{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", " \n", "## [mlcourse.ai](https://mlcourse.ai) – Open Machine Learning Course \n", "Author: [Dmitry Sergeyev](https://github.com/DmitrySerg), Zeptolab. This material is subject to the terms and conditions of the [Creative Commons CC BY-NC-SA 4.0](https://creativecommons.org/licenses/by-nc-sa/4.0/) license. Free use is permitted for any non-commercial purpose." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#
Assignment #4. Spring 2019\n", "##
Time series analysis\n", "\n", "Prior to working on the assignment, you'd better check out the corresponding course material:\n", " - [Time series analysis with Python](https://nbviewer.jupyter.org/github/Yorko/mlcourse_open/blob/master/jupyter_english/topic09_time_series/topic9_part1_time_series_python.ipynb?flush_cache=true), the same as an interactive web-based [Kaggle Kernel](https://www.kaggle.com/kashnitsky/topic-9-part-1-time-series-analysis-in-python)\n", " - [Predicting future with Facebook Prophet](https://nbviewer.jupyter.org/github/Yorko/mlcourse_open/blob/master/jupyter_english/topic09_time_series/topic9_part2_facebook_prophet.ipynb?flush_cache=true), the same as a [Kaggle Kernel](https://www.kaggle.com/kashnitsky/topic-9-part-2-time-series-with-facebook-prophet)\n", "\n", "You can also practice with demo assignments, which are simpler and already shared with solutions:\n", " - \"Time series analysis\": [assignment](https://www.kaggle.com/kashnitsky/a9-demo-time-series-analysis) + [solution](https://www.kaggle.com/kashnitsky/a9-demo-time-series-analysis-solution)\n", " \n", "Also, checkout mlcourse.ai [video lecture](https://mlcourse.ai/lectures) on time series\n", "\n", "### Your task is to:\n", " 1. write code and perform computations in the cells below\n", " 2. choose answers in the [webform](https://docs.google.com/forms/d/1D9tmL8O6ujxUD7orX-Iv_qCiYTjdDRW-uO84BeJniaI). Solutions will be shared only with those who've filled in this form \n", " \n", "###
Deadline for A4: 2019 April 7, 20:59 GMT" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# importing necessary libraries\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", "import random\n", "random.seed(42)\n", "\n", "import seaborn as sns\n", "import pandas as pd\n", "import numpy as np\n", "\n", "from sklearn.linear_model import LinearRegression, RidgeCV, LassoCV\n", "from sklearn.metrics import