh7ERMezJ+uHchDy7bXCXcT0mJ58tqBml8nIi7lX8lFGtW7d2/WrFnDjTfeSEhICLGxsZ7ukohfSugQxqKbhpBXbKOovJKo0CBiI4MV6kTE5RTs2pHHH3+cu+66i5SUFCoqKjAMw9NdEvFbMeEKciLifgp2fmDJkiX1tq9atarO5Ysvvpht27a5vkMiIiLiET6zQfHzzz/PwIEDiY6OJjo6mtGjR/Ppp596ulsiIiIiXsNngl2PHj3405/+xKZNm9i4cSNTpkzh6quvZteuXZ7umoiIiIhX8Jmh2KuuuqrO5T/84Q88//zzfPPNN/Tr189DvRIRERHxHj4T7H7MbrfzzjvvUFJSwujRoz3dHRERERGv4FPBbseOHYwePZry8nIiIyN5//336du3b4O3r6iooKKiouZyYWGhO7opIiIi4hE+M8cOoE+fPmzdupVvv/2We+65hxkzZrB79+4Gb//EE08QExNT85WYmOjG3oqIiIi4l8Xw4c3Mpk6dSkpKCi+++GK919dXsUtMTKSgoIDo6Og6ty0vL+fAgQMkJSURGhrq0n63F3pPRURE2q6wsJCYmJh688u5fGoo9lwOh6NOcDtXSEgIISEhbuyRiIiItBcFpTbyim0UllcSHRZEbITnNyb3mWD38MMPM23aNHr27ElRURFvvPEGq1at4vPPP/d010RERKSdyckv48Fl21l7zpnQf7p2IAkdwjzWL5+ZY3fy5Eluv/12+vTpQ3p6Ohs2bODzzz/nkksu8XTX2oVVq1ZhsVjIz8/3dFdEREQ8qqDUdl6oA1iTmcdDy7ZTUGrzUM98qGL397//3dNd8DoWi6XR6x999FH++7//u8WPO2nSJAYPHswzzzzTuo6JiIj4sbxi23mhrtqazDzyim0eG5L1mWAn5zt27FjNv9966y0eeeQR9u7dW9MWGRlZ82/DMLDb7QQG6iMXERFpi8LyykavL2rielfymaFYOV/Xrl1rvmJiYrBYLDWX9+zZQ1RUFJ9++inDhg0jJCSEdevWMXPmTKZPn17nce6//34mTZoEwMyZM1m9ejULFizAYrFgsVg4ePBgzW03bdrE8OHDCQ8PZ8yYMXWCpIiISHsQHRrU6PVRTVzvSirfNMQwoLLUM88dFA5NDLM210MPPcTTTz9NcnIyHTt2bPL2CxYs4IcffqB///48/vjjAMTFxdWEu9/97nf8+c9/Ji4ujrvvvpvZs2ezfv16p/RVRETEF8RGBjMhLZY19QzHTkiLJTbScytjFewaUlkKf0zwzHP/NgeCI5zyUI8//niLFpjExMQQHBxMeHg4Xbt2Pe/6P/zhD0ycOBEwQ+OVV15JeXm59qkTEZF2IyY8mD9dO5CHlm2vE+4mpMXy5LUDPbrliYKdnxs+fLhTH2/gwIE1/+7WrRtgrlju2bOnU59HRETEmyV0CGPRTUPIK7ZRVF5JVGgQsZHax857BYWblTNPPbeTRETUrfxZrVbOPWyksrL5kzyDgmrnDVSvynU4HG3ooYiIiG+KCfd8kDuXgl1DLBanDYd6k7i4OHbu3FmnbevWrXUCW3BwMHa73d1dExERkTbSqth2ZsqUKWzcuJFXX32VzMxMHn300fOCXu/evfn22285ePAgeXl5qsiJiIj4CAW7duayyy7jv/7rv/jNb37DiBEjKCoq4vbbb69zm//8z/8kICCAvn37EhcXx+HDhz3UWxEREWkJi3HuhCs/VlhYSExMDAUFBURHR9e5rry8nAMHDpCUlKQVnk6i91RERKTtGssv51LFTkRERMRPKNiJiIiItMLWI/nMXrKBjQdPe7orNbQqVkTEDxSU2sgrtlFYXkl0WBCxEa3fhsGZjyXijzYdOsPCjExW/5ALgN1hsHT2SA/3yqRgJyLi43Lyy3hw2XbWnrMD/p+uHUhChzCPPZaIv9lw8DQLlmeyLsv8/giwWvjpkO7MmZzq4Z7VUrATEfFhBaW284IYwJrMPB5atp1FNw1pdrXNmY8l4k++3neKhRmZfL3/FACBVgvXDu3BnMmp9OzsvEMFnEHB7hzas8159F6KuF5ese28IFZtTWYeecW2ZocxZz6WiK8zDIOv9p1iQUYm3x0w59AFBVi4fngi90xMIbGTdwW6agp2ZwUHB2O1WsnJySEuLo7g4OCaI7OkZQzDwGazkZubi9VqJThYvwhEXKWwvPEjAYuauN5VjyXiqwzDYG1mHgszMtl46AwAwQFWfjYikbsnpdDdy6ckKNidZbVaSUpK4tixY+TkeOiMWD8THh5Oz549sVq1+FrEVaJDgxq9PqqJ6131WCK+xjAMVu3NZUFGJluP5AMQHGjl5pE9uXtiCl1jfGM/VgW7HwkODqZnz55UVVXprNQ2CggIIDAwUFVPEReLjQxmQlosa+oZQp2QFktsZPMr5s58LBFfYRgGGd+fZOGKTLYfLQAgNMjKzSN7cffEZOKjfSPQVdPJEyIiPi4nv4yHlm2vE8gmpMXy5LUD6daKVbHOeiwRb+ZwGHz5/QkWZmSyK6cQgLCgAG4b3Ys7xycTFxXi4R7Wakl+UbATEfED1XvPFZVXEhUaRGxk2/exc8ZjiXgbh8Pgs13HWZiRyZ7jRQCEBwdw++je/Hx8ErGR3hPoqrUkv2goVkTED8SEOy98OfOxRLyF3WHwyY5jLFqRyQ8nigGIDAlkxphe3DEumU4R/vF/XsFORERE/JbdYfDx9hwWrcgi66QZ6KJCApk1tjezxyXRwc/+iFGwExEREb9TZXfwr205PLsii/15JQBEhwYye1wSs8YmERPmn6u8FexERETEb1TaHXywJZvnVmZx8FQpAB3Cg/j5uCRuH9O7yW19fJ2CnYiIiPg8W5WD9zYf5blVWRw5XQZAx/Ag7pyQzO2jexMZ0j4iT/t4lSIiIuKXbFUO3t10lOdWZpGdbwa6zhHB/GJCMrde3IuIdhLoqrWvVysiIiJ+oaLKztsbjvD8qn3kFJQDEBcVwl0TkrllVC/CggM83EPPULATERERn1Feaeef3x3mhdX7OV5oBrr4qBDumZTCTSN7EhrUPgNdNQU7ERGRVqrezLmwvJLosCBiI7QHoKuU2ey8/u0hXlyzn9yiCgC6xYRyz6QUbhie2O4DXTUFOxERkVbIyS/jwWXbWXvO8Wt/unYgCTp+zWlKbVX845tDvLRmP3nFNgC6dwjj3skpXDesByGBCnQ/pmAnIiLSQgWltvNCHcCazDweWradRTcNUeWujYorqnjt60P8be1+TpeYgS6xUxhzJqVyzdAeBAdaPdxD76RgJyIi0kJ5xbbzQl21NZl55BXbFOxaqai8kle/PsTLa/dzprQSgF6dw5kzOZWfDulOUIACXWMU7ERERFqosLyy0euLmrhezldQVsmS9Qf5+7r9FJZXAZAcG8HcKan8ZFACgQp0zaJgJyIi0kJNnV4Q5eenGzhTfqmNV9YfZPH6AxSdDXQpcRHMT0/jPwYmEGC1eLiHjcjZAhsXw6AbodcYT/cGULATERFpsdjIYCakxbKmnuHYCWmxxEZqGLYpp0ts/H3dfpZ+dYjiCjPQXdAlkvnpaUzr3817A52tBHa+BxtfgZzNZ9uKFexERER8VUx4MH+6diAPLdteJ9xNSIvlyWsHan5dI04VV/C3tQd49euDlNrsAFzYNYr70tO4rF9XrE0EOo9tMXNiN2xaDNvegooCsy0gGPpeDcPvcP3zN5OCnYiISCskdAhj0U1DyCu2UVReSVRoELGR2seuIblFFfxt7X5e+/oQZZVmoOuXEM389DQuuahLk4EOPLDFTGU5fP8vszp3+Ova9o5JMHwWDL4FImKd/7xtoGAnIiLSSjHhCnJNOVlYzgur9/PGd4cor3QAMLBHDPOnpJF+UTwWS/OGXN26xcypfWZ1bsvrUHbabLMEwIVXwPDZkDQJrN65mMNngt0TTzzBe++9x549ewgLC2PMmDE8+eST9OnTx9NdExERkXMcKyjjxdX7eeO7w9iqzEA3OLED901NY9IFcc0OdNVcvsWMvRL2fmJW5/avqm2P7g7DZsKQ2yC6W+sf3018JtitXr2aOXPmMGLECKqqqvjtb3/LpZdeyu7du4mIiPB090RERATIzi/j+VVZvL3hKDa7GeiG9erIfelpjE+LbXGgq+ayLWbyj8DmpbD5VSg+cbbRAqlTYcQdkHoJBPhMXPKdYPfZZ5/VubxkyRLi4+PZtGkTEyZM8FCvREREBODI6VL+umof7246QqXdAGBkUifuT09jdErnVge6ak7dYsZhh6zlZnUu8wswzABKRDwMvQ2GzoCOvdrQW8/xmWB3roICc0VKp06dPNwTERGR9uvwqVKeW5nFss1HqXKYgW5MSmfmp6dxcXJnpz2PU7aYKToBW16FTUuh4Ehte9IEc+5cnysh0LfnTFoMwzA83YmWcjgc/OQnPyE/P59169Y1eLuKigoqKipqLhcWFpKYmEhBQQHR0dHu6KqIiIhfOpBXwnMrs3h/Szb2s4FufFos89PTGNHbNUWXnPyyBreY6dbQqliHAw6uMatze/4NDnPPPEI7wJBbzflzsWku6a+zFBYWEhMT06z84pMVuzlz5rBz585GQx2YCy4ee+wxN/VKRETE/2WdLOa5lVl8uDWbs3mOiRfEMT89jWG9Orr0uVu0xUzpadj6unkyxOl9te2Jo8zqXN+rIcgFW6R4mM9V7ObOncuHH37ImjVrSEpKavS2qtiJiIg4R+aJIhatyOKj7TlUJ4cpF8YzPz2NwYkdPNq3GoYBR741q3O7PgD72QwQHAWDfgbDZkHX/q16aI9tjIyfVuwMw2DevHm8//77rFq1qslQBxASEkJISIgbeiciIuKf9hwvZFFGFp/sPFYT6C7p24X5U9IY0CPGs52rVl4A2982A93J3bXtXQea1bkB10NIZKsf3u0bI7eBzwS7OXPm8MYbb/Dhhx8SFRXF8ePHAYiJiSEszLveVBERaZ88WdVxtl05BSzKyOKzXcdr2i7v15V56an0S/CSQJezxQxzO96FylKzLTAMBlxrBrqEodDG1bhu3RjZCXwm2D3//PMATJo0qU774sWLmTlzpvs7JCIi8iO+VNVpzI6jBSxckcmXu8093SwWuKJ/N+ZOSeWibl4wjclWAjuXmYEuZ0tte9yFZpgb+DMI6+C0p3P5xshO5jPBzsemAoqISDvia1Wd+mw9ks+ijEwy9pwEzED3HwMTmDcllQu6RHm4d8CJ3eYxX9v+CRWFZltAsLkIYvhs6Dm6zdW5+rhsY2QX8ZlgJyIi4q18rarzY5sPn2HB8kxW/5ALgNUCVw/uzpzJqaTGt35emlNUlsP3/zKrc4e/rm3vmHT2mK9bISLWpV1w6sbIbqBgJyIi0ka+VtUB2HjwNAsyMmsCaYDVwvTB3ZkzOYXkOA8HulP7zOrclteh7LTZZgmAC68wq3NJk8BqdUtXnLIxshsp2ImIiLSRL1V1vt1/igUZmXy17xQAgVYL1wztzr2TUukd68Gz1+2VsPcTszq3f1Vte3T3s9W52yC6m9u7FRMezJ+uHdjgxsjeVolVsBMREWkjb6/qGIbB1/tPsWB5Jt8eMCtgQQEWrhvWg3snpZLYKdxzncs/ApuXwuZXofjE2UYLpF1iVudSL4EAz8aVFm2M7GEKdiIiIm3krVUdwzBYl5XHwoxMNhw8A5iB7obhidwzKYUeHT0U6Bx2yFpuVucyvwDDYbZHxMPQ22DoDOjYyzN9a0BMuHcGuXMp2ImIiDhBY1Udd+9vZxgGq3/IZWFGJpsP5wMQHGjlphGJ3DUxxXPbrxQdhy2vwaalUHCktj1polmd63MFBHp/ePJmCnYiIiJOUl9Vx5372xmGwYo9J1mYkcm2owUAhARauXlUT+6emEKX6FCnPl+zOBxwYLVZndv7CTiqzPawjjD4FvOYr9hU9/fLTynYiYiIuIi79rczDIMvd59g4YpMdmabe7yFBlm57eJe3DkhmfgoDwS6klOw9XVzdevp/bXtiaPM6lzfqyHIdzZu9hUKdiIiIi7i6v3tHA6Dz3cdZ+GKLL4/Zga68OAAbhvdizvHJxMb6ebz0g0DjnxrVud2fQD2CrM9OAoG3mAGuq793dundkbBTkREXMqfzk9tKVftb+dwGHyy8xiLMrLYe6IIgIjgAGaM6c3PxyfTKcLN7295AWx/2wx0J3fXtncdCCPugP7XQYiH98ZrJxTsRETEZfzl/NTWcvb+dnaHwcfbc3h2RRaZJ4vNxwgJZNbY3swel0QHdwfmnC1mmNvxLlSWmm2BYTDgWrM6lzDUJcd8ScMU7ERExCX84fzUtnLW/nZVdgcfbc9h0Yos9ueWABAdGsjscUnMGpNETLgbN0C2lZhBbtNiM9hVi7sQht9hDrmGdXBff6QOBTsREXEJZ8wv8/Vh3Lbub1dpd/DBlmyeW5nFwVNmRaxDeBA/H5fE7WN6N1kRdKoTu83q3Pa3oMKcz0dAMPSdblbnel6s6pwXULATERGXaOv8Mn8Zxm3NqQW2KgfvbznKcyv3cfi0Geg6hgdx54Rkbh/dm8gQN/36riyH3R+age7IN7XtHZPMMDf4Fojo7J6+SLMo2ImIiEu0ZX6Zvw3jNvfUAluVg3c2HeGvK/eRnV8GQOeIYH4xIZlbL+5FhLsC3al95lDrltehzDyCDEsAXHilGeiSJoLV6p6+SIso2ImIiEu0ZX5ZfmklM8f05qaRPQkNCmDz4TO8su4ApTa7U7YJ8TYVVXbe3nCE51ftI6egHIC4qBDumpDMLaN6ERYc4PpO2CvNDYQ3vgL7V9W2R/eAYTNhyK0Q3c31/ZA2UbATEWkDX58D5kqtnV+Wk1/G//tgB2uzTtW0jU3tzMKbhjD/zS2U2uyt3ibE25RX2vnnd4d5YfV+jheaga5LdAh3T0ypCbUul38ENi+Fza9C8YmzjRZIu9SszqVdAlY39EOcQsFORKSV/GUOmCu1dH5ZzRDsj0IdwPqzl2ePS+LZFVkt3ibE25TZ7Lz+7SFeXLOf3CJzE99uMaHcMymFG4Ynuj7QOeyQ+aU53Jr5BRgOsz0iHobebn517OXaPohLKNiJiLSCv80Bc6Xmzi+DxlfSrs86xeyxSS3aJsTblNqq+Mc3h3hpzX7yim0AdO8Qxr2TU7huWA9CAl0c6IqOw5bXYNNSKDhS25400azOXXglBPh2aG7vFOxERFqhsQCy8dAZ8ksrNUTbCk2tpAWatU2ItymuqOLVrw/y8toDnC4xA12PjmHMnZzKNUN7EBzowoUIDgccWG3Ondv7CTiqzPawjuaq1mGzIDbVdc8vbqVgJyLSCg0FkPDgABbeNOS8OWIaom2eplbS9uwUTjcfeg+LyitZ+tVBXl53gPxS8/9Mr87hzJmcyk+HdCcowIWBruQUbH3dHG49vb+2PfFiGD7L3H8uKNR1zy8eoWAnItIKDQWQ2eOSWLz+QM2csGrteYi2JQtMmlpJGx/l5kPtW6mgrJIl6w/y93X7KSw3K2RJsRHMnZzK1YMTCHRVoDMMOPKtWZ3b9QHYzfl7BEfBoBvNQNeln2ueW7yCgp2IeC1vXnHaUAAZktiBZ1dk1Xsff9ymoyktXWDS1pMaPC2/1MYr6w+yeP0Bis4GupS4COZNSeOqQQkEWF10MkN5AWx/2wx0J3fXtncbZB7z1f9aCIl0zXOLV1GwExGv5O0rThsKIE3xl206mqO1C0xac1KDp50psfHyuv0s/eoQxRVmoLugSyTzpqRxxYBurgt02ZvNMLdzGVSaJ1QQGAYDrjMXQ3Qf6rSn8uY/tKSWgp2IeB1fWXFaXwBxGEaj9/H1bTpaorlnxTYUGLzhM27KqeIK/rb2AK9+fZBSmx2AC7tGMT89jcv7dcXqikBnK4Ed75qB7tjW2va4i8yh1oE/g7AOTn1Kb/9DS2op2ImI13HG4fHucm4AKSi1tfq0BX/TnLNifTUw5BZV8Le1+3nt60OUVZqBrm+3aOanp3Fp3y6uCXQndsHGxbD9LagoNNsCgs1FEMNnQ8+LweL85/WVP7TEpGAnIl6nrYfHe5KvzxFzpqZWuEaEBPpcYDhZWM4Lq/fzxneHKK80N/Ud0D2G+elpTL0oHouzg1VlOez+0KzOHfmmtr1jkhnmBt8CEZ2d+5zn8KU/tETBTkS8UFsOj/cGvjhHzBWaWuEaHGD1mcBwvKCcF1bv443vDmOrMgPdoMQO3J+exqQ+cc4PdHlZ5jYlW1+HsjNmmyXA3EB4+GxzQ2GrC7dK+RFf/kOrPVKwExGv05bD472Fr8wRc6Wmqpcni8obvb83BIbs/DJeWLWPtzYcwWY3A93Qnh24b+oFTEiLdW6gs1fCnn+b1bkDq2vbo3vAsJkw5FaI7ua852smX/9Dq71RsBMRr+Otw5laFVhXc96PxqqX1YsNGuLJwHDkdCnPr97HOxuPUGk3F8SM6N2R+9IvYGxqZ+cGuvzD5hFfW16D4hNnGy2QdqlZnUu7BKwuPmqsEf7wh1Z7omAnIl7J24YzfW2Sv6tDaEvej4aql94SGH78XhVXVPHe5qN8tO0YVQ4z0F2c3In56WmMTnZioHPYIfNLszqX+QVwdjV1RDwMvR2GzYAOPZ3zXG3krX9oSf0shtHE2nw/UlhYSExMDAUFBURHR3u6OyIeoapTyxWU2pj75pZ654NNSIv1ukn+rg6hznw/cvLLGgwM7jg6rL73qtq41FjmTUllVLITFycUHYfNr8GmJVB4tLY9aaJZnbvwSgjwzqHN6p8d3vCHVnvTkvyiip1IO+JrVSdv4UurAt2xNYUz3w9PVmYLSm3Me3MLmw6dOe+6QT1ieO5mJwV2h8OcM7fxFXMOnXF2CDqso7mqddgsiE1t+/O4mOaN+gYFO5F2QntRtZ4vrQp0Rwh19vvhicCQdbKIJz7ZU2+oA9h2tKDt71XJKXNV66bFcHp/bXvP0WZ17qKfQFBo6x9fpB4KdiLthC9VnbyNL60KdEcI9aX341x7jxexaEUm/95xjKYmIrXqvTIMOPyNWZ3b/QHYbWZ7SDQMutGsznXp2/LHFWkmBTuRdsKXqk7exlsm+TeHO0KXL70f1XbnFLJoRSaf7jxe0zYuNZZ1WQ2f89ui96q8ALa9ZQa63O9r27sNhhF3QP9rITiiFT0XaRkFO5F2wperLJ7mS6sC3RG6fOn92JldwMKMTL7YbW4jYrHAFf27MXdKKgkxocx7c0vb3qvszWaY27kMKkvNtqBwM8gNnw3dhzrz5Yg0SatiRdqJ6oniDf0S0xy7pvnKqsDDp0r47fs7WJd1qqZtXGpn/vjTAfTs7LyqkTe/H9uO5LMwI5OMPScBM9D9x8AE5k1J5YIuUTW3a9Wq3IpiM8htfAWOba1tj7vIDHMDb4CwDi54VdJetSS/KNiJtCOe3lriXNp6xfkKSm386p1tXNgtmiGJHaiochASaGXLkXz2Hivk6esH+fV7vPnwGRZmZLJqby4AVgv8ZFACc6ekkRofWe99mh1QT+yCjYth+1tQUWi2BQRDv5+agS5xlJkgRZzMb7c7WbNmDU899RSbNm3i2LFjvP/++0yfPt3T3RLxGd606a+2XnGNvGIby78/yfLvTzZ4vT8Gu40HT7MgI7Pm/1OA1cL0wd2ZMzmF5Lj6A121RlflVpbD7g/N6tyRb2rbOyWbYW7QzRDhxH3uRNrIp4JdSUkJgwYNYvbs2VxzzTWe7o6IT/KGvai09YrrtLdFMt/uP8WCjEy+2mcOOwdaLVwztDv3Tkqld2wbhp3zssxtSra+DmVnt0SxBpobCA+fDb0ngNXqhFcg4lw+FeymTZvGtGnTPN0NEWkjbb3iOu1hkYxhGHy9zwx03x44DUBQgIXrhvXg3kmpJHYKb90D2yvNDYQ3vmJuKFwtuod5xNfQ2yGqqxNegetpmkP75VPBrqUqKiqoqKiouVxYWOjB3ohItfZWVXInX9yKpLkMw2BdVh4LMzLZcNCsogUHWLlhRA/unphCj46tDHT5h2HTUtjyGhSfONtogbRLKRlwO8fjx1NocxBdHkRsgPf/0aFpDu2bXwe7J554gscee8zT3RCRc7SHqpKn+NJWJM1lGAarf8hlQUYmWw7nAxAcaOWmEYncPSmFbjGtCCsOO2R+aVbnMr8Azq4jjOxiVuaG3k4OcWcD0rqau3l7QNI0B/HrYPfwww/zwAMP1FwuLCwkMTHRgz0SEfDvqpI38KZFMm1hGAYr9pxkYUYm244WABASaOXmUT25e2IKXaJbcRxX0XHY/BpsWgKFR2vbkyeZc+f6XAEBQWZAenOLzwUkTXMQvw52ISEhhISEeLobInIOf6wqeRtvWCTTWoZh8OXuEyxckcnObHMKTWiQlVtH9eIXE5OJj2phoHM4zDlzG1+BvZ+Ao8psD+sEg282A13nlDp38dWApGkO4tfBTkS8l79UlcR5HA6DL3YfZ0FGFt8fMwNdeHAAt43uxZ3jk4mNbOEf6iWnzFWtmxbD6f217T1Hm2Huop9AUP0h0VcDkqY5iE8Fu+LiYrKysmouHzhwgK1bt9KpUyd69uzpwZ6JSGv4clVJnMfhMPh053EWrchkz/EiACKCA5gxpjc/H59Mp4gW/B8xDDj8jVmd2/0B2G1me0g0DLoRhs2CLn2bfBhfDUia5iA+Few2btzI5MmTay5Xz5+bMWMGS5Ys8VCvRESkNewOg4+35/DsiiwyTxYDEBUSyKyxvZk9LokOLQn95QWw7S0z0OV+X9vebTCMuMM8uzW4+fva+WpA0jQH0ZFiItJm2jNLWqLK7uCj7TksWpHF/twSAKJDA5k9LolZY5KICW9BNSx7sxnmdi6DylKzLSgc+l8Dw++A7kNb3U9vO4KvJbzhHF/9XHAevz1STES8j/bMkuaqsjv4YGsOz63M4kCeGehiwoL4+bgkZozt3eTwZ42KYtj5rhnojm2rbY+7yKzODbwBQmPa3F9fngfq6WkO+rngOarYiUirFZTamFvPlhBg/hD31i0hxL0q7Q7e23yU51bu4/Bps6rWMTyIOyckc9vFvZo/X+3ELjPMbXsLbOZcPAKCoe90czFEz4vBYnHNi5Bm088F51PFTkTcwle3hBD3sFU5eHfTUZ5bmUV2fhkAnSOC+cWEZG69uBcRIc34FVRZBrs/NAPdkW9r2zslmwshBt8CEZ1d9AqkNfRzwbMU7ESk1Xx1SwhxrYoqO29vOMLzq/aRU1AOQGxkCHdPTObmUT0JD27Gr568LHObkq2vQ5l5fBiWALjwSrM6lzQRrFYXvgppLf1c8CwFOxFpNV/dEkJco7zSzj+/O8wLq/dzvNAMdPFRIdw9MYWbRvYkLDig8QeossHef5vVuQNratuje8CwmTDkVoju5roXIE6hnwuepWAnIq3mq1tCiHOV2ey88d1hXly9j5NFFQB0jQ7lnkkp/GxEIqFBTQS6M4dg81LzqK+Sk2cbLXDBZWZ1LnUqWJt4DPEa+rngWVo8ISJt4stbQriTP279UGqr4vVvDvPimv3kFZuBLiEmlHsmp3LD8B6EBDYSxhx2yPzCrM5lfgmc/VUU2QWG3m5+dfCPjef98bNvin4uOFdL8ouCnYi0mTfsmeXN/G3rh5KKKl775hB/W7OfUyXmyQ49OoYxZ3Iq1w7tQXBgI3PfCo/Bltdg01IoPFrbnjzJrM71uQIC/Geozt8++5bQzwXnUbBrgIKdiLibP239UFReyatfH+Lltfs5U2pOgO/ZKZy5k1P56dDuBAU0EOgcDjiwyqzO7fkEDLvZHtYJhtxirm7tnOKeF+FG/vTZi2dpuxMRES/hD1s/FJZXsmT9Qf6+7gAFZWagS4qNYO7kVK4enEBgQ4GuJM9c1bpxMZw5UNvec7RZnbvoJxAU6oZX4Blt+ewLSm2cKrFR5TBwGAalFVXEhAe3i2FcaRsFOxERF/LlrR8KSit5Zf0BXll/gKLyKgCS4yKYPyWN/xjYrf5AZxhw+GuzOrf7Q7CbQ7WERMOgG83qXJe+Tuib989ba+1nn5NfxiMf7uTGkT1ZvP4A67NO1VzXXoZxpfUU7ETEa/nCL++m+OLWD2dKbLyy/gBL1h+kqMIMdGnxkcxLT+PKAd0IsNZzukNZPmx/ywx0uXtq2xOGmNW5/tdCcIRT+ucr89Za89kXlNp4cNl2BiV2OC/UgVnpe2jZdg3jSoMU7ETEK/nKL++m+NLWD6eKK3h53QFe/eogJTZzHtyFXaOYn57G5f26Yj030BkG5Gw2w9yOZVBlni5BULgZ5IbPhu5DndrH6uBz7hCnNwae1nz21cO3M8f05tkVWfU+rq8M4YtnKNiJiNfxpV/eTYkJD+ZP1w5scOsHb3gduUUVvLx2P699c4jSs4Gub7do5qencWnfLucHuopi2PmuGeiObattj+9rhrmBN0BojEv66ktzFlvz2VcP31ZUORp9bG8ewhfPUrATEa/jS7+8myOhQxiLbhridVs/nCws56U1+/nHt4corzSDxIDuMcxPT2PqRfFYLOcEuhO7zDC37S2wFZltASHQb7oZ6BJHwbn3cTJfm7PY0s++evg2pLEtY/DOIXzxDgp2IuJ1vPWXd1vm/MWEez7IVTteUM4Lq/fx5neHaypDgxI7cH96GpP6xNUNdJXlsPsDM9Ad+ba2vVMKDJ8Fg2+B8E5u67svzllsyWdfPXy75Ug+Y1M7nzfHDrxvCF+8i4KdiHgdb/zl7Q9z/nLyy3hh9T7+ueEItrOBbmjPDtw39QImpMXWDXR5WbBpsbldSdkZs80aaG4gPOIO6D0BrI1XlVzBl+Ystkb18O2jH+5k1tgkgPNWxXrLEL54J21QLCJep6DUxrw3tzT4y9vdc+x8faPZo2dK+euqfbyz8QiVdvNH/sjenbhvahpjUjrXBroqG+z9t1mdO7Cm9gFiEmHYDBhyG0R19cArqKs9HFdVvY+d3WFgdxiU2uzEhHnHEL64nzYoFhGf5m0LDnx1zt/hU6X8dVUW7246SpXDDHQXJ3fivvQLuDi5U22gO3MINi+Fza9Bycmz97bABZeZc+dSp4K1kXNf3cxb5yw6kzcN3YtvUbATEa/kDb+8q+fUVZ+H2hBvm7B/MK+E51Zm8d6WbOxnA9241FjmTUllVHJn80YOO/zwhVmdy/wSODt4E9kFht5ufnXo6ZkX0AwKPiL1U7ATEa/lyV/eP55T9/cZwxu9rbdM2N+fW8yzK7L4YGs2Z/McEy6I4770VIb1OrvAofAYbHkNNi2FwqO1d06aaM6d63MFBHjH6xGRllOwExE5x7n76Hn7CsWsk0UsWpHFR9tyagLd5D5xzE9PY0jPjuBwwL4VZnVuzydgmHvVEdYJhtwKw2ZC5xSP9V9EnEfBTkR8kiuPGzt3Tt0r6w6w8KYhgHetUNx7vIhFKzL5945jVC+Dm3pRF+anpzKwRwcoyYP1C2DjYjhzoPaOPUebc+cu+gkEhXqk7yLiGgp2IuJzXL31yLn76JXa7Mx/cwuzxyUxe2wSUaFBdI4Idtucv3ND7OniChZ/dZBPdhyvuc1l/bowb0oa/ROi4fDXsOwV2P0h2M/ODwyJhkE3wrBZ0KWvy/ssIp6hYCciPsUdx43Vt49eqc1ec3ZnxgMTSYmPbNNzNFd9IfbHrhjQlXlT0riogwO2/xM+eAVy99TeIGGIWZ3rfy0ER7ilzyLiOQp2IuJT3LH1iLdsgttQiAWIiwzm+VuGMjz4IHz3MOxYBlVl5pVB4TDgOrM6132oW/rqbq4cihfxZQp2IuJT3HHcmLfso7c2M6/eUBdOOVPLMhjwyWOQu6P2ivi+ZnVu4A0QGuOWPnqCP5wCIuIqCnYi4lPcddyYJ/fR23ToNM8szzwv1F1oOcwtAcuZHrCeKEsZ5AIBIdBvuhnoEkfBj48F80PuGIoX8WUKdiLiU9w5TOruffS+3X+KhSsya1beWi0QZNi40voNtwRmMMyaWXPbA44uRI37BbFjZ0FEZ7f10dN89RQQEXdRsBMRn+Itw6TOYhgGX+8/xYLlmXx74DQAgVYLd/d3MDN4BaG73ybSUQRApRHAF45hvGFPJzB5IgvHDQMfe71t5Y6heBFfpmAnIj6nOcOk3j653jAM1mXlsTAjkw0HzwAQHmDnv1L381P7F4T+sL7mtnkB8Swun8Tb9onk0rFmPpk3vR53cddQvIivUrATEZ/U2DCpN0+uNwyD1T/ksjAjk82H8wFIDsjj0e4bGFf8KQGHzvbZYoW0y2D4LIISJnBNqZ1L/PTA+5bwlhXLIt7KYhjV+5X7v8LCQmJiYigoKCA6OtrT3RERFygotTH3zS31zsOakBbrscn1hmGwcu9JFmRkse1IPgHYuTRoGw90XE9q4TdYOPujOLIrDL3d/OqQ6PZ++oKc/LIGh+K7aVWs+KGW5BdV7ETEr3jb5HrDMPhy9wkWrshkZ3YhXTjNA8GrmRGympjKk1B49obJk2D4HdBnGgRoOLExnlyxLOLtFOxExK94y+T6MyUVfLg1hyVfHeTQqWLGWXfyt5AM0i2bsWKHSiCsEwy5FYbNhM4pbumXv3D3imURX6FgJ+Ik3j5Zv71w9uT6ln6uDofBG98d5o+ffE+o7QzXBazm5uAV9LaeqL1RzzHmvnN9fwKBIS3qjyv77k7e3DcRX6ZgJ+IE3jxZv71x5uT6lnyudofBv3cc45kv99L51Gb+GLicaSHfEWKpAqDQCOebqEsYfcN/EtVzYCtfXfN58/9Jb+6biK/T4gmRNvLWyfrtmTMm1zf3c62yO/hoew6vZGxl6JkvuCVgORdYs2tuu82RzD/sU/nYfjFlhJLxwERS4iPb/iKd0HdP8Oa+iXgrv1488dxzz/HUU09x/PhxBg0axKJFixg5cqSnuyXtmLdN1hfnTK5v6nM9UVjBl7tPsDzjMyYXfczbAV8RFmQDoNQI4QP7GN6wp7PTSK5zX3fM8fPm/5Pe3DcRf+BTwe6tt97igQce4IUXXmDUqFE888wzXHbZZezdu5f4+HhPd0/aKW+ZrC91tXVy/Y8/1/DgAGaPS2JIYgdKbXZ2HMhm2ct/4D9sn3Kd9WDNT1J73EWcvuhWpnzRhSLC631cZ2+gW99cNW/+P+nNfRPxBz4V7P7v//6PO++8k1mzZgHwwgsv8O9//5tXXnmFhx56yMO9k/ZKO+H7p+rPNTw4gIU3DeHv6/azfOUKbg7IYF7AOqIsZWCFKmswRt/pBI38OQGJIwkuq2TIgS1u2UC3oblqv7vyokbv58n/k/p+EXEtq6c70Fw2m41NmzYxderUmjar1crUqVP5+uuvPdgzae+qJ+vXRzvh+67qz/WOi7uy4cPn+M8j8/gs5CFuD/ySKEsZ+x1d+Uf0Lyids4Og6/4GPUeBxVJzlu25/yecfZZtQantvFAH5nDm5sP5Xvt/Ut8vIq7lMxW7vLw87HY7Xbp0qdPepUsX9uzZU+99KioqqKioqLlcWFhY7+1E2sLfDqUXU2jhfn7pWELydx8SQwlYodII4HPHcF63T+Ubx0UYJ62Mtkdy7lRmd2yg29hctd9/vJtP5o/nkQ93et3/SX2/iLiWzwS71njiiSd47LHHPN0NaQd+/Iu8oKyS8OAArFYLZZV2Cko1GdxnVNmw7f6IvJUvkHDmO4acbT5qxPJG1RTesU8ilw517tLQnDBXb6Db2Fy1UpudwjKb157OoJMjRFzHZ4JdbGwsAQEBnDhxok77iRMn6Nq1a733efjhh3nggQdqLhcWFpKYqLMXxTViwoMpsdn57492aX8uX3PmEJUbFlO58VXCbadIAOyGha8DhpPX5xYe2BKLo4GZK56aE9bUXLWIkCCvPp2hJX3TZsYizeczwS44OJhhw4aRkZHB9OnTAXA4HGRkZDB37tx67xMSEkJIiOt2dRf5scbmPD20bLv25/I2DjtkfkHVd38nYN9ygjAIAk4YHfgk6BI6jb+TaWNHUGarYlyxexZDtIQzN2L2ZtrMWKRlfCbYATzwwAPMmDGD4cOHM3LkSJ555hlKSkpqVsmKeJL25/IRhTmw+TUcm5diLcyu+SG4xj6AL8OmMTD9Jm4d3pugALNCFxzonXPC2sNcNf2xJNJyPhXsfvazn5Gbm8sjjzzC8ePHGTx4MJ999tl5CypEPEH7c3kxhwP2r4SNr2Ds/RSLYccKnDYieds+ibXR/8E16eN5dHACgQHnD7l665wwZ/TLm4c59ceSSMv5VLADmDt3boNDryKe5K37c3nzL26XK8mDra/DxsVw5gAAFuBbx4W8XpXO3k6TuCe9H0sHdqs30P2Yt85Xa0u/vH2YU38sibSczwU7EW/ljXOevP0Xt0sYBhz6Cja+At//C+zmMV9FRhjv2ifwhj0d4i5kXnoafxnQjQCrxcMd9gxfGOb01j+WRLyZgp2Ik3jbnCdf+MXtVGVnYNtbZqDL21vTvMNI4bWqKXxkH02vrnH8Mj2Ny/t1xdpOA101Tw1ztqSC7I1/LIl4OwU7ESfyprlY7WJ+kmFA9iZzqHXnMqgqA8BmDeUD+1hetU1mp5FM327R/CU9jUv7dnFZoPO1IW9PDHO2tILsbX8sifgCBTsRJ/OWuVh+PT+pogh2vGtW545vr2k+GZbM8yWTeLd8DEWEM6B7DH9LT2PqRfFYLK6r0PnikLe7hzlbW0H2pj+WRHyBgp2In/LL+UnHd5jVue1vg60IACMghO0xk3ni5Gi+OZMKWBiU2IH70lOZ3Me1gQ58d8jb3cOcbakge8sfSyK+oMXBbsaMGdxxxx1MmDDBFf0RkbPaOrTnN/OTKstg1wdmde7odzXNVR2SWR5xJY8cGsjJnAgAhvbswH1TL2BCWux5gc5VQ6W+OuTt7mFOv64gi3iRFge7goICpk6dSq9evZg1axYzZsyge/furuibSLvljKE9n5+flJdpVue2vg7l+WabNZDSlGm8aZ/Kk3vjsR03ABjRuyP3pV/A2NTO9VboXDlU6suBxZ3DnH5ZQRbxQhbDMIyW3ik3N5fXXnuNpUuXsnv3bqZOncodd9zB1VdfTVCQ935zFhYWEhMTQ0FBAdHR0Z7ujki9CkptzH1zS71VoAlpsS0e2quuVPnE/KQqG+z52KzOHVxb2x7Tk/y+N/PsmYtZsr2MKof5Y+vi5E7MT09jdHL9gQ6c/36ea9/JYtL/b3WD12c8MJGU+MhWP76/KCi1Me/Nho9m89YhaxFv0JL80qo5dnFxcTzwwAM88MADbN68mcWLF3PbbbcRGRnJrbfeyr333ktaWlqrOi/S3jl7aM8n5iedOQiblsKW16Ak12yzWOGCyzlxwc38eV93lq0+jt1RCsDY1M7Mn5LGqOTOTT60q4dK/WbI28V8voIs4iPatHji2LFjfPnll3z55ZcEBARwxRVXsGPHDvr27cv//u//8stf/tJZ/RRpN3x5aK9F7FWQ+YVZnctaDpwdPIjsCsNmcKjXtSzYWMaHy3KwO44BMD4tlvvS0xjeu1Ozn8bV76cCS/NphauI67U42FVWVvKvf/2LxYsX88UXXzBw4EDuv/9+br755pry4Pvvv8/s2bMV7ERawe/nIhXmwObXYPNSKMyubU+ZAsNnk9VhLItWH+KjL7I4O+LK5D5xzEtPY2jPji1+One8nwoszecTFWQRH9biYNetWzccDgc33XQT3333HYMHDz7vNpMnT6ZDhw5O6J5I++OXQ3sOB+xfaVbn9n4Kht1sD+8MQ26FoTPYWxnPohWZ/HvH11TP/J16UTzzpqQxKLFDq5/aXe+nAouIeIMWL5547bXXuP766wkNDXVVn1xGiyfEV+TklzU4tNfNSze8rVdJHmz5B2xabM6jq9ZrLAyfDRddxfe5FSxakcknO47XXH1p3y7MT0+jf/cYp3TDb95PEWmXWpJfWrUq1lcp2Ikv8anVrD9mGHDoK7M6t/tDcJydwxYSA4NvgmGzIP5CdmYXsDAjky92n6i567T+XZk3JY2+Cc7//vTZ91NE2j2Xr4oVEdfzuaG9sjOw7S0z0OXtrW1PGGpW5/pfA8ERbD+az8KlG1j+/UkALBa4ckA35k1Jo0/XKJd1z+feTxGRVlCwE5HWMwzI3myGuZ3LoKrMbA+KgAHXmYEuYTAAWw6fYWHGLlbuNbczsVrgqkEJzJ2cSloX1wU6b+Gqky9ERH5MwU5EWq6iGHa8Ywa649tr2+P7wfBZMPAGCDXnx206dJoFGVms+aE20E0f0p05k1NJiWsfG/e68uQLEZEfU7ATkeY7vsM85mv722ArMtsCQqDfT83qXOJIc2wV+O7AaRZk/MD6rFPmzawWrjkb6HrHRnjqFbhdQantvFAH5ubIDy3brhMXRMSpFOxEpHGVZbDrA7M6d/S72vbOqTBsJgy+BcLNDYMNw+CbfadYkPED3+w/DUCg1cJ1w3pw76RUenYOd3//PczVJ1+4koaPRXyPgp2I1C8v06zObX0dyvPNNmsgXHSVWZ3rPb6mOmcYBuuzTrEwI5PvDpqBLijAwvXDE7l3Ugo9Ora/QFfNV08S0fCxiG9SsBORWlU22POxWZ07uLa2PaYnDJ8Jg2+FqC41zYZhsCYzj4UZmWw6dAaA4AArN45M5O6JKQoA+OZJIho+FvFdCnYiYm4evGkpbHkNSsxFDliscMHlZnUuZQpYA2pubhgGq/bmsiAjk61H8gEICbRy08ie3D0xha4xvreBuav44kkivjx8LNLeKdiJtFf2Ksj8wqzOZS0Hzu5VHtkVht4GQ2dAh8Q6dzEMg+Xfn2RhRiY7sgsACA2ycuuoXvxiQjLx0Qp054oJD+ZP1w5s8OQLbwxIvjp8LCIKdiLtT2EObH4NNi+Fwuza9pQp5qkQfaZBQN3hQYfD4IvdJ1iYkcnuY4UAhAUFcNvoXtw5Ppm4qBB3vgKfk9AhjEU3DfGZky98cfhYREwKdiLtgcMB+1ea1bm9n4JhN9vDO8OQW83qXOeUeu5m8Nmu4yzMyGTPcXN7k4jgAG4f05ufj0uic6QCXXP50skXvjh8LCImBTsRF/L4dhElebDlH7BpsTmPrlqvsebcuYuugsDzw5ndYfDJjmMsWpHJDyeKAYgKCWTm2N7MHptExwj9Yvdnvjh8LCImBTsRF/HYdhGGAYfWm9W53f8Cx9n5UCExMOhGM9DFX1jvXavsDj7ebga6fbklAESFBjJ7bBKzxyYRE64huPbC14aPRcSkYCfiAh7ZLqLsDGz7pxno8n6obe8+zAxz/a6B4Pr3k6uyO/hwaw7PrsziQJ4Z6GLCgrhjXBIzxvQmJkyBrj3ypeFjETEp2Im4gNu2izAMyN5khrmdy6Cq3GwPioAB15mBLmFwg3evtDt4f3M2z67M4vDpUgA6hAdx5/hkbh/dy2smyXt8SFtExEco2Im4gMu3i6gogh3vmIHu+I7a9vh+MGI2DLgBQqMbvLutysGyzUd5bmUWR8+UAdA5Ipg7JyRz68W9iAzxnh8NOgFBRKT5vOent4gfcdl2Ecd3mGFu+9tgMxc1EBAC/a8xq3M9RtQc81Wfiio772w8yvOr9pGdbwa62Mhg7pqQwi0X9yQ82Lt+JHjDCQiqFoqIL/Gun+IifsKp20VUlsGu981Ad3RDbXvnVHPfucE3Q3inRh+ivNLOWxuO8PyqfRwvNIdr46JCuHtiCjeP7ElYcECj9/cUT5+AoGqhiPgaBTuRZmhp1cYp20Xk/mBuU7L1DSjPN9usgeYWJcNnQ+/xjVbnwAx0b3x7mBdW7+NkUQUAXaNDuWdSCj8bkUhokHcGumqePAHBG6qFIiItpWAn0oTWVm1atV1ElQ32fAQbF8PBtbXtMT1h+EwYfCtEdWmyz6W2Kl7/5jAvrtlPXrEZ6BJizEB3w4hEQgK9O9BV8+QJCJ6uFoqItIaCnUgj2lq1afZ2EWcOwqYl5mbCJblmm8UKF1xuVudSpoC16TBWUlHFa98c4m9r9nOqxAZA9w5hzJmcynXDehAcaG26L17EHScgNFSN1XmpIuKLFOykQZo07uKqjb0KMj83585lZQCG2R7ZlfKBt3I85QbOBMWb7325nZjwhoNdUXklr359iJfX7udMqRk4enYKZ+7kVH46tDtBAb4V6Kq5+gSExqqxTe3d5+xqob7fRMQZFOykXpo0bnJJ1aYwBza/CpuWQlFObXvKFBg+m5z4iTz4wfesXZEFZAENv/eF5ZUsXX+Ql9cdoKDM7EvvzuHMnZLG1YMTfDbQ/VhTQ9qtDURNVWOfun6Q285L1febiDiLgp2cR5PGazltjpfDAftXUPnt3wnM+hyLYTebwzpjHXorDJsJnZLN9/7NLU2+9wWllbyy/gCvrD9AUXkVAMlxEcybkspVAxMI9INA92MNDWm3JRA1VY0tLq9yy3mp+n4TEWdSsJPzaNJ4rTbP8SrOha3/MOfPnTlIdQz81nEhr1dNpbjH5fzPiOE1IaSp935fbgkr9x5gyfqDFFWYgS41PpJ5U1L5j4EJBFgbXyXrT9oaiJpTjU2Jj3T5ean6fhMRZ/KZYPeHP/yBf//732zdupXg4GDy8/M93SW/pUnjtVo1x8sw4NB6c+7c7n+Bw3y/SiwRvF05jtft6WQZPczbZhXWCSFNvfc3v/wN5ZUOAPp0iWJ+ehrT+nfF6qZA503zwNoaiJpbjXX1ean6fhMRZ/KZYGez2bj++usZPXo0f//73z3dHb/myS0mvFGzty0pOwPb/mkGurwfatu7D+PkBbcw4dOOlBNy3uP/OIQ09d6XVzq4qFs096Wncmlf9wU68L55YG0NRO5Ycdsc+n4TEWfymWD32GOPAbBkyRLPdqQd8JZfeN6kwaqNYUD2JjPM7VwGVeapDgRFwMDrzZMhEgaTffgM5XzV4ONXh5DG3vvIkAD+Z3p/rh7cHUsTGxO3RHOqcN44D6ytgcjVK26bS99vIuJMPhPsWqOiooKKioqay4WFhR7sje/wll94Xq2iCHa8Ywa64ztq2+P7wYjZMOAGCI2uaW5uCCmvctA1JhSrBRxG7fX9ukXzt9uHkdAx3Kkvo7lVOG+cB+aMQNSqTaSdTN9vIuJMfh3snnjiiZpKn7SMN/zC80rHd5hhbvvbYCs22wJCoN9PYcQd0GNEvcd8NRVC7A4Hj364kzc3HMFWZc6hu6hbFNcP68GEtDjiokLa9N7XV5UDml2F88Z5YM4KRK6eQ9cc+n4TEWfxaLB76KGHePLJJxu9zffff8+FF17Yqsd/+OGHeeCBB2ouFxYWkpiY2KrHao+84ReeV6gsg13vm4Hu6Iba9s6p5qkQg26C8E6NPkRDIWRk7450jgzhPxatx2Y3A93wXh25b2oa41JjnTLk2lBV7ndXXtTsKpy3zgPzp0Ck7zcRcQaPBrtf/epXzJw5s9HbJCcnt/rxQ0JCCAk5f7K6SLPk/gCbFsPW16G8wGyzBsJFV5mBrvf4eqtzDflxCMk6WcS/th3j813H+e7gGQBGJXXivqlpjE7u7LQ5dI3NjZtxpqzR+/64CufN88AUiEREank02MXFxREXF+fJLojUVWWDPR/BxsVwcG1te4ee5ibCQ26DyPhWP3x+WSUvrtnHe5uzqTo7iW5MSmfmp6dxcXLnNnb+fI3NjWvKj6twmgcmIuIbfGaO3eHDhzl9+jSHDx/GbrezdetWAFJTU4mMjPRs58T3nTlobiK85R9Qkmu2WaxwweVmdS5lClgbPqu1Kftzi3l2ZRYfbs3BfjbQjU+LZX56GiN6Nz6M2xaNzY3bciSf8Wmx9Qa/+qpw/jTsKSLir3wm2D3yyCMsXbq05vKQIUMAWLlyJZMmTfJQr8Sn2asg83Nz7lxWBnB2GWpkVxg2A4beDjE92vQUWSeLeHZFFv/allOzynVSnzjmTUljWK+Obet/MzQ2N+6VdQf4ZP54HvlwZ7OrcBr2FBHxbhbDMIymb+YfCgsLiYmJoaCggOjo6KbvIP6pMAc2vwqblkJRTm17yhSzOnfB5RDQtsUAP5woYtGKLD7enkP1d1j6hfHMT09jUGKHNj12SxSU2pj35pYG58Ytusn8A0lVOBER79WS/OIzFTuRNnE4YP8Kc+7c3k/BsJvt4Z1hyK3m/LlOrV+oU+37Y4UsWpHJJzuO17Rd2rcL89PT6N89ps2P31LNnRunICci4h8U7MS/FefC1n+Y8+fOHKxt7zXWrM5ddBUEtn3l9K6cAhZmZPL5rhM1bdP6d2XulFT6JTg/0LXkzFbNjRMRaT8U7MT/GAYcWm/Ondv9L3CcXUAQEgODbzKP+Ypv3d6I59p+NJ+FGVks/94MdBYLXDmgG/OmpNGna5RTnuNcrTmz1Zlz41oSKkVExL0U7MR/lJ2Bbf80A13eD7Xt3YeZ1bl+10Cwc47k2nokn4UZmazYcxIAqwWuGpTA3MmppHVxTaADz5/ZWl+oHJ8Wy3//pB8WoLNCnoiIRynYiW8zDDi60Qxzu96DqnKzPSgCBl5vVucSBjvt6TYdOsOCjEzW/GBuiWK1wPQh3ZkzOZWUONdvu+PMM1tbWnlrKFSuzczjkQ93MqRnR7YfyW+0cigiIq6lYCe+qaLIPK9142I4saO2Pb4fjJgNA26AUOetfP7uwGkWZmSyLssMNQFWC9ecDXS9YyOc9jxNcdaZra0Zzm0sVK7POsXssUk8uyLLLZVDERGpn4Kd+JZj283q3I53wFZstgWEQP9rzOpc4sgWHfPVGMMw+Gb/aRZk/MA3+08DEGi1cN2wHtw7KZWenZ0zrNsSzjiztbXDuU2FyooqR83jtKRyKCIizqNgJ97PVgq73jcDXfbG2vbOqebcuUE3QbjzTm8wDIOv9p1iwfJMvjtoBrqgAAvXD0/k3kkp9Ojo/kBXzRlntrZ2OLepUBkSaK35d3MrhyIi4lwKduJxDc71yv3BDHPb3oDyAvPG1iBzi5Lhs6H3OKdV58AMdGsy81iYkcmmQ2cACA6w8rMRidwzKcUr5o0548zW1g7nNhYqx6Z2ZsuR/JrLzakcupNW8opIe6FgJx517lyvYCq5r/sefh66ipDsr2tv2KGnOdQ65FaIjHdqHwzDYNXeXBZkZLL1bDgJCbRy08ie3D0xha4xoU59vqY0FULaui9da4dzGwqVY1M7M2tsEvPf3AI0v3LoLq2ZTygi4qsU7PyQr1QnfjzXK9FygpsDVnB9wGpiTxUCYFisWC64HIbfYR73ZbU28YgtYxgGGd+fZOGKTLYfNSuCoUFWbhnVi7smJBMf7d5AB80PIW3Zl64tw7k/DpX5ZTYqKh18tf8U89/cQqnN3qLKoTt4ensYERF3U7DzM75UncgrLCVs36csDcpgYsD2mvbjRkf+aZ/M9NkP0zv5Aqc/r8Nh8MXuEyxakcmuHDNEhgUFcNvoXtw5Ppm4qLafRNEa7gohbR3O/XGoLCi10SU6lKkXxnvliRbO3B5GRMQXKNj5EZ+pThRkw+ZXSdywhJeCa89UXW0fyOv2dDIcQ7ETwKTAOKc+rcNh8Nmu4yzMyGTP8SIAIoIDuH1Mb34+LonOkSEUlNrYd7LYI9VOd4YQZx0z5swTLVzBWdvDiIj4CgU7P+LV1QmHA/atMBdD/PApGA6CgTwjmnfsE3nTPoXDRpc6d3HWBHy7w+CTHcdYtCKTH06YW6REhgQyc0xv7hiXRMcI8z3xdLXT3SHE20OZMzhjexgREV+iYOdHvLI6UXwStvwDNi2B/EO17b3GUjpwBr/ZksCKrMLz7uaMCfh2h8HH23NYtCKLrJNmoIsKDWT22CRmj00iJrz2l7o3VDsVQpzPGdvDiIj4EgU7P+I1wcAw4OA6szr3/UfgOBsoQ2Ng0M0wfBbE9SEc+J+UsjZt3VGfKruDD7fm8NzKLPbnlQAQExbEHeOSmDGmNzFh578P3lDtVAhxPmdsDyMi4ksU7PyIx4NB6WnY9k8z0J3KrG3vPtzcd67fTyG47ua+zprrBVBpd/D+lmyeW5nFoVOlAHQID+LO8cncPrpXo8HWE9XO+lYvezKE+Mpq6pZy5v8xERFvp2DnRzxSnTAMOLrRDHO73oOqcrM9KAIG3mBW57oNarLfbembrcrBss1HeW5lFkfPlAHQKSKYO8cnc9voXkSGNP3f3N3Vzobm8z157UCPhBBPzy90tfYwn1BEBMBiGIbh6U64S2FhITExMRQUFBAd7bwD4r1NdeXFpcGgogi2vw0bF8OJHbXtXfqb1bkB10Ooa9/jiio772w8yvOr9pGdbwa62MhgfjEhmVsv7kV4cPP/bikotTHvzS0NVjudOceuoNTG3De31Dv06+zn8sX+iIhIXS3JL6rY+SGXVieObTerczveAZu5IIHAUOh3jVmd6zHCqcd81ae80s7bG4/w/Kp9HCswK4RxUSHcPTGFm0f2JCw4oMWP6c5qpzfM5/Pm/oiISOsp2EnTbKWw630z0GVvrG3vnGZW5wbdCOGdXN6N8ko7b3x7mBdW7+NkUQUAXaJDuGdiCjeO7EloUMsD3Y+5ay6Wt61e9rb+iIhI6ynYScNyf4BNi2Hr61BuHrmFNQguusoMdL3HuaQ6d+4k/vCgAP694xgvrN5PXrEZ6BJiQrlncirXD+vR5kD3Y+6Yi+U1q5fP8rb+iIhI6ynYSV1VNtjzkTl37uDa2vYOPWHYLBhyK0TGu+zp65vEHxRgodJuTgXt3iGMOZNTuXZYd0ICnRfo3Mnjq5e9vD8iItJ6WjwhptMHYPNS2PwalJ79BW+xwgXTzLlzKelgtbq0C41N4g8NtPLgtAu59eJeBAW4th/ukJPf8P593c5ZheqObUha0h8REXEvLZ6Q5rFXQebn5ty5rAzgbMaP6gZDZ8DQ2yGmu9u6c/BUaYOT+MurHExIi/OLUAfNn8/nrm1ItNebiIh/ULBrjwqyYctrsGkpFOXUtqekm3PnLrgcAtz3X6OgtJLFXx3gb2v3N3o7f5vE39R8Pncfc6a93kREfJ+CXXvhcMC+FWZ17odPwXCY7eGx5ry5YTOgU7Jbu5RfauPv6w6wZP1Biiqqmrx9e5vEr21IRESkpRTs/F3xSdjyD9i0BPIP1bb3GmfOnbvoKggMcWuXTpfYeHntfpZ+dZASmx2APl2i+Pn4JP61NZu1WafOu097nMSvbUhERKSlFOz8kWHAwXVmde77j8BxNgCExsCgm81AF9fH7d06VVzBS2v389rXhyg9G+gu6hbN/CmpXNavK1arhbGpsTqw/SxtQyIiIi2lYOdPSk/Dtn+age5UZm179+Hm3Ll+P4XgcLd3K7eogpfW7OMf3xymrNIMdP27RzN/ShpTL+qC1Vq7F54m8dfSNiQiItJSCna+zjDg6AYzzO16H6rMI7YIioCBN5jVuW6DPNK1E4XlvLh6P69/e4iKKnNO36AeMcxPT2PKhfFYGtjcWJP4Te485kxERPyDgp2vKi+EHW+bGwmf2Fnb3qW/WZ0bcD2ENm+vPmfvk3asoIwXVu3jzQ1HsJ0NdEN6duC+9DQmXhDXYKCT8/ljBdMd+/KJiLRXCna+5tg2M8zteAdsxWZbYCj0u8YMdD2Gt+iYL2fuk5adX8bzq7J4e8NRbHYz0A3v1ZH7pqYxLjVWga6V/KmC6a59+URE2iudPOELbKXmMOvGVyB7Y2175zQzzA26EcI7tfhhGzvpYUJabLP3STtyupS/rsri3U1Ha47+GpnUifvT0xid0lmBrp2rrtDZDYPff7SrwVXPzt6XT0TEX+jkCX+Ru9eszm17A8oLzDZrkLlFyfDZ0Htci6pz52rrPmmHTpXw3Mos3tucTZXDDHRjUjozPz2Ni5M7t7pf4j9+XKH7+4zh9YY60L58IiLOomDnbaoqzC1KNi6GQ+tq2zv0MhdCDL4VIuOc8lSt3Sdtf24xz63cxwdbs7GfDXTj02KZn57GiN4trxyKfzr35IzqBTQN0b58IiJtp2DnLU7vNzcR3vIPKD1b1bBYoc8VZqBLngJW556T2tJ90rJOFvPsikz+tS2Hs3mOSX3imDcljWG9Ojq1b+L7zq0IhwQ2/v9X+/KJiLSdgp0n2avM4702vmIe91UtKsE84mvIbRDT3WVP39x90n44UcSiFVl8vD2H6hmZ6RfGMz89jUGJHVzWP/Ft51aEtxzJZ2xqZ9Z70ckiWqErIv5Gwc4TCrJh86uweSkUHTvbaIHUdHPuXNplEOD6j6apfdKOFZbz2/d38snOYzWB7pK+XbgvPY3+3WNc3j/xbedWhF9Zd4CFNw0BqBPuPLUvn1boiog/8olVsQcPHuT3v/89K1as4Pjx4yQkJHDrrbfyu9/9juDg5v8y8OiqWIfDrMptfMWs0hln5xuFx8KQW2HYTOiU5N4+nVVdtajeJy2vuILF6w/y2a7jNbeZ1r8rc6ek0i9BgU6ap6DUxrw3t9T5oyE8OIDZ45IYk9yZ0KAAYsI8sy+fs1aEi4i4g9+tit2zZw8Oh4MXX3yR1NRUdu7cyZ133klJSQlPP/20p7vXuOKT5ry5TYsh/3Bte+/x5ty5C/8DAkM81z9q90nbcbSAJz7dw/LvTwDmgtsrBnRj3pRULuzqQ9vDiFeoryJcarOz/Ug+t4zsSTcPVsXauiJcRMRb+USwu/zyy7n88strLicnJ7N3716ef/557wx2hgEH15rVue8/BsfZuUahMTD4FrM6F9fHo138sa1H8lmYkcmKPScBM9BdNTCBeVNSSesS5eHeiS/z1pMzWrsiXETE2/lEsKtPQUEBnTo1vrVGRUUFFRUVNZcLCwtd2yl7JXz3krlVyanM2vYeI8y5c/1+CkHeM3dn06EzLMjIZM0PuQBYLTB9cHfunZxKanykh3sn/sIbT85o6YpwERFf4ZPBLisri0WLFjVZrXviiSd47LHH3NQrwBoIm5aaoS44EgbeAMNmQbeB7utDM3x34DQLMzJZl2UORQVYLfx0SHfmTE4lKTbCw70Tcb3mrggXEfE1Hl088dBDD/Hkk082epvvv/+eCy+8sOZydnY2EydOZNKkSbz88suN3re+il1iYqJrF0/sfA/K82HA9RDiXcOYX+87xYKMH/hm/2kAAq0Wrh3agzmTU+nZOdzDvRNxr5z8sgZXhHty/p+IyLlasnjCo8EuNzeXU6fqP2KoWnJycs3K15ycHCZNmsTFF1/MkiVLsLZww16fPSu2DQzD4Kt9p1iQkcl3B8xAFxRg4bphidw7KYXETgp0raU90HzfuSvCvWH+n4jIuXxmVWxcXBxxcc07His7O5vJkyczbNgwFi9e3OJQ194YhsHazDwWZGSy6dAZAIIDrPxsRCJ3T0qhuyoSbaI90PyDN87/ExFpC5/Yxy47O5tJkybRq1cvli5dSkBAQM11Xbt2bfbjtIeKnWEYrPohlwXLM9l6JB+A4EArN4/syd0TU+gaE+rZDjqBpytl2gNNRETcyWcqds315ZdfkpWVRVZWFj169KhznQ/kUrcwDIMVe06yMCOTbUcLAPNszltG9eLuicnER/t+oAPvqJRpDzQREfFWPhHsZs6cycyZMz3djSZ5opLkcBh8+f0JFmZksivH3M4lLCiA20b34ufjk4iP8o9AB+b7e26oAzNMPbRsu9sqZf6wB5qnq54iIuIaPhHsfIG7K0kOh8Hnu46zICOTPceLAPO4pttG9+LO8cnERnr2NAtX8JZKma/vgeYNVU8REXENrUBwgqYqSQWlNqc9l91h8PH2HKYtWMs9r29mz/EiIkMCmTM5hXUPTuHhaRf5ZagD76mUVe+BVh9v3wPNnf9XRUTE/VSxcwJ3VJKqA92iFVlknSwGICo0kFljk5g9tjcd2sEwmrdUyuo7AxVq90Dz5iFNb6l6ioiIayjYOYErK0lVdgf/2pbDsyuy2J9XAkB0aCB3jEtm5tjexIR597CfM3nTaQHeegZqU7yl6ikiIq6hYOcErqgkVdodfLAlm+dWZnHwVCkAHcKD+Pm4JGaM6e3187hcwdsqZb64B5q3VD1FRMQ1FOycwJmVJFuVg/c2H+W5VVkcOV0GQKeIYH4+PonbR/cmMqR9f2S+WinzFt5U9RQREefziQ2KncWVGxS39dzJiio77246yl9X7iM73wx0sZHB/GJCMreM6kVEOw904jw6I1VExLf4zFmx7ubqkydac+5keaWdtzce4flV+zhWUA5AXFQId50NdGHBAY3eX6Q1dEaqiIjv8LuTJ3xFS+ZclVfaefO7w7yweh8nCisA6BIdwj0TU7hxZE9CgxToxHV8cX6giIg0TcHOjQpKbRw9U8a7m4/y4dYcTpeYe4Z1iwnl3kkpXD88UYFOREREWk