mean_absolute_error, mean_squared_error\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.model_selection import TimeSeriesSplit, cross_val_score\n", "\n", "import matplotlib.pyplot as plt\n", "%matplotlib inline\n", "\n", "\n", "def mean_absolute_percentage_error(y_true, y_pred): \n", " return np.mean(np.abs((y_true - y_pred) / y_true)) * 100" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will take real time-series data of total ads watched by hour in one of our games. It's stored in the [course repo](https://github.com/Yorko/mlcourse.ai)." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "df = pd.read_csv('../../data/ads_hour.csv',index_col=['Date'], parse_dates=['Date'])" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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qsrVCLUrjjNfpiP086cEHw3XN+xhFaPb6gD1d7IA62wO1tgdqbQfU2R6o9c7Q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Q4lv7BGGcYe6bDONkpRdoUlBrOkJKc54Jj6TP+GSD/pdY7iBs5O7ubsyNs6Hk5RVZ6Ql+bIIs\nqq7V6isJ8tkWbeGOqPya8Ql+uWCT8h///UuQyHnReNL9eFwGLTTspGiSOvVvv+Z+a7/hUh5/7013\n4FWLE8fTkB6Q9EynQTcVLSnvisCJkcvpcaSUx3/4ugfxn7/xYbEl/k5JatPr75rC//dNj+Alp9Pn\nnZVjyp7mHto9D7HaJXKBP3tpiH2/x3pQ4QoJ3hE54NrChnQldbmUXg+ycR4cZGM9OMjGOh0yN84U\nmJtzh9pQ6JJWVqFmlL28ncfmNEqPo+P7xgABAC7t1rE0Zw9jvdWxLN1934/9MEuy12h1rMkgDwF0\n5exx0qLlwDVNiCYPLwtDGum8hjx5xkbdpewNFaJQTzkh1EovtIRKRteCt0krFUFjMzc3h1xYF2uv\n1obv+5ZZDEelmEejrVvOS2VPunFG32mb4xvyGl6vfEiom23fkDQ50XWRcolyIYd6q2PqPh6XsheF\nrwZ/E4GdHen/xO56kfRMp0E3NVNOgDVTDh7e6lL2AOCs4s6oh3Emr4hejxNncPygzwdh1IC2iJVU\nPJzw8PwIPn1pDw8vdA/XoVDoo6DfY53BxiFbgJwdLqqhno+dGcPXPXIKPoBXXpjA6QQn07TIxnlw\nkI314CAb63TIyF4KbG5uYnhYdweMFJh46AoRlHIhZ9Wz6jA7hxe2avjhTz6Pv/KKs3jpmfgq+0Gj\nbRm0rGzVsDRnT4qe3bRVvWbbjxX63mu0YvtwcOIjFSOzT5cwThmuCMRVLl5Dz63sRWqaCfUUiiZX\nIsmghcpA8L7RtUtSIil0cnNzE2fPnjX7Xd1vmO/LPLdyIQfynJTXmk+ifd9XjWuMsteylT1+nnIh\nh2a7bcJ4XUW4u+V08rZqfekXpLKn5XCeFCQ902nQjexJZe/Hvnoptk/ZCuM8WuiKdoWPidMbyD5v\nHMYtsnlop4vs/e03LOJjX1hXQwQlCkeMigD6P9YZbHzw8QWsbNXwoZedxmvuiOdkAsH9/3+8Qi+D\n0i9k4zw4yMZ6cJCNdTpkYZwpkFQk2pA9xWSgyWq04xiwdQAAIABJREFU5SwCEO3zL3/nRTy9UcX3\nfPxp9fiHDfu4u0q+35YwL9HComLKnmgvr1vHFSPed6PcOcodNJg6SBBmnOaaFLmyJ0I0uZpWzHnI\ne0Dbd5R5YGUgiLxxQmfIXo7CJrVj5MI2BoooHe+ffXIFLnClT8s7i4hPdI34fiVHzh4nRhQCR2Mn\nC5AHJRaC72p5MgTp9nd8ZC9U9sJLLN1OTxK6FX4/Kt5+3wwA4OXnxtXtXOGqFHPqGPDPjuzQqFzi\nbuUgrhfSofFd98fJGr/nXSUCpoeL+OYnTvfkqiqfgV7Q77HOYOOOqQr+7dc+4CR6NwrZOA8OsrEe\nHGRjnQ6ZspcCSTKymbQLghUoOhEh4avsfBJ2wBSr31vZieUxHQpFSwvZk8pOtdmOraLLgu6S7LVY\nCGaBE6yOH5EpFjqpOWm2FIMWIgB+qGYap808U/ZEW+rMFMXzPJSLeRw02qi1OkYhabO2RM6Vdl4g\nEKkbpDBotfhoPkrjPFTIodFu4/PXDuDCEFPzknIwffDC7PHvmDZrZC9sM42dVDU8z0MlvDaHDbfp\nz6NnRi3197i4Fx3XRzA+HT/gIMdFLq8H/Q4NecfSDBanys76gJabaw/mFNLxtRu0K3w95je9gCuR\nj58dwz2z8b73EsZ5pHP2UMJCIgsDGgxk4zw4yMZ6cJCNdTpkyl4KrK6uOre58s7afjDpzXnBZDfH\npmN8oYJP0r7/V5+NHV9O4mUB8uDcvvg7TgjJoZEmaLL8giQb5WI8xDLaJ4dyIehRnVn6N0WJAYAV\nVacwzlakdvIacFpbiNhpxJKfK1IiqQRBtF9UeiHJoCXYRuNMk+Q7pvRix4BtPKEreyHJ9X1zrYsJ\nyp4WxmnIXp1y9uLnoXpVksxzvPKCvYBwXEobLznByfhJRNIznQY5z8ND86NOU5QkN1cNvezDcVPI\nHmuji8j1EsbZC77tlWdxfmII73no6D/8/R7rDCcT2TgPDrKxHhxkY50OGdlLgdHRUee2ISV3DeDh\nisF2ruz51n7RX5qL2aEgQpLYAfF8Ns3KnIgQTbhcYZw0OScSW9eUu9AVsiJKJ2ilF8z/wmZHdes8\nZ+kFWYbAmLQ0420p5DyjlND2hqXseWGb4sren17eN8cAonGmvtNc+a8ouSYlK4wzPm48V7HJTGmi\n79thpZuh46pWEN3k7CkkjXK7dmvu2o3zo7ZBSu7YDFqCfzu+rlSeJCQ908cBTrySQjTfft80ZkeK\nMYLeDZrZylDheK89LxXhKpLNW3BUAsvx3odP4d993YOYrHQP9ZS40WOd4eYgG+fBQTbWg4NsrNMh\nC+PsM1wGLXKCf3o8ch+z8+Ci/8tJOaCFccYVHBkGKZUy3h6acLmUvaIgWKqyF/ZpuJTHYbODg0Yb\nI6W8pdoRIjdO3zrvUCEXyw2kfWWul0YKm6wtRDqJGPP8NeIastTBn12JSmXIMEOamG+FBOyc4n7Y\nLWePjtgBy91UlT0f1/Yb+JNLe6Y/8hz7obmOppKRa+PaQdwcg8Bt/ElpPg54TNk76WTvRqNg5ey5\nyd53v34R7Y7flzF6/KyeP9gv8H64yB5/Zq/X/TNDhgwZMmTI0B2ZspcC+/vxGnqEksOghbtFAsBX\nPRiZF3AvDV7cXDNfoTBOKvGgOS9KollVCCFNvklVaHZpL03kDhoKwQr3GQn3IULaUBQs6cbJa+gF\nTpqepQTx89CEl9TTphpSypW9trUNiFSsyI0zOMbnVqMxpf7QOBPJovqGmhIzxFU6VdmLwjh/eXkj\ntl9EPjuG6PG2AJFqt3kYV/3kPqv7UemNn3ivXdeuzCblvdR7Swuj7HVOPtlLeqaPA1xN7VZnsx9E\n78NfdgZfcf/MdR8nCdyNc8ThHppUMP1G4UaPdYabg2ycBwfZWA8OsrFOh4zspcD8/LxzWzmcPF/c\nrlnErWEMT4KJWymfw/lQIeI5e02WX7ZXb8Uc9A7CydJU6FSn5ePJMM4kZY+UIOny2RLtJTWI1/iT\nRdOHSznrWMZFkxEK+h/1q87COAG9VlxbqIw0+eUkjodxSmWPh2pSTbnISCeeG0eEhMZZlmnQws+4\nsqcRqBwjuU+uBkYvfOJbZO3hc3tOjmZGgjG/ulcPvpNA9q6FZO/s+BDuFDXcbhThyhsV9+SHcSY9\n08eN43DJlFf5LXdPH1u4LqHcQxinporfaNzMsc5w45CN8+AgG+vBQTbW6ZCRvRRYW1tzbjszMYTh\nYg71to/ltUPzeeTEyYiPCGkEbOfIjh8naqTsTYe5Kr0pe/Y+PKxuajgsGl7X6+7R5Hw8JIU8F0xO\n4CtC2eMumgQZusXDOAHdfEXm7NGcUlP/ioqyx1VL4hqSVPKJMJ2HxnlIkDfNGdEK41Ryo+gT3uaG\nkp8pFVZe8HwmJPirewGRSwrjJGWvW72347TjN2Y8t4Cyl/RMHzeSymSkheR1NyJisheDltfdOYm/\n/prz+MmveeD4G+TAzRzrDDcO2TgPDrKxHhxkY50OGdlLgaRck0LOw9JcYDnO8+u0MgQypBGIJn5E\nHmSOHv1NNaikYQsA1ELCQOGGMnSKK3KGxMXq7tm14MbK8f1IhTQ5e0T2GkSywmNYOXvBvx0/CGn8\n1HNb1nmGknIDDdnLWZ8DdumF5Jw9IqY22eOOndRuGueScFTUVItubpx0LD4WvI88Z4+DK46G7IVE\nLimMk5S9bvXZ2sdANAiRG6etvJ5E3Mz8sWMhe/LvG9A9XkLiofkRdZ+c5+FdD8ziwlT5+BvkQJYr\nOBjIxnlwkI314CAb63TIyF4KTE9PJ24nwsIdLpsiLBLgboVM2QsnfhQ2KcMr6e+z44F5y3Y17rpI\neXAjYVjlv/vDS9Z2o