3Bzk2yThZx56sbOZBXWtMWEmjlvvQ07hifREigAp2IiIi0jYKdixVXVPHS6n38dfU+qux1pzNWVDn4Zv8pbhnVU8FOmqWpM151BqyISPumYOciheWVvPrVQV5ed4D80oY3fdVu/9JcTZ3xqjNgRUREZ8U6WUFZJQuWZzLuTyt4+osfyC+tpHsTv1S12780pakzXnPyy3jw3W06A1ZEpJ1Txc6JyivtpP95NXnF5irX1PhI5k1J5aKu0Vz6zJoG76fd/qUpTZ3xeqbExtqsUw1er6qwiEj7oGDnRKFBAVw5oCvf7D/NvPRUpvXvRoDVQkGpTbv9S5s0dcZrYXlVo9erKiwi0j4o2DnZg9MuJDQwAKvVUtPmbWeciu9p6ozXyNDGF9+oKiwi0j4o2DlZeHD9b6nOOJW2aOyM17GpnTlZWMHY1M6sr2c4VlVhEZH2Q4sn3CgmPJiU+EgG9+xISnykQp00W3XVd0JabJ328WmxzBqbxIPLtjNrbBJjUzufd72qwiIi7YfOihXxIeee8RoZGsj/e38HX35/kvDgAGaPS2JIYgcqqhx0CAsiJT6SLtGhnu62iIi0gc6KFfFT9Z3x+tjV/amoMudvPrsiC6idv6lQJyLSvijYifg4zd8UEZFqCnYifqC+Sp6IiLQ/WjwhIiIi4idUsWuHdFC8iIiIf1Kwa2d0ULyIiIj/0lBsO9LUQfI6KN7/FZTa2HeymC2Hz7Avt1ifuYiIn1HFrh1p6iB5dx4Ur+Fg91O1VkTE/ynYtSNNHSTvroPiFTDcr6lq7aKbhihYi4j4AQ3FtiNNHSTvjoPiNRzsGc2p1oqIiO9TsGtHqg+Sr4+7DopXwPAMb6nWioiIaynYtSMNHSQ/wY0HxStgeIY3VGtFRMT1NMeunfH08VMKGJ5RXa1dU0+11F3VWhERcT1V7NqhmPBgUuIjGdyzIynxkW6dNO8Nw8HtkTdUa0VExPUshmEYnu6EuxQWFhITE0NBQQHR0dGe7k67lZNfxkPLttepHlUHjG5aFetS1dvMeKJaKyIirdOS/KKhWHE7Tw8Ht2cx4XqfRUT8mYKdeIQChoiIiPNpjp2IiIiIn/CZYPeTn/yEnj17EhoaSrdu3bjtttvIycnxdLdEREREvIbPBLvJkyfz9ttvs3fvXpYtW8a+ffu47rrrPN0tEREREa/hs6ti//WvfzF9+nQqKioICmre3mdaFSsiIiK+piX5xWcqdj92+vRpXn/9dcaMGdPsUCciIiLi73wq2D344INERETQuXNnDh8+zIcfftjo7SsqKigsLKzzJSIiIuKvPBrsHnroISwWS6Nfe/bsqbn9r3/9a7Zs2cIXX3xBQEAAt99+O42NJD/xxBPExMTUfCUmJrrjZYmIiIh4hEfn2OXm5nLq1KlGb5OcnExw8Pn7nR09epTExES++uorRo8eXe99KyoqqKioqLlcWFhIYmKi5tiJiIiIz/CZkyfi4uKIi4tr1X0dDgdAneB2rpCQEEJCQlr1+CIiIiK+xidOnvj222/ZsGED48aNo2PHjuzbt4//+q//IiUlpcFqnYiIiEh74xOLJ8LDw3nvvfdIT0+nT58+3HHHHQwcOJDVq1erIiciIiJylk9U7AYMGMCKFSs83Q0RERERr+YTFTsRERERaZqCnYiIiIifULATERER8RMKdiIiIiJ+QsFORERExE8o2ImIiIj4CQU7ERERET+hYCciIiLiJxTsRERERPyEgp2IiIiIn1CwExEREfETCnYiIiIifkLBTkRERMRPKNiJiIiI+AkFOxERERE/oWAnIiIi4icU7ERERET8hIKdiIiIiJ9QsBMRERHxEwp2IiIiIn5CwU5ERETETyjYiYiIiPgJBTsRERERP6FgJyIiIuInFOxERERE/ISCnYiIiIifULATERER8RMKdiIiIiJ+QsFORERExE8EeroD4r8KSm3kFdsoLK8kOiyI2IhgYsKDPd0tERERv6VgJy6Rk1/Gg8u2szYzr6ZtQlosf7p2IAkdwjzYMxEREf+loVhxuoJS23mhDmBNZh4PLdtOQanNQz0TERHxbwp24nR5xbbzQl21NZl55BUr2ImIiLiCgp04XWF5ZaPXFzVxvYiIiLSOgp04XXRoUKPXRzVxvYiIiLSOgp04XWxkMBPSYuu9bkJaLLGRWhkrIiLiCgp24nQx4cH86dqB54W7CWmxPHntQG15IiIi4iLa7kRcIqFDGItuGkJesY2i8kqiQoOIjdQ+diIiIq6kYCcuExOuICciIuJOPjcUW1FRweDBg7FYLGzdutXT3RERERHxGj4X7H7zm9+QkJDg6W6IiIiIeB2fCnaffvopX3zxBU8//bSnuyIiIiLidXxmjt2JEye48847+eCDDwgPD2/WfSoqKqioqKi5XFhY6KruiYiIiHicT1TsDMNg5syZ3H333QwfPrzZ93viiSeIiYmp+UpMTHRhL0VEREQ8y6PB7qGHHsJisTT6tWfPHhYtWkRRUREPP/xwix7/4YcfpqCgoObryJEjLnolIiIiIp5nMQzD8NST5+bmcurUqUZvk5yczA033MBHH32ExWKpabfb7QQEBHDLLbewdOnSZj1fYWEhMTExFBQUEB0d3aa+i4iIiLhDS/KLR4Ndcx0+fLjO/LicnBwuu+wy3n33XUaNGkWPHj2a9TgKdiIiIuJrWpJffGLxRM+ePetcjoyMBCAlJaXZoU5ERETE3/nE4gkRERERaZpPVOzO1bt3b3xgBFlERETErXwy2LVWdRjUfnYiIiLiK6pzS3OKWu0q2BUVFQFoPzsRERHxOUVFRcTExDR6G59YFessDoeDnJwcoqKi6myd4myFhYUkJiZy5MgRrb71Y/qc2wd9zu2HPuv2wRc/Z8MwKCoqIiEhAau18eUR7apiZ7Va3bqKNjo62mf+00jr6XNuH/Q5tx/6rNsHX/ucm6rUVdOqWBERERE/oWAnIiIi4icU7FwgJCSERx99lJCQEE93RVxIn3P7oM+5/dBn3T74++fcrhZPiIiIiPgzVexERERE/ISCnYiIiIifULATERER8RMKdi508OBB7rjjDpKSkggLCyMlJYVHH30Um83m6a6Jk/3hD39gzJgxhIeH06FDB093R5zoueeeo3fv3oSGhjJq1Ci+++47T3dJnGzNmjVcddVVJCQkYLFY+OCDDzzdJXGyJ554ghEjRhAVFUV8fDzTp09n7969nu6WSyjYudCePXtwOBy8+OKL7Nq1i7/85S+88MIL/Pa3v/V018TJbDYb119/Pffcc4+nuyJO9NZbb/HAAw/w6KOPsnnzZgYNGsRll13GyZMnPd01caKSkhIGDRrEc8895+muiIusXr2aOXPm8M033/Dll19SWVnJpZdeSklJiae75nRaFetmTz31FM8//zz79+/3dFfEBZYsWcL9999Pfn6+p7siTjBq1ChGjBjBs88+C5jHEiYmJjJv3jweeughD/dOXMFisfD+++8zffp0T3dFXCg3N5f4+HhWr17NhAkTPN0dp1LFzs0KCgro1KmTp7shIk2w2Wxs2rSJqVOn1rRZrVamTp3K119/7cGeiUhbFRQUAPjl72MFOzfKyspi0aJF3HXXXZ7uiog0IS8vD7vdTpcuXeq0d+nShePHj3uoVyLSVg6Hg/vvv5+xY8fSv39/T3fH6RTsWuGhhx7CYrE0+rVnz54698nOzubyyy/n+uuv58477/RQz6UlWvM5i4iId5szZw47d+7kn//8p6e74hKBnu6AL/rVr37FzJkzG71NcnJyzb9zcnKYPHkyY8aM4aWXXnJx78RZWvo5i3+JjY0lICCAEydO1Gk/ceIEXbt29VCvRKQt5s6dy8cff8yaNWvo0aOHp7vjEgp2rRAXF0dcXFyzbpudnc3kyZMZNmwYixcvxmpVkdRXtORzFv8THBzMsGHDyMjIqJlI73A4yMjIYO7cuZ7tnIi0iGEYzJs3j/fff59Vq1aRlJTk6S65jIKdC2VnZzNp0iR69erF008/TW5ubs11+ovfvxw+fJjTp09z+PBh7HY7W7duBSA1NZXIyEjPdk5a7YEHHmDGjBkMHz6ckSNH8swzz1BSUsKsWbM83TVxouLiYrKysmouHzhwgK1bt9KpUyd69uzpwZ6Js8yZM4c33niDDz/8kKioqJp5sjExMYSFhXm4d86l7U5caMmSJQ3+AtDb7l9mzpzJ0qVLz2tfuXIlkyZNcn+HxGmeffZZnnrqKY4fP87gwYNZuHAho0aN8nS3xIlWrVrF5MmTz2ufMWMGS5YscX+HxOksFku97YsXL25yyo2vUbATERER8ROa8CUiIiLiJxTsRERERPyEgp2IiIiIn1CwExEREfETCnYiIiIifkLBTkRERMRPKNiJiIiI+AkFOxERERE/oWAnIiIi4icU7ERERET8hIKdiIiIiJ9QsBMRaaXc3Fy6du3KH//4x5q2r776iuDgYDIyMjzYMxFpryyGYRie7oSIiK/65JNPmD59Ol999RV9+vRh8ODBXH311fzf//2fp7smIu2Qgp2ISBvNmTOH5cuXM3z4cHbs2MGGDRsICQnxdLdEpB1SsBMRaaOysjL69+/PkSNH2LRpEwMGDPB0l0SkndIcOxGRNtq3bx85OTk4HA4OHjzo6e6ISDumip2ISBvYbDZGjhzJ4MGD6dOnD8888ww7duwgPj7e010TkXZIwU5EpA1+/etf8+6777Jt2zYiIyOZOHEiMTExfPzxx57umoi0QxqKFRFppVWrVvHMM8/w2muvER0djdVq5bXXXmPt2rU8//zznu6eiLRDqtiJiIiI+AlV7ERERET8hIKdiIiIiJ9QsBMRERHxEwp2IiIiIn5CwU5ERETETyjYiYiIiPgJBTsRERERP6FgJyIiIuInFOxERERE/ISCnYiIiIifULATERER8RMKdiIiIiJ+4v8Dj0na9AP4NwUAAAAASUVORK5CYII=", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "lm = LinearRegression(fit_intercept=False)\n", + "lm.fit(x.reshape(-1, 1),y.reshape(-1, 1))\n", + "print([lm.coef_, lm.intercept_])\n", + "\n", + "x_space = np.linspace(np.min(x), np.max(x))\n", + "sns.scatterplot(x=x, y=y)\n", + "plt.plot(x_space, lm.predict(x_space[:, np.newaxis]), label='Fit')\n", + "plt.plot(x_space, true_slope*x_space, label='Truth')\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.title('Linear Regression')\n", + "plt.tight_layout()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Polynomial Fit\n", + "\n", + "The above simple linear regression worked quite well, given the sparsity of the data.\n", + "\n", + "Let's now try some data with a more complicated shape and generate data from a polynomial function. The NumPy library provides a number of [convenience functions for polynomial](https://numpy.org/doc/stable/reference/routines.polynomials.html). In particular, we can specify a list of coefficients and then use ```np.polynomial.polynomial.Polynomia``` to \"convert\" this into a corresponding polynomial function." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": [], + "source": [ + "def generate_data_from_func(func, noise, n_samples):\n", + " x = 5*np.random.rand(n_samples) - 2.5\n", + " y = func(x) + norm.rvs(scale=noise, size=n_samples)\n", + " #return np.transpose([x]), y\n", + " return x,y" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "True degree of polynomial: 3\n" + ] + } + ], + "source": [ + "true_coefficients = [0, 1, 8, -8]\n", + "true_degree = len(true_coefficients) - 1\n", + "print('True degree of polynomial: {}'.format(true_degree))\n", + "\n", + "true_poly = np.polynomial.polynomial.Polynomial(true_coefficients)\n", + "x, y = generate_data_from_func(true_poly, 5, 25)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.2513288 -0.92424404 1.50522857 2.00048027 -1.56661735 2.32554123\n", + " -0.26011933 0.60682477 0.9031809 -1.64544008 -2.44007169 -1.75932259\n", + " -1.71453087 0.5592937 -2.37104837 -0.36964595 -1.22398804 1.88411752\n", + " -2.40492839 1.82486903 -0.3881358 1.32519684 -1.66128279 0.24652489\n", + " 0.80629894]\n" + ] + } + ], + "source": [ + "print(x)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.scatterplot(x=x, y=y)\n", + "plt.xlabel('x', size=15)\n", + "plt.ylabel('y', size=15)\n", + "plt.title('Polynomial of degree {}'.format(true_degree))\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Now we fit the polynomial. Before we can use the linear regression above, we need to create the relevant features for the polynomial, corresponding to the respective power of the polynomial, but also their (potential) interaction. This means for two variables $x_1, x_2$, we need to look at the following higher order terms: $x_1^2, x_1 \\cdot x_2, x_2^2$.\n", + "\n", + "More information can be found in the [documentation](https://scikit-learn.org/stable/modules/preprocessing.html#polynomial-features) and the [class description](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html) of the sklearn package." + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "# create polynomial features: define method\n", + "\n", + "degree = true_degree + 10 #this is a parameter you need to set (hyperparameter)\n", + "polynomial_features = PolynomialFeatures(degree=degree, include_bias=True)\n", + "\n", + "# now take the input features (x) and \"transform\" then according to the above specification\n", + "x_poly = polynomial_features.fit_transform(x.reshape(-1, 1))" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0.00000000e+00 3.77599406e+00 -1.17106404e+01 1.34687995e+01\n", + " 5.01438825e+01 -6.02634021e+01 -3.70942434e+01 5.05172394e+01\n", + " 1.13420607e+01 -1.83594716e+01 -1.43165319e+00 3.00477707e+00\n", + " 5.75438986e-02 -1.81672078e-01]\n" + ] + } + ], + "source": [ + "# now we can do the linear regression again:\n", + "\n", + "lm = LinearRegression(fit_intercept=True)\n", + "lm.fit(x_poly, y)\n", + "print(lm.coef_)" + ] + }, + { + "cell_type": "code", + "execution_count": 53, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x_space = np.linspace(np.min(x), np.max(x), 101)\n", + "x_space_poly = polynomial_features.fit_transform(x_space[:, np.newaxis])\n", + "sns.scatterplot(x=x,y=y,label='Data')\n", + "\n", + "plt.plot(x_space, lm.predict(x_space_poly), label='Linear Regression', color='black')\n", + "\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that this fit does not describe the data too well, in particular, it's too \"wiggly\". We can therefore assume that the model is prone to overfitting.