4LlPXMeqeyRKkakiFbqLWVPTODpfESy6iwfj0C9930fv/nsNi7vNsJ9bCMY\nrmjGyV48jJPnD5LCQGUguOkNCauRo2fQT56LSASJxlnm4Gl10bjap+Xs0Vhz8m6TvShnjxM+3scZ\nQfC1cNHRkLxf61nZS9x8XeB19szCwAkle92e6ePEsRBu8YN4I676UCGHD7/8DL71FWdTuWTeKNzM\nsc5w45CN8+AgG+vBQTbW6ZCRvRToJiNr6pQWxhmZdkTfpck9kasDh7J3fjJYGd84bMZC8ehc9K8Q\ni6wyEJpiB0SKF5l5TFeC/b64FhUWj0Ingz4NizDOz4W5aSWL4IZ9BvCZy5ERiQzjrCs5ewWRs8cn\nyS3Wp5woA8Fz9u4K89co5JT6eRCqkQ/Pj+BM6JRK48xJ1XAxpxpm8Dy+pHpmvE4iN/Hhyh7PueQL\nBkT2CEk5e1RH0eX0eCM4l+d5hmTIUh4nDTcjNOQlC4GF9GsWJ/t+bHmVjztfj/C+R+fxNY+cuiHn\nSossDGgwkI3z4CAb68FBNtbpkJG9FBgfT7Ywj/LOmPKUUHOOpvPtjo+OH3w+OmSHRBKISE1WChgb\nyqPV8WM11UhFed9L9ERWroJRGOceO8bnru5HuXSiVMQfX9zDpZ0aAL30ArW53urg89dCsqcUlu74\nNlmTYZxVhSgT2aNrSOfv+L4htHR5o1DOthWi+RefOA0gnhtI5PIdS5FjIY0zJ1Vavh5gh0smFVXn\n5P3xs2Pm/0VSg1sdq++NVlzZI2gq2bhwQXTVMsvfoMk/NZFI60lV9ro908eBH/jyu/ADb7sL7z0G\ncnQzwjhvFdyMsc5w45GN8+AgG+vBQTbW6ZCRvRRot+OlDDiG2MSdoIVxmglYOJ/neWeyMDiB/h4u\n5s3kf+PQrqlG5OjO6Sgvhqt/nHiOCyUIAD7ysS+xNoZkbyyq+ffF0HhGhnESwfrpP7lqCn8DkWoG\ncFdKH23WJjI1SVL28kLZI7LHwzypveb6NaKwyHcuzRilq5QPVKdm20e74xsywlU8Gmc+Zq4cOE4C\nJyvu8pU8LPcDL12Ivs/yDHkI6ysuRC+24VLeKKyyXQQyaImOq7e3m91/v5ALx4pIdSF3Ml853Z7p\n48BIKY9XLU4cDwEWh7xRyt6tgJsx1hluPLJxHhxkYz04yMY6HU7mzOuE4+DgIHE7KTucsDQMwVLc\nOEPSwxU3o5KJME5O1LqRvVI+pxueMIOWMWPQEs/94zjDisCT0sUdMAFbhby8Wzf/32F5hR4L42wp\nyp5WMF0WeC94NtmTyh9gK3sNhysoD/XUagLSOHNlz2Upzw1apAIHxHP2XnF+3FI86bj7jZZR9r7j\nVediYZiPnonUQI0kjAplr+IipwmFvPsJ6iEVpHe5NN5sdHumbzXElL2b0oqTidttrDPoyMZ5cJCN\n9eAgG+t0yMheCiwsLCRu18oHNNs2YQGYWUn4L1eoRkIiciDCOFvM6GI2rLu2fiDIHlMR1bZ0IhVr\nrBzWz6slkz3P8/C2e6etY8kwTq4qPb0elZ34Cw9EBeQjgxaAVxlIytmLlV7IS7IXJ3NcGW0qRJuf\nq9bssGNE+9A4F9hnLmWPE1ctp4+EFRpPaZxC126/3jbXVzNXuYvVzNNUsriypz/irnDUfoOUPbpH\np4dPJtnr9kzfapCOZZmwF+F2G+sMOrJxHhxkYz04yMY6HTKylwJXr15N3K66cbbjYZxS2eOKW2R2\nYodxcqMXKr8QI3tsH408NawwzpBkNNpda67J2nTSJfMr7o/y3Z7fCvL67psdtlTByIFU5ux56jm0\n89C/9H1ZJgIQyp5CBoP+R+NEuXF8HxpnTtBdZO/xs2O4Z6aCb3hUz5Mkq5LIJdM+zigLpyWDlrJC\n1C5MRqG5WijmUN6zPncZtHRz6ewXqCUbRPZOqEtjt2f6VkM8Zy9je4Tbbawz6MjGeXCQjfXgIBvr\ndMjIXgoUi8kTViIMlhuncK4E4nX2uFJWoTIGMWUv2mcqnDhvS4MWRuY08sRVxnzOw3Axh44fqU7k\n6Pjmu6es40qVsCXy3CrFPN7z0BwAYDMMLZWkwmOJipxcmjDOnurs2WGkmvlNhSl7snB7dE5e7iAk\nhGwfGudecvaGCjn86/fcj295+Rl1O4Xa/uLn14N+iusShXG2TV5mpRA/1xTL2dPCOD3PM+MHwCjE\nEo+H4aBayGk/QSrnZjXo/0RCPuPNRLdn+lZH9qKPcLuPdYYA2TgPDrKxHhxkY50OJ3PmdcIxMTGR\nuJ1C5A6aSp6cYtDSMWQvCtF0GbRw4jMZ5j/tONw4A7IXJ54tYRYzXi7gsNnAbq1thQF++6vOWcfl\nRExzwAQickc5WpJgGQdSPwrxAxRlT6uzl3cpe/EQTE5MNfMV/nez7as5ezTOveTsHRUyZ45y2V7Y\nrpm8Pk3Z4+GXLmOP6UoRm4fB9Xcpex94bAETlQJetZh8L18vSL2m+28ooSzFzUS3Z/pWgxTyMmEv\nwu021hl0ZOM8OMjGenCQjXU6nMyZ1wnH+vp64naj0jDTEzWME1RnTxq05AwZkHX2ONkjlWSn6lL2\ndIMWmcNmyi+E7TUTc0HUeI4bN03hIWLUblJyypLsMTVTKyZtztHuruyZnL1OnEjbZC9O5Pjfjbbu\nxknjXOwhZ++oqIjrwh08KSxX7gMAI4y8yfEhnJuIwmalYQuhVMjhvQ+fwumxIXV7v0BXvH7CSy90\ne6ZvNdysOnu3Am63sc6gIxvnwUE21oODbKzTISN7KdBtZYGbbRAiQhIP4yRaw0nJCKtZx6Epe84w\nzpxnQgEPGnGyRxPvcTJpqbfg+77qbgmwYvHtjlEqpRkJKXvbDmUvKqruW6Ymk2FIqqbsyfaY0gtU\nPL6VrOxp5iv872a7wxxM48peoYcwzm542bkx628Z3qpNxnVlL/psyhESeW4iyus77jDNbqCo5Sev\nBg5aJ7Wo+m23WpgZtDhx2411BhXZOA8OsrEeHGRjnQ4Z2UuBRqORuH1MqV2nunGymnOATVoqrO4a\nByd7dJ79hiR7kYqo7SNr/pnyC7U2On7gDprz4kRuSFP28pLs5a12SmWPwJW9v/rKs4ZEae6hpLrR\n+aWy98xmNdYWIkr1VscolXGDlkjZ0wghjXMvBi3d8H1vvcv6WwuvfPT0qPW3du34Z9J5k3CWKXsu\nQnijIEmsHIOTgm7P9K2Ok3nVbw5u97HOECAb58FBNtaDg2ys0yEjeylQrVYTtxtnxUZyGCc5NJLA\nVTcmIe46e6aQed4zxIScJM25mIqoqoyxME4ipy1nfhtg5+xRLqHMwZJkSFr8czdOasc9s8PqOQhE\n/MqS7IUk+V/97kUAwGev7JvvcGKquXXyv5sdPdSTxtk2aEn3yJQLOSxORYqbRhq/63UXrL9HFTLH\nQ2YpH1OCq3naON5IyKjNkxrG2e2ZvtWQuXG6cbuNdQYd2TgPDrKxHhxkY50OmUFLCnSr8zExVEDe\nA7YOW7i238Cp0RIaShinnPdyUkIuilVG9nzftwqv87BKQrvjo+MHk72851AZRZHyMZOz11YVSAJ3\n9iRTGOmuKMMTJTkyaiZ8tP14uKhWVL0hcgiJfFFbNUQKISu9UHAoey1fNXmhceYOqqOl9I/MGCN4\nVCORY5wVHB8q5JyqKIGXYeB4ZGEUr1mcsEj0zYJU9rTagCcBt1vtHn7VTyi/vmm43cY6g45snAcH\n2VgPDrKxToeTOfM64ehW56NUyOFl58bhA3jyaqA2JYVxUgkCTjiMQQvLtSNuk/OCSXSJkZ6OMHkp\n5j3Lhn/PMouxQzBpn916yxmeCdhEzJC9sizibStWI+Jvz5jSxI1XAKiGMjIMkwxweJ9ibbVy9lzK\nHi+9YDt+AtE4U04jkF7ZA2yzlDmF7PEC6Enn+Y/vfwj/6quXMDtSUrfncx6+/2134QOP3fyXoiQa\n2n11EnC71e7hHPtkXvGbh9ttrDPoyMZ5cJCN9eAgG+t0yMheCpRK+iSb43RYSHwzNCpJKqpO5eZ4\nYW8tjLMlFDnP8zAkavo1RRgmqUXbVSWk1Bi0KMqeRvY0Za/cTdkTZI+FcWpkT+bsVZtt1EWdPGrv\nbi2B7BV5GKdu0ELXiPIiiznPUqJonO+YqpjPZFjqUcD7Ka8bYIfaybZyzI+VcN8JUO16gVT2NMX4\nJKCXZ/pWRebEaeN2HusMEbJxHhxkYz04yMY6HTKylwJjY2Nd95keDibzW2ExbY1E8ZpzgK3slfIe\nch7VgLOLmBcYEaAi4KRMSQXxTEg6L+3WzXdaIqR0fCgiT1Gtv+ScvZ6VPUfOHuBH+YdKHTvKMfzR\n33qBfTfYz1VfcGlOyf1rdy+9sB86nkqCS+M8Xi5gaW4YC2MlU8g+DXhoarccqiSydyshFsZ5QpW9\nXp7pWwmWsncyL/lNw+021hl0ZOM8OMjGenCQjXU63B4zyhuMjY2NrvtMh6SA6s1FqhzP2YvKEAC8\nvl0QgklEicxQmj2EPUpSeZaRPeP6KUgWD+NsJCh7PGePVLXxoyp7zJRGU/bGBZH7zee2Y+2I9mkb\nlRIAfujtd8fb2uyYnD+XsncQhoPK7Xyc/8VX3oef/NoHrstg5JCF5HbDSQ13PCok0Tipyl4vz/St\nBI8Fb2bmLDZut7HOoCMb58FBNtaDg2ys0yEjeykwNTXVfR8ie4fuQuU8pBGIu2RG5RcC5UnNccsL\nsteJh3EWcx6qzSh3TYaUWmGcIlSUgyt7VNtvUpA9WRvOFcbJSy/wEg/DxRwKOQ81VjJBwtQXrDZN\nCOZoKW8RT62oelEYtFDbKNRWGrjwcc7nvOtW27