\n", + "We can now follow two avenues: Either adjust the degree of the polynomial used in the fit to the data and/or apply some regularisation.\n", + "\n", + "Here, we will use [Ridge](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.RidgeCV.html) and [Lasso](https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html) approaches, making use of the cross-validation feature to give us the best set of parameters when exploring a wide range of regularisation parameters" + ] + }, + { + "cell_type": "code", + "execution_count": 61, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0. -0.2968025 0.32205431 -0.43769424 0.44309384 -0.5667587\n", + " 0.49217658 -0.62464414 0.34366079 -0.41388409 -0.10927938 0.18683133\n", + " 0.00659839 -0.01739491]\n" + ] + } + ], + "source": [ + "ridge_regressor = RidgeCV(fit_intercept=True,alphas=[0.1, 0.5,1,2,5,10,15,20,100])\n", + "ridge_regressor.fit(x_poly, y)\n", + "print(ridge_regressor.coef_)" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[ 0. -0. 0. -0. 0. -0.74469888\n", + " 1.24288479 -1.25077109 0. -0. -0.04913807 0.10036106\n", + " 0.00305207 -0.01149239]\n" + ] + } + ], + "source": [ + "lasso_regressor = LassoCV(fit_intercept=True, max_iter = 100000000, eps=0.01, alphas=[0.1, 0.5,1,2,5,10,15,20,100])\n", + "lasso_regressor.fit(x_poly, y)\n", + "print(lasso_regressor.coef_)" + ] + }, + { + "cell_type": "code", + "execution_count": 63, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x_space = np.linspace(np.min(x), np.max(x), 101)\n", + "x_space_poly = polynomial_features.fit_transform(x_space[:, np.newaxis])\n", + "sns.scatterplot(x=x,y=y,label='Data')\n", + "\n", + "plt.plot(x_space, lm.predict(x_space_poly), label='Linear Regression', color='black')\n", + "plt.plot(x_space, ridge_regressor.predict(x_space_poly), label='LR + Ridge')\n", + "plt.plot(x_space, lasso_regressor.predict(x_space_poly), label='LR + Lasso')\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that the regularised fit is much smoother and closer to what we would expect from the process underlying the data.\n", + "In this case, Lasso and Ridge regressions have resulted in very similar fits, but this does not always have to be the case." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Linear Regression with Outliers\n", + "\n", + "In the next step, we want to investigate how regularisation can help us in data with outliers.\n", + "Outliers are a common issue when dealing with \"real-world\" data. They arise from two sources: Either there is something wrong with the way we acquire the data. For example, an instrument may have a glitch, is miscalibrated or faulty. If data have to be entered manually, we may, for example, make a mistake in this process. ON the other hand, an outlier may represent a rare but genuine event. For example, in regions with moderate weather, we may typically experience low to moderate wind speeds. However, in rare events, a hurricane may occur. In this case, the outline is a genuine data point, albeit not being described by the bulk of the data.\n", + "\n", + "Dealing with outliers requires great care and we need to investigate the source of the outlier. If the outlier is due to an error in the way the data are acquired, we can, for example, remove these data points from our dataset, *provided* we have fixed the source of the errors. If the outliers are due to genuine events, we need to treat them differently and discuss for the concrete case which steps are most appropriate.\n", + "\n", + "In our exercise here, we want to investigate how the regularisation methods we have encountered so far deal with outliers.\n", + "\n", + "In a first step, we generate data similar to what we did in the beginning and then add one (but extreme) outlier." + ] + }, + { + "cell_type": "code", + "execution_count": 64, + "metadata": {}, + "outputs": [], + "source": [ + "def generate_test_data(slope, noise, n_samples):\n", + " x = norm.rvs(size=n_samples)\n", + " y = slope * x + norm.rvs(scale=noise, size=n_samples)\n", + " return x,y" + ] + }, + { + "cell_type": "code", + "execution_count": 65, + "metadata": {}, + "outputs": [], + "source": [ + "true_slope = 1.0\n", + "noise_level = 1\n", + "n_samples = 100\n", + "\n", + "x, y = generate_test_data(true_slope, noise_level, n_samples)" + ] + }, + { + "cell_type": "code", + "execution_count": 66, + "metadata": {}, + "outputs": [], + "source": [ + "# add one outlier \n", + "x_1=np.append(x,[2.0])\n", + "y_1=np.append(y,[-50.0])" + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "sns.scatterplot(x=x_1, y=y_1)\n", + "plt.xlabel('x', size=15)\n", + "plt.ylabel('y', size=15)\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In a first step, we try the standard linear regression - but do not expect this to do well." + ] + }, + { + "cell_type": "code", + "execution_count": 70, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[array([[-0.26607019]]), 0.0]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "lm = LinearRegression(fit_intercept=False)\n", + "lm.fit(x_1.reshape(-1, 1),y_1.reshape(-1, 1))\n", + "print([lm.coef_, lm.intercept_])\n", + "\n", + "x_space = np.linspace(np.min(x_1), np.max(x_1))\n", + "sns.scatterplot(x=x_1, y=y_1)\n", + "plt.plot(x_space, lm.predict(x_space[:, np.newaxis]), label='Fit')\n", + "plt.plot(x_space, true_slope*x_space, label='Truth')\n", + "plt.xlabel('x')\n", + "plt.ylabel('y')\n", + "plt.ylim(-4.0,4)\n", + "plt.title('Linear Regression')\n", + "plt.tight_layout()\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now try both Lasso and Ridge regression\n", + "(here we do not use the cross-validation approach but set the regularisation parameter manually. You can explore this setting)" + ] + }, + { + "cell_type": "code", + "execution_count": 83, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Lasso coefficient [-0.02131139]\n", + "Ridge coefficient [[-0.26542696]]\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "alpha = 0.2\n", + "\n", + "lasso = Lasso(fit_intercept=False, alpha = alpha)\n", + "lasso.fit(x_1.reshape(-1,1), y_1.reshape(-1,1))\n", + "print('Lasso coefficient {}'.format(lasso.coef_) )\n", + "\n", + "ridge = Ridge(fit_intercept=False, alpha = alpha)\n", + "ridge.fit(x_1.reshape(-1,1),y_1.reshape(-1,1))\n", + "print('Ridge coefficient {}'.format(ridge.coef_) )\n", + "\n", + "plt.scatter(x_1,y_1)\n", + "x_space = np.linspace(np.min(x_1), np.max(x_1))\n", + "plt.plot(x_space, lasso.predict(x_space[:, np.newaxis]), label='Fit - Lasso', color='black')\n", + "plt.plot(x_space, ridge.predict(x_space[:, np.newaxis]), label='Fit - Ridge', color='red')\n", + "plt.plot(x_space, true_slope*x_space, label='Truth', color='blue')\n", + "plt.ylim(-4.0,4)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can see that neither of these methods perform well due to the outlier.\n", + "\n", + "What is the underlying issue?\n", + "When we perform the linear regression, we minimise the following loss function: $\\mathcal{L} = \\sum_i (y_i - \\hat{y_i})^2$, where $y_i$ are the data points and $\\hat{y_i}$ are the corresponding values of our linear prediction model.\n", + "This works fairly well in the case of no outliers, and, as we have seen in the example of the polynomial fit, Lasso and Ridge regression can help us to avoid overfitting.\n", + "However, here we have one extreme outlier that dominates the loss function because its large deviation from the prediction.\n", + "\n", + "It now depends on what we need to do (and this depends on the unique circumstances of each specific analysis). Ideally, we would remove the outlier from the data, either because they are errors in the data or we have a separate model for such rare events. \n", + "However, this may not be practical in all circumstances. We can then use a different approach in the fit and replace the purely quadratic loss function above with, for example, the Huber loss. This is, essentially, a combination of the quadratic loss we have used so far (for the bulk of the data), together with a linear loss function for detected outliers. The linear part of the loss function places less weight on the outlier compared to the quadratic loss function. In scikit-learn, this is implemented as the [Huber Regressor](https://scikit-learn.org/stable/modules/linear_model.html#huber-regression)\n", + "\n", + "\n", + "Reference: Huber, P. J. (1964). Robust estimation of a location parameter: Annals Mathematics Statistics, 35. Ji, S., Xue, Y. and Carin, L.(2008),‘Bayesian compressive sensing’, IEEE Transactions on signal processing, 56(6), 2346-2356." + ] + }, + { + "cell_type": "code", + "execution_count": 85, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Huber coefficient [1.00612488]\n" + ] + } + ], + "source": [ + "huber = HuberRegressor(alpha=alpha, epsilon=1.35)\n", + "huber.fit(x_1.reshape(-1,1), y_1)\n", + "print('Huber coefficient {}'.format(huber.coef_)) " + ] + }, + { + "cell_type": "code", + "execution_count": 86, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x_1,y_1)\n", + "x_space = np.linspace(np.min(x_1), np.max(x_1))\n", + "plt.plot(x_space, huber.predict(x_space[:, np.newaxis]), label='Fit - Huber', color='red')\n", + "plt.plot(x_space, true_slope*x_space, label='Truth', color='blue')\n", + "plt.ylim(-4.0,4)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As we can see, this works well in this specific case.