Q8PRdOKik6KiRnvdnuoC708kzfSsgMWty43cY6\ng45snAcH2VgPDrKxTofrcuNcWlo6BeDTAN4GoAXgpxCUaXsSwHcsLy93lpaWvh/AXwi3/83l5eU/\nXFpauqfXfa+nfceFarWK8fHxxH1MGGeo7JmyClbOXvAv5ezVRT25ciEPoGlIj25oEpmMAHq4aLmY\nQ7PeRq3VQamQizmDUumF3VrLhFb2ruzJME0PlWLOqJEyrNP02dEfz/MwXs5j87CFXYcBS6mQw2S5\ngO1aC5d2gvBUqSiWw2LyAdnTlT0qUXA5DHGV23sZ56PgW195FvCAr33kVNd9b9swzhPKPPo91jcd\nmUGLE7fdWGdQkY3z4CAb68FBNtbpkHpGubS0VATwEwCo6MWPAvje5eXl1yGYX7x7aWnpcQBvAPAK\nAF8P4MdS7HviUKvVuu5DYZxboWpE5iu2nT4ZtJAbp62qlVkoIgA0W3EiFoVx6jl7QKT+Uc5YS+Sw\nDZfyyHmBUUmtFeavJeTs1ZosZ0+pBVdJdJWM+qyRPX7M3VoLD8+PAAAeOGUbkpwaDZJ0V7aC20+S\nStugRc/Zo/IHVwzZs7f3Ms5HwexICR99851Ymhvpuu/tEsYpcVLJXr/H+maDX+UsjNPG7TbWGXRk\n4zw4yMZ6cJCNdTpcj3zwzwH8GwCXw7+fAPCb4f//F4C3AngtgF9ZXl72l5eXXwBQWFpamjvivicO\nvdT5GC8XkPOC3LNmu8MKpsfr7FEYZ0uof0PCmZJCJ3koaEmGcSqun7J2nczZy3meqbVHYaeakUYQ\nyujBB7B2ECiWss4eEKlqAFBxKHuunD3+nVqzY/b5K684a+1DRO2F7Vr4HansBX9v11o4CA1YZAF4\nUvZ262TQYm+/GfVcvu2VZ1HMe/jwl5254ec+DsRy9k4oib3davdkYZxu3G5jnUFHNs6Dg2ysBwfZ\nWKdDqjDOpaWlDwFYW15e/t9LS0t/L/zYW15epirXewAmAIwD4NmU9PlR9l1ztWN7exs7OzuYnZ3F\nzs4Oms0mFhYWcPXqVYyMjCCfz2N3dxdzc3PY3NyE7/uYm5vD6uoqRkdHAQD7+/uYn5/H2toaPM/D\n9PQ01tbWMD4+jna7jYODA3PMYrGIiYkJPPPMM7hw4QIajQaq1arZXiqVMDY2ho2NDUxNTaFS8HDQ\n9LF9UMV+NVCPmrVDrKysYWZmBvVwhaLZbGJlZQW7B8E+uzvbODgYhdduBG2s1rGysom/9aubwfbD\nOg4PD7G5uYlOM/jOi1eu4kK5gfWQ/OQBvPjii/A8DySurW1uY7hVwPbeHgBgZ2sTly83MDExgUqu\ngx0AL1zbCr/vY2VlJdanobyHRtvH6n7QtsbeFnbzTWxtbWFmZgZ7e3toNZtmjDbW11Aqlcw4bWys\nAwA6fseQ273dbawd7JtxQtjv5y9dwX4tONb22ipqEwUzTmNh+tsLmwfBzdduoF6vm3EaHYvL/J1W\nAyuXVk2fttfsW6vgASsrKyiXy6hUKnj++edx1113YW9vD41Gw4xzpVKx+tTPe++JsSpe/1UXAD+4\nT+S9t76+jomJia73XrVaRa1WM9upT3ycbkSfzEpGiMsXX8S5M6dPXJ+azSbK5XLf3hE3u09b21vm\nmvudDmq12i3fp369y5eXlzE7O3tb9el2HKfr7dPy8jLm5+dvqz7djuPUjz4dHh5iYWHhturT7ThO\n/ejT1atXMTw8fFv1qV/jlJTP6FEI4VGwtLT0WwjSrnwALwXwFIDHl5eXC+H2dyPI43sKQHl5efmf\nhp9/Jvz8T5eXl8/1su/y8vK6qx1bW1tHb3wfsLq6ivn5+a77fePPPYn1gyb+09c/hI/80lNYO2ji\nP77/IcyPBSGI/+Q3nsdvPLOFv/vGRbz5nmn8i99+AR//4gb++mvO410PzOIffeI5fOq5bXz0zXfg\nDXdN4ct/8jPm2L/y4ccAILbPH724i4/+72fwxNkx/JN33gMA+MgvPYXPrR7gR951Lx5ZGMU//sRz\n+K3ntvH333QH3nh3cHP8zf/xFD5/7QDveXgOv/DkGl57xyS+7613xvr0Tf/5c4boAcD/+ksvtQxW\nAOBD//VzuLzbsNpJ+PzqAf7mLz2FpblhLK8dqsf4gV99Fr+zsoPve8ud+Dd/cBHX9pv46fc/iIWx\nIbPPT/3xZfzsn67izqkyntuq4TWLE/j+t91lnYtfr2Lew//8lpda2w8bbXz1T/+Z+ZtfM6D3cc7g\nxnf+4rIZ50dPj+L/b+/OgyQt6zuAf3uOnp6da+faGY5ldxF45FTBAwWXVcFlxaNisFwDYkhJmRIl\nWCTB4ohi8IgSE7ziVRRIYYyAlsYqItEIIkGxEFKi8UHBIIezu7PHXDuzM9Mz+eN93+n3fft5p3ue\n7u337ef