\n", + "However, we do not treat the outlier well now:" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "<Figure size 640x480 with 1 Axes>" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.scatter(x_1,y_1)\n", + "x_space = np.linspace(np.min(x_1), np.max(x_1))\n", + "plt.plot(x_space, huber.predict(x_space[:, np.newaxis]), label='Fit - Huber', color='red')\n", + "plt.plot(x_space, true_slope*x_space, label='Truth', color='blue')\n", + "\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This is the same plot as above, with the only difference that we no longer force the range of the $y$ axis that is displayed in the plot.\n", + "We can see that the bulk of the data are described well - but the outlier remains an outlier in the model. Whether or not this a good approach needs to be discussed in the context of the specific application." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "datascienceintro-eVBNPtpL-py3.10", + "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": "3.10.12" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/datascienceintro/PyTorch_GraphNN_MoleculePrediction.ipynb b/datascienceintro/PyTorch_GraphNN_MoleculePrediction.ipynb index d50a6f925f7bb9f8ad49ee791694f9ecc735a109..045b5632eb905a1382e3cf2afc387e6d7305211c 100644 --- a/datascienceintro/PyTorch_GraphNN_MoleculePrediction.ipynb +++ b/datascienceintro/PyTorch_GraphNN_MoleculePrediction.ipynb @@ -39,16 +39,27 @@ "# Only on Colab, etc\n", "# see https://pytorch-geometric.readthedocs.io/en/latest/notes/installation.html\n", "# only works for pip at the moment\n", - "# !pip install pyg-lib torch-scatter torch-sparse torch-cluster torch-spline-conv torch-geometric -f https://data.pyg.org/whl/torch-1.13.0+cu117.html" + "# !pip install pyg-lib torch-scatter torch-sparse torch-cluster torch-spline-conv torch-geometric -f https://data.pyg.org/whl/torch-1.13.0+cu117.html\n", + "!pip install --upgrade pip\n", + "!pip install pyg_lib torch_scatter torch_sparse torch_cluster torch_spline_conv -f https://data.pyg.org/whl/torch-2.0.0+cpu.html" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "id": "1kINuHRifGPY" }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kerzel/.cache/pypoetry/virtualenvs/datascienceintro-eVBNPtpL-py3.10/lib/python3.10/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", + " from .autonotebook import tqdm as notebook_tqdm\n" + ] + } + ], "source": [ "import torch\n", "\n", @@ -90,17 +101,6 @@ "outputId": "3df4e904-725b-47ae-9e18-074580e74529" }, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "Downloading https://data.pyg.org/datasets/qm9_v3.zip\n", - "Extracting data/qm9/raw/qm9_v3.zip\n", - "Processing...\n", - "Using a pre-processed version of the dataset. Please install 'rdkit' to alternatively process the raw data.\n", - "Done!\n" - ] - }, { "name": "stdout", "output_type": "stream", @@ -278,7 +278,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] diff --git a/datascienceintro/PyTorch_MNIST.ipynb b/datascienceintro/PyTorch_MNIST.ipynb index 162835aa24a0568fc58ceaabb01742d794a63f33..52ef5dc2757b717d8a4a87091a08d5bbb535a4fc 100644 --- a/datascienceintro/PyTorch_MNIST.ipynb +++ b/datascienceintro/PyTorch_MNIST.ipynb @@ -25,11 +25,20 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 1, "metadata": { "id": "SbsUiK9_lXNS" }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kerzel/.cache/pypoetry/virtualenvs/datascienceintro-eVBNPtpL-py3.10/lib/python3.10/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", + " from .autonotebook import tqdm as notebook_tqdm\n" + ] + } + ], "source": [ "import torch\n", "from torch import nn\n", @@ -584,8 +593,16 @@ "name": "python3" }, "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", "name": "python", - "version": "3.10.6 (main, Nov 14 2022, 16:10:14) [GCC 11.3.0]" + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.6" }, "vscode": { "interpreter": { diff --git a/datascienceintro/Pytorch_SimpleLinearRegression.ipynb b/datascienceintro/Pytorch_SimpleLinearRegression.ipynb index b7946a9dbd3c915b5507d83a0aef5ac314d98804..2916496d0d738572a3b9a11d96e416fd950dfdb3 100644 --- a/datascienceintro/Pytorch_SimpleLinearRegression.ipynb +++ b/datascienceintro/Pytorch_SimpleLinearRegression.ipynb @@ -21,11 +21,20 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "id": "1sga7qkdmqq6" }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kerzel/.cache/pypoetry/virtualenvs/datascienceintro-eVBNPtpL-py3.10/lib/python3.10/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", + " from .autonotebook import tqdm as notebook_tqdm\n" + ] + } + ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", @@ -433,7 +442,16 @@ "name": "python3" }, "language_info": { - "name": "python" + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.6" } }, "nbformat": 4, diff --git a/datascienceintro/Regression_WineQuality.ipynb b/datascienceintro/Regression_WineQuality.ipynb index 1b9b98545a875181ba10fc51b14f1fee86b9e0b3..e5cfca78d67df277878d785b4343efcdea94de37 100644 --- a/datascienceintro/Regression_WineQuality.ipynb +++ b/datascienceintro/Regression_WineQuality.ipynb @@ -838,6 +838,13 @@ "#plt.show()" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, { "attachments": {}, "cell_type": "markdown", diff --git a/datascienceintro/__pycache__/profile_plot.cpython-310.pyc b/datascienceintro/__pycache__/profile_plot.cpython-310.pyc index 681f7b82e66a684ea2b68724920a584c73b6bd42..b7bb79d8b4c1b0ff7ffe04c199411d77c32f7b16 100644 Binary files a/datascienceintro/__pycache__/profile_plot.cpython-310.pyc and b/datascienceintro/__pycache__/profile_plot.cpython-310.pyc differ diff --git a/datascienceintro/solutions/Solution_Classification_DecisionTree.ipynb b/datascienceintro/solutions/Solution_Classification_DecisionTree.ipynb index 69cc835fea1af0d8465af9074f65c623e2a3abdf..af0adbc8f550d3125e2032fd242a7110240b3000 100644 --- a/datascienceintro/solutions/Solution_Classification_DecisionTree.ipynb +++ b/datascienceintro/solutions/Solution_Classification_DecisionTree.ipynb @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": 124, + "execution_count": 1, "metadata": { "id": "khH_Ht3WS2hp" }, @@ -48,7 +48,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 2, "metadata": { "id": "fcQJAxNJTdv1" }, @@ -78,7 +78,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 3, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -91,10 +91,7 @@ { "data": { "text/html": [ - "\n", - " <div id=\"df-04d645ad-76e3-46c8-a19d-23dc0407acb7\">\n", - " <div class=\"colab-df-container\">\n", - " <div>\n", + "<div>\n", "<style scoped>\n", " .dataframe tbody tr th:only-of-type {\n", " vertical-align: middle;\n", @@ -222,83 +219,7 @@ " </tr>\n", " </tbody>\n", "</table>\n", - "</div>\n", - " <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-04d645ad-76e3-46c8-a19d-23dc0407acb7')\"\n", - " title=\"Convert this dataframe to an interactive table.\"\n", - " style=\"display:none;\">\n", - " \n", - " <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n", - " width=\"24px\">\n", - " <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n", - " <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n", - " </svg>\n", - " </button>\n", - " \n", - " <style>\n", - " .colab-df-container {\n", - " display:flex;\n", - " flex-wrap:wrap;\n", - " gap: 12px;\n", - " }\n", - "\n", - " .colab-df-convert {\n", - " background-color: #E8F0FE;\n", - " border: none;\n", - " border-radius: 50%;\n", - " cursor: pointer;\n", - " display: none;\n", - " fill: #1967D2;\n", - " height: 32px;\n", - " padding: 0 0 0 0;\n", - " width: 32px;\n", - " }\n", - "\n", - " .colab-df-convert:hover {\n", - " background-color: #E2EBFA;\n", - " box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n", - " fill: #174EA6;\n", - " }\n", - "\n", - " [theme=dark] .colab-df-convert {\n", - " background-color: #3B4455;\n", - " fill: #D2E3FC;\n", - " }\n", - "\n", - " [theme=dark] .colab-df-convert:hover {\n", - " background-color: #434B5C;\n", - " box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n", - " filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n", - " fill: #FFFFFF;\n", - " }\n", - " </style>\n", - "\n", - " <script>\n", - " const buttonEl =\n", - " document.querySelector('#df-04d645ad-76e3-46c8-a19d-23dc0407acb7 button.colab-df-convert');\n", - " buttonEl.style.display =\n", - " google.colab.kernel.accessAllowed ? 'block' : 'none';\n", - "\n", - " async function convertToInteractive(key) {\n", - " const element = document.querySelector('#df-04d645ad-76e3-46c8-a19d-23dc0407acb7');\n", - " const dataTable =\n", - " await google.colab.kernel.invokeFunction('convertToInteractive',\n", - " [key], {});\n", - " if (!dataTable) return;\n", - "\n", - " const docLinkHtml = 'Like what you see? Visit the ' +\n", - " '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n", - " + ' to learn more about interactive tables.';\n", - " element.innerHTML = '';\n", - " dataTable['output_type'] = 'display_data';\n", - " await google.colab.output.renderOutput(dataTable, element);\n", - " const docLink = document.createElement('div');\n", - " docLink.innerHTML = docLinkHtml;\n", - " element.appendChild(docLink);\n", - " }\n", - " </script>\n", - " </div>\n", - " </div>\n", - " " + "</div>" ], "text/plain": [ " Age WorkClass fnlwgt Education EducationNum \\\n", @@ -323,7 +244,7 @@ "4 0 0 40 Cuba <=50K " ] }, - "execution_count": 16, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -352,7 +273,7 @@ }, { "cell_type": "code", - "execution_count": 49, + "execution_count": 4, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -364,14 +285,12 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "<Figure size 434.875x360 with 1 Axes>" + "<Figure size 604.125x500 with 1 Axes>" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -384,7 +303,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 5, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -396,14 +315,12 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ - "<Figure size 434.875x360 with 1 Axes>" + "<Figure size 604.125x500 with 1 Axes>" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -411,13 +328,13 @@ "sns.displot(data=df,x='MaritalStatus',hue='Income')\n", "plt.ylabel('count', size = 20)\n", "plt.xlabel('Marital Status', size = 20)\n", - "plt.xticks(rotation=45)\n", + "plt.xticks(rotation=-45)\n", "plt.show()" ] }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 9, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -429,14 +346,12 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "<Figure size 434.875x360 with 1 Axes>" + "<Figure size 604.125x500 with 1 Axes>" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -449,7 +364,7 @@ }, { "cell_type": "code", - "execution_count": 53, + "execution_count": 6, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -461,14 +376,12 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "<Figure size 434.875x360 with 1 Axes>" + "<Figure size 604.125x500 with 1 Axes>" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -476,13 +389,13 @@ "sns.displot(data=df,x='Race',hue='Income')\n", "plt.ylabel('count', size = 20)\n", "plt.xlabel('Race', size = 20)\n", - "plt.xticks(rotation=45)\n", + "plt.xticks(rotation=-45)\n", "plt.show()" ] }, { "cell_type": "code", - "execution_count": 55, + "execution_count": 7, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -494,14 +407,12 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "<Figure size 434.875x360 with 1 Axes>" + "<Figure size 604.125x500 with 1 Axes>" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -533,7 +444,7 @@ }, { "cell_type": "code", - "execution_count": 54, + "execution_count": 8, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -545,14 +456,12 @@ "outputs": [ { "data": { - "image/png": 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", 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"text/plain": [ - "<Figure size 432x288 with 1 Axes>" + "<Figure size 640x480 with 1 Axes>" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -564,6 +473,41 @@ "plt.show()" ] }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Age 0\n", + "WorkClass 0\n", + "fnlwgt 0\n", + "Education 0\n", + "EducationNum 0\n", + "MaritalStatus 0\n", + "Occupation 0\n", + "Relationship 0\n", + "Race 0\n", + "Gender 0\n", + "CapitalGain 0\n", + "CapitalLoss 0\n", + "HoursPerWeek 0\n", + "NativeCountry 0\n", + "Income 0\n", + "dtype: int64" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "df.isna().sum()" + ] + }, { "cell_type": "markdown", "metadata": { @@ -1011,7 +955,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 16, "metadata": { "id": "85Y0URWyTuOs" }, @@ -1038,7 +982,7 @@ }, { "cell_type": "code", - "execution_count": 57, + "execution_count": 17, "metadata": { "id": "4b0ICzaEly5h" }, @@ -1048,6 +992,34 @@ "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25)" ] }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "count 24420.000000\n", + "mean 0.239967\n", + "std 0.427072\n", + "min 0.000000\n", + "25% 0.000000\n", + "50% 0.000000\n", + "75% 0.000000\n", + "max 1.000000\n", + "Name: Income, dtype: float64" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "y_train.describe()" + ] + }, { "cell_type": "markdown", "metadata": { @@ -1820,7 +1792,15 @@ "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": "3.10.6" }, "vscode": { diff --git a/datascienceintro/solutions/Solution_PyTorch_MNIST.ipynb b/datascienceintro/solutions/Solution_PyTorch_MNIST.ipynb index 6ca59a8103d40efd71dd363c41da80328a61c480..0176a882658226b27eca3893065a39260280a51f 100644 --- a/datascienceintro/solutions/Solution_PyTorch_MNIST.ipynb +++ b/datascienceintro/solutions/Solution_PyTorch_MNIST.ipynb @@ -1,22 +1,10 @@ { - "nbformat": 4, - "nbformat_minor": 0, - "metadata": { - "colab": { - "provenance": [] - }, - "kernelspec": { - "name": "python3", - "display_name": "Python 3" - }, - "language_info": { - "name": "python" - }, - "accelerator": "GPU" - }, "cells": [ { "cell_type": "markdown", + "metadata": { + "id": "XerGI0BJSAQH" + }, "source": [ "# Image classification with PyTorch\n", "\n", @@ -32,18 +20,24 @@ "However, in our case here we stick with the original data, as we want to explore how to setup a system and reduce our depencency on GPUs for now.\n", "\n", "We will also make use of the [TorchVision](https://pytorch.org/vision/stable/index.html) library. This provides convenient access to a number of datasets (such as MNIST), but also pre-trained models or commonly used image augmentation methods.\n" - ], - "metadata": { - "id": "XerGI0BJSAQH" - } + ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 1, "metadata": { "id": "SbsUiK9_lXNS" }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/kerzel/.cache/pypoetry/virtualenvs/datascienceintro-eVBNPtpL-py3.10/lib/python3.10/site-packages/tqdm/auto.py:22: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html\n", + " from .autonotebook import tqdm as notebook_tqdm\n" + ] + } + ], "source": [ "import torch\n", "from torch import nn\n", @@ -59,17 +53,22 @@ }, { "cell_type": "markdown", + "metadata": { + "id": "eGyFnO2taTn5" + }, "source": [ "# Data access\n", "\n", "Now we download the data using the convenience function from TorchVision for the [MNIST](https://pytorch.org/vision/stable/generated/torchvision.datasets.MNIST.html#torchvision.datasets.MNIST) data. It is essentially a wrapper function that downloads the data from Yann LeCun's webpage and add it to the local directory." - ], - "metadata": { - "id": "eGyFnO2taTn5" - } + ] }, { "cell_type": "code", + "execution_count": 9, + "metadata": { + "id": "_9RmXMt0mc4G" + }, + "outputs": [], "source": [ "# Download training data from open datasets.\n", "training_data = tv.datasets.MNIST(\n", @@ -86,15 +85,13 @@ " download=True,\n", " transform=tv.transforms.ToTensor(),\n", ")" - ], - "metadata": { - "id": "_9RmXMt0mc4G" - }, - "execution_count": 9, - "outputs": [] + ] }, { "cell_type": "markdown", + "metadata": { + "id": "5-6a5r_obCp5" + }, "source": [ "Next, we need to make these data accessible to PyTorch.\n", "This can be done using the [DataLoader](https://pytorch.org/docs/stable/data.html) provided by PyTorch. This function provides some common functionality when dealing with the data.\n", @@ -112,33 +109,11 @@ "The array/vector/tensor ```y``` contains the corresponding true labels for each image (supervised training).\n", "\n", "Note the grayscale values due to the anti-aliasing that was applied when creating the data.\n" - ], - "metadata": { - "id": "5-6a5r_obCp5" - } + ] }, { "cell_type": "code", - "source": [ - "batch_size = 64\n", - "\n", - "# Create data loaders.\n", - "train_dataloader = DataLoader(training_data, batch_size=batch_size)\n", - "test_dataloader = DataLoader(test_data, batch_size=batch_size)\n", - "\n", - "# define the loop over the test data (even if we only use one image)\n", - "for X, y in test_dataloader:\n", - " print(\"Shape of X [N images per batch, # colours, height, width]: \", X.shape)\n", - " print(\"Shape of y: \", y.shape, y.dtype)\n", - "\n", - " #print an example\n", - " # since PyTorch tensors are of the form [#Channel, #pix X, #pix Y], need to \n", - " # transform back into image format\n", - " index = 0\n", - " plt.imshow(tv.transforms.ToPILImage()(X[index]), cmap='Greys')\n", - " print('True label: {}'.format(y[index]) )\n", - " break" - ], + "execution_count": 10, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -147,11 +122,10 @@ "id": "df3m1KRNnZCl", "outputId": "c71efc53-bdd5-402c-80fd-c3ce5c971f91" }, - "execution_count": 10, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Shape of X [N images per batch, # colours, height, width]: torch.Size([64, 1, 28, 28])\n", "Shape of y: torch.Size([64]) torch.int64\n", @@ -159,21 +133,44 @@ ] }, { - "output_type": "display_data", "data": { + "image/png": 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"text/plain": [ "<Figure size 432x288 with 1 Axes>" - ], - "image/png": 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+ ] }, "metadata": { "needs_background": "light" - } + }, + "output_type": "display_data" } + ], + "source": [ + "batch_size = 64\n", + "\n", + "# Create data loaders.\n", + "train_dataloader = DataLoader(training_data, batch_size=batch_size)\n", + "test_dataloader = DataLoader(test_data, batch_size=batch_size)\n", + "\n", + "# define the loop over the test data (even if we only use one image)\n", + "for X, y in test_dataloader:\n", + " print(\"Shape of X [N images per batch, # colours, height, width]: \", X.shape)\n", + " print(\"Shape of y: \", y.shape, y.dtype)\n", + "\n", + " #print an example\n", + " # since PyTorch tensors are of the form [#Channel, #pix X, #pix Y], need to \n", + " # transform back into image format\n", + " index = 0\n", + " plt.imshow(tv.transforms.ToPILImage()(X[index]), cmap='Greys')\n", + " print('True label: {}'.format(y[index]) )\n", + " break" ] }, { "cell_type": "markdown", + "metadata": { + "id": "ituN_KKZekHR" + }, "source": [ "# Network definition\n", "\n", @@ -221,13 +218,35 @@ "\n", "*Note* \\\n", "We use the [Functional](https://pytorch.org/docs/stable/nn.functional.html) to pass the data through the various elements, e.g. the activation function." - ], - "metadata": { - "id": "ituN_KKZekHR" - } + ] }, { "cell_type": "code", + "execution_count": 17, + "metadata": { + "colab": { + "base_uri": "https://localhost:8080/" + }, + "id": "8RJBMA0fnpKc", + "outputId": "f082448e-d863-4709-9c84-cd73d7df7a02" + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Using cuda device\n", + "NeuralNetwork(\n", + " (conv1): Conv2d(1, 32, kernel_size=(3, 3), stride=(1, 1))\n", + " (conv2): Conv2d(32, 64, kernel_size=(3, 3), stride=(1, 1))\n", + " (fc1): Linear(in_features=9216, out_features=128, bias=True)\n", + " (fc2): Linear(in_features=128, out_features=10, bias=True)\n", + " (dropout1): Dropout2d(p=0.25, inplace=False)\n", + " (dropout2): Dropout2d(p=0.5, inplace=False)\n", + ")\n" + ] + } + ], "source": [ "# Get cpu or gpu device for training.\n", "device = \"cuda\" if torch.cuda.is_available() else \"cpu\"\n", @@ -299,35 +318,13 @@ "\n", "model = NeuralNetwork().to(device)\n", "print(model)" - ], - "metadata": { - "colab": { - "base_uri": "https://localhost:8080/" - }, - "id": "8RJBMA0fnpKc", - "outputId": "f082448e-d863-4709-9c84-cd73d7df7a02" - }, - "execution_count": 17, - "outputs": [ - { - "output_type": "stream", - "name": "stdout", - "text": [ - "Using cuda device\n", - "NeuralNetwork(\n", - " (conv1): Conv2d(1, 32, kernel_size=(3, 3), stride=(1, 1))\n", - " (conv2): Conv2d(32, 64, kernel_size=(3, 3), stride=(1, 1))\n", - " (fc1): Linear(in_features=9216, out_features=128, bias=True)\n", - " (fc2): Linear(in_features=128, out_features=10, bias=True)\n", - " (dropout1): Dropout2d(p=0.25, inplace=False)\n", - " (dropout2): Dropout2d(p=0.5, inplace=False)\n", - ")\n" - ] - } ] }, { "cell_type": "markdown", + "metadata": { + "id": "dfa4uLhxtFTF" + }, "source": [ "Next, we need to define the further parameters of the network.\n", "Two very important ingredients are:\n", @@ -338,13 +335,15 @@ "\n", "Instead of stochastic gradient descent [SGD](https://pytorch.org/docs/stable/generated/torch.optim.SGD.html), we will use the [Adam](https://pytorch.org/docs/stable/generated/torch.optim.Adam.html?highlight=adam#torch.optim.Adam) optimiser, which is more efficient. We could also use, e.g. [AdamW](https://pytorch.org/docs/stable/generated/torch.optim.AdamW.html?highlight=adam#torch.optim.AdamW) as a modern variant.\n", "We need to pass the model parameters (i.e. the network weights) to the optimiser. This essentially \"tells\" the optimiser, which parameters need to be tuned during training." - ], - "metadata": { - "id": "dfa4uLhxtFTF" - } + ] }, { "cell_type": "code", + "execution_count": 18, + "metadata": { + "id": "_DSpxVO6n52R" + }, + "outputs": [], "source": [ "##\n", "## Optimizer and Loss Function\n", @@ -353,15 +352,13 @@ "\n", "# Choose the optimizer\n", "optimizer = torch.optim.Adam(model.parameters(), lr=1e-3)" - ], - "metadata": { - "id": "_DSpxVO6n52R" - }, - "execution_count": 18, - "outputs": [] + ] }, { "cell_type": "markdown", + "metadata": { + "id": "Mc3GlViTuv9n" + }, "source": [ "# Network training\n", "\n", @@ -378,13 +375,15 @@ "Note:\n", "- We need to tell PyTorch explictly if we train the model, so that the weights can get updated: ```model.train()```. Otherwise, we switch to evaluation mode ```model.eval()```.\n", "- Our network has 10 output nodes, i.e. each note tells us how likely it is that this image corresponds to the label represented by this node. We need the node with the highest value to identify the most likely classification which we can do with ```argmax```." - ], - "metadata": { - "id": "Mc3GlViTuv9n" - } + ] }, { "cell_type": "code", + "execution_count": 19, + "metadata": { + "id": "y2bcXu2DoC3L" + }, + "outputs": [], "source": [ "#\n", "# Training loop\n", @@ -467,42 +466,20 @@ " correct /= size\n", " print(f\"Test Error: \\n Accuracy: {(100*correct):>0.1f}%, Avg loss: {test_loss:>8f} \\n\") \n", " return correct" - ], - "metadata": { - "id": "y2bcXu2DoC3L" - }, - "execution_count": 19, - "outputs": [] + ] }, { "cell_type": "markdown", - "source": [ - "Now we use these functions for the actual training." - ], "metadata": { "id": "vANwQ3QFwMMX" - } + }, + "source": [ + "Now we use these functions for the actual training." + ] }, { "cell_type": "code", - "source": [ - "##\n", - "## The actual training/evaluation\n", - "##\n", - "epochs = 5\n", - "loss_values = []\n", - "accuracy_values = []\n", - "\n", - "for t in range(epochs):\n", - "\n", - " print(f\"Epoch {t+1}\\n-------------------------------\")\n", - " loss = train_epoch(train_dataloader, model, loss_fn, optimizer)\n", - " loss_values.append(loss)\n", - "\n", - " accuracy = test(test_dataloader, model, loss_fn)\n", - " accuracy_values.append(accuracy)\n", - "print(\"Done!\")" - ], + "execution_count": 20, "metadata": { "colab": { "base_uri": "https://localhost:8080/" @@ -510,27 +487,26 @@ "id": "Jh-MwE-PonOb", "outputId": "ec49db09-a97d-4386-9da9-22b1463d466d" }, - "execution_count": 20, "outputs": [ { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "Epoch 1\n", "-------------------------------\n" ] }, { - "output_type": "stream", "name": "stderr", + "output_type": "stream", "text": [ "/usr/local/lib/python3.8/dist-packages/torch/nn/functional.py:1331: UserWarning: dropout2d: Received a 2-D input to dropout2d, which is deprecated and will result in an error in a future release. To retain the behavior and silence this warning, please use dropout instead. Note that dropout2d exists to provide channel-wise dropout on inputs with 2 spatial dimensions, a channel dimension, and an optional batch dimension (i.e. 3D or 4D inputs).\n", " warnings.warn(warn_msg)\n" ] }, { - "output_type": "stream", "name": "stdout", + "output_type": "stream", "text": [ "loss: 2.302431 [ 0/60000]\n", "loss: 0.516572 [ 6400/60000]\n", @@ -608,19 +584,29 @@ "Done!\n" ] } + ], + "source": [ + "##\n", + "## The actual training/evaluation\n", + "##\n", + "epochs = 5\n", + "loss_values = []\n", + "accuracy_values = []\n", + "\n", + "for t in range(epochs):\n", + "\n", + " print(f\"Epoch {t+1}\\n-------------------------------\")\n", + " loss = train_epoch(train_dataloader, model, loss_fn, optimizer)\n", + " loss_values.append(loss)\n", + "\n", + " accuracy = test(test_dataloader, model, loss_fn)\n", + " accuracy_values.append(accuracy)\n", + "print(\"Done!\")" ] }, { "cell_type": "code", - "source": [ - "fig, axes = plt.subplots(2, sharex=True)\n", - "axes[0].set_ylabel(\"Loss\", fontsize=14)\n", - "axes[0].plot(loss_values)\n", - "axes[1].set_ylabel(\"Accuracy\", fontsize=14)\n", - "axes[1].set_xlabel(\"Iteration\", fontsize=14)\n", - "axes[1].plot(accuracy_values)\n", - "plt.show()" - ], + "execution_count": 21, "metadata": { "colab": { "base_uri": "https://localhost:8080/", @@ -629,42 +615,74 @@ "id": "TxwSKJM31JdH", "outputId": "3c86b053-47cb-4d91-b826-d8d58273f378" }, - "execution_count": 21, "outputs": [ { - "output_type": "display_data", "data": { + "image/png": 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", "text/plain": [ "<Figure size 432x288 with 2 Axes>" - ], - "image/png": 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\n" + ] }, "metadata": { "needs_background": "light" - } + }, + "output_type": "display_data" } + ], + "source": [ + "fig, axes = plt.subplots(2, sharex=True)\n", + "axes[0].set_ylabel(\"Loss\", fontsize=14)\n", + "axes[0].plot(loss_values)\n", + "axes[1].set_ylabel(\"Accuracy\", fontsize=14)\n", + "axes[1].set_xlabel(\"Iteration\", fontsize=14)\n", + "axes[1].plot(accuracy_values)\n", + "plt.show()" ] }, { "cell_type": "markdown", + "metadata": { + "id": "NJ_rwY8vxAom" + }, "source": [ "Even with the very simple fully connected network, we can achive an accuracy of 96%-97%. This isn't bad as such, indeed, in many applications, this would be considered phenomenal. However, the best classifiers achieve around 99.8%, the code at [MNIST-0.17](https://github.com/Matuzas77/MNIST-0.17) has an error rate of only 0.17%.\n", "This illustrates why we use MNIST for learning how to use neural networks for image processing and how to set the system up - but the data are not suitable (anymore) to develop performant neural network architectures." - ], - "metadata": { - "id": "NJ_rwY8vxAom" - } + ] }, { "cell_type": "markdown", + "metadata": { + "id": "Hrh_VH-swZgF" + }, "source": [ "The network with a few convolutional neural entwork layers is much better than the one without - we achieve an accuracy of 99% after just 5 epochs of training.\n", "This is still quite far from the current state of the art, but then again, we do not want to build a model to beat it.\n", "However, feel free to try and improve the model." - ], - "metadata": { - "id": "Hrh_VH-swZgF" - } + ] } - ] -} \ No newline at end of file + ], + "metadata": { + "accelerator": "GPU", + "colab": { + "provenance": [] + }, + "kernelspec": { + "display_name": "Python 3", + "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": "3.10.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}