3/VRZznS//b7P299lpn/zXJ+64PiUW2TmWtZ3/3I3vvSz5wB426PcefGpKbcoO1zLmsyY\nsxzMWg5mnay/vz9xHI/VME6t9Vat9Tla620AHgNwCYB7lFLb/EN2AHgAwIMAtiulWpRSxwBo8Yu3\nR9dwbOZ0dnZWPgjRFSGDYZbhFR/j++zFV6eMbzAeCNdWZZuqLxmGcca3Z1gqn/sXbL+wz98XMGm4\nXXi4ZE9Ha1mhB5TmHpoEIyWDe8oBZecIrjG7WFxZ6CU+HHS9Pyfyj1PzZe0yWTS0Kf6a+KIo1eZM\nycLJnjRSea5iWlzLOjx8lsM4o1zLmsyYsxzMWg5mbaeeS/5dBeAGpdRDAPIA7tJaPwKvkHsIwN0A\nLrc4NnP2799f+SCUiqxfjU2vzAsLzxsrrUxpXlwlvodeILz4SuKm6qHrdMQXejHM6wu2LQjm7CUt\n/R9eCCW+oXogacsEoLTv39P75yJtCwvm/M0uLOGgP98uXpgF2y8ERWO8GASAj59f2nfPVH7GF66I\nL9BSbc6ULPwWt2Z4oRDXss4lfE3uZU1mzFkOZi0Hs7ZT09YLAOD37gXOMTz/YQAfjj32RLXHZtHg\n4GBVxwWFzG2/+GPZY0Cp2FiO9ey1GVbjLIbmPrVGtl4wL74SLtaCQmn3zHzsmGgvHQDs9Xv2TAu0\nANF99HoNK3EG7U3S3dGGo3o78Jy/AuY6Q49ccI3JQ0UUl733I97rdmRfR+R703nOOLoXfYW2lZVD\nK1kX2xOw2pwpWXRz7xQbUoHLWXM1ziiXs6YS5iwHs5aDWdtxYzOvBpvyFzippLCyX17pbQ4XavHV\nOBdixV5QfMzMF1f2igOA8IjEoKdwfpXVOE9J3AIjAAAdeUlEQVQd9SaI/vyZSf+Y8mGcvSurcfrD\nOA1bLwBAZ+heTCtxAkBLrGcy7pWb+la+jhdYQKk4DdpiGqK5aX0h0mNh6tkDSttaVCNeMFabMyWL\nDifMbtHhctYZfttT4XLWVMKc5WDWcjBrOyz2LMzPz1c+CKViJyjmThiK7hWXi+2zt9Kz5xdhwWbn\nU/PFyLy9pVABEwzjDLZ2WFgqH8a5aX0BAFbmvy0a5uz1xoZFJs3Z6woVZ6Y99gDghvO2YKQ7j49u\nP9b4/AsGS2OuTYVcULjt8ReCie+hB3jv7ZG9HaHXmP8pVyr1PnD2xpWv87HitNqcKVmzbAHgWtbh\n3rwsv+9pcC1rMmPOcjBrOZi1HRZ7Fqrd5yPo0QuGRp6vot3PweexoIyL9+wFQyunDi2ubMoOAEuh\nIZ2F2AIt8Y3ZgVLhN19cwtShRTwxfjByHaBUWK68JuETYrC/HZDcs3f6Ub24fefJOO2IHuPzR4RW\n1TQVcsG8vt/4qzgmFXJbBgql8xh6CAHg0pd6+9Vdcro5sx0vHFr5Or6IC/dzqYMmmbPnWtbROXvZ\nfd/T4FrWZMac5WDWcjBrOyz2LIyNjVV1XNCzFwyb7IoVJMFn36CjbrEYL/a8YmrqUDGy6Ml5x5eK\nxpUFWhaDBVrKe+aCrxeKy7j9F2Ohx8Nz9qKFW1LP3nB3PvQac4FVydGh+Xam6wRFXDDXzlQQAohs\nxZBUEF7wwkHc9vaTcNFLKv+AWIjtCVdtzpQsXGhkuYfJtay5Gmcy17ImM+YsB7OWg1nbYbFnoeqt\nF2IFSFc++n1LbBjn4io9e3OhOXvvfdXRoXOWjgHMq3HmQz17u0N75EWHcUYLqqQFWoZDPXudCXPy\nKulNWMUzMNKdj8yfSyrkwquBJhWEuVwOR/R0VLVIxVJsfh+X+K1duNDI8kIhLmed4bc9FS5nTSXM\nWQ5mLQeztsNiz0I+n698EIBCa7zYS+jZ87+PF3v9/l5yu6cXVhZgOWlDV2TBl6F13jHBUNGV+XiR\n7Rm8r+eLy5EP3+Fj1hdKRZz3nPmfRrioiheza/HXW49BR1sLzt68vuy5XC6Hzf3heX3mQi5c7FXa\nZ281l738SKwvtOHCUzdEHq82Z6pOlnuYXMuawziTuZY1mTFnOZi1HMzaDos9CxMTE1UdV96zFy1a\n4qtxxhdOGe5qR3e+FRNzi3je36ogfs5Bv6ft8V0zmJxbNA7jDPfshVdEDPf+9a9ri8zhq2ZT9aTV\nNqvx+hMG8Z13nYY3hObMhW1cH57XZ9+zV423nTaCf7volMiwUKD6nClZZJ+9DFd7rmUd7kVlz16U\na1mTGXOWg1nLwaztsNizMDRkLlDiCm2VevbMwziDD8W5XA6b+r35a78dnwVQXmANriv1yP382Unj\napzBZuHzxeXIB7/2yDYQucgQzaQFWoINz033t1arLcV/VF/l+Xib+gtoyXm9GOG22zANMaw2Z0oW\nXY0zu1WHy1ln+X1Pg8tZUwlzloNZy8Gs7bDYs1DtXxbihVlXu3kYZ1nPXqjQ2uAviPLc5ByA8gKr\ns711pefr4HzRuIde0LO3UFxCaOpfWe/dUFc+9FzCPnuhwqvWYm81o93hYs/ca3dkbwe+/NYTccc7\nTkZ3wjYQteBfkGrXLD1MrmUdfq+z/L6nwbWsyYw5y8Gs5WDWdljsWVhYWKjquHAx1JIr76EKlqIv\nrvTseZVYeLhb0GP1zIFDZecMBEMhZxeW8MPf7QMQLRhbW3JoyXlFZbCQyw41WFbQhbdfONzDOCsJ\nLxiz2ny8Y/oLkSK1nqrNmZI1S8+ea1lH3vfUWpFNrmVNZsxZDmYtB7O2w88BFqrd5yNcDK1rby0b\nKtixsm2Cv9n5yh55pdcFwzR3+atomgqsoGfv/w7MlfbZixVyQe9eUOy97riBsvOEt19IKrDC188n\n9P7VQ29Hfebj1YL7udQuMmcvu7Wec1lHFmjJ8PueBteyJjPmLAezloNZ22GxZ6HafT7CvXDx+XoA\n0NEW3RB9zv//8CIswYqcpdcYij3/3Lun5kOPRrcRCObtTR4qll0jEO5N60vYHqFRvTPhwrPbcj+/\nWnE/l/rKcs+ec1lHhs9m931Pg3NZkxFzloNZy8Gs7bDYs9DV1VXVcRWLPb9nbG5xGeMz8zi4sFT2\nur7OaNFlKvaCOW3jB0vd2wdmFyPHBAXT+Ix3THxbCCDam1ZpLzwAGFhX26IoqwkXnscOpLOvSrU5\nU7KWJpmz51rWuYSvyb2syYw5y8Gs5WDWduq/qoUAra3V9TSFe8/MPXve84cWl/C+7+jS+SP730Uj\nKhjGwnX519kzU+rZWx/rEdzU34nnJ0vPm3r2hkIrWvatsuDJbW8/CTOHiom9f/VQaGtBoa0Fc4tL\nOGZ94bBdZzXV5kzJmmXOnmtZh9/qLL/vaXAtazJjznIwazmYtR327FmYnJys6rjwXLOufPlbvVLs\nFZew7+Bi2fNAebFn6tkLeu2ClTgBYOuW6Gbl8YLJtNDLySPdK1+vtijKET0dOG5oXeLz9ZDL5XD7\nzpPxzYtOSW1/tmpzpupkec6ea1lzzl4y17ImM+YsB7OWg1nbYc+eheHh4aqOW0vPXpKu2Hw1U49c\nfDjlm04cKiuQqikaR3ryuGrrMehsa8nEPJ/D2XNYjWpzpmTN0sPkctYZ3ss+FS5nTSXMWQ5mLQez\ntsOePQv79u2r6rhoz155sRf0rs0uFBPP0d6Si/SImIq0gdiQTVORFJ4Dl0NpwZa47ScMYuux/Ynt\nkaTanClZDs0xZ8/lrHOctRfhctZUwpzlYNZyMGs7LPYsLC8vVz4I0YLKNGwyKNwefX468Ry5XA6F\nUNFoOk9PR2tkX7xTRssnsIYLwEJ7Nnrusq7anClZs/TsuZY1N1VP5lrWZMac5WDWcjBrOyz2LFTb\njRwuqEyrW5oKN5PO0HEdhlU0c7lcZCXNjYYFTcLP96S0lUGz4XCB2oXrjMO4LWPNXMu6WXpU0+Ba\n1mTGnOVg1nIwazsZ/viVXbt27Vrza+JDLQFgi2FLgS+99YVlj4Xn6ZmGcQLRYaK9hpU0w8XmaHfH\n6o0lAHY5U1Sz9Oy5nHULh3FGuJw1lTBnOZi1HMzaDos9C93d3ZUP8p1z7Hr0drTizGN6y55ra8nh\nxUeWznXsQKexAOysothrqTCvLzyMc7QnX1XbpVtLzpSk9A8zywuFuJY1h3Emcy1rMmPOcjBrOZi1\nHa7GeZhd85rNWFxaRnvCGLbOtlKPXNJ2B4XQMabVOAGguLT6OOZ1odcdzs3QicJaIkUHq45Gie5v\nmFoziIiIKGXs2bMwPZ28oEpcLpdLLPSAaPGWNIcvXAQWEs51cCF5+4agHYF1hj3/qNxaciazyJy9\nDBcdrmUdrasz/ManwLWsyYw5y8Gs5WDWdvip38LIyEjdzhUu8JJ69ka6S8Mu8wkFYfBxrr+zcmdt\n+HyUrJ45i9Ukc/bcy7o5hs+mwb2syYQ5y8Gs5WDWdljsWdizZ0/dzhXp2Ws3r5J5dF9pQZV1CQXh\nB1+zGSduWIdPveH4xGtd+9rN2KEGsXUL99GrRj1zlio6nDC7VYdrWYff6Qy/7alwLWsyY85yMGs5\nmLUdztmzUM+5R+Gevb6ELRHOV4N4ZuIQzj1uIPHapx3RjZvfrFa91jnH9uMcbpheNc4xq134Pczy\n2+la1s2yCmoaXMuazJizHMxaDmZth8WehYGBgbqdKzx007QXn3dMK644a2PdrknVqWfOUkXn7GX3\nh7RrWecSvib3siYz5iwHs5aDWdvhME4L9exGPqq3tAF6X0KxR+ngcIHaRXuY0mtHJc5lzZ69RM5l\nTUbMWQ5mLQeztsNiz0Jvb/meebZOGula+bo7bx7GSemoZ85SNcucPdeyzqE5hs+mwbWsyYw5y8Gs\n5WDWdljsWSgWi3U71+C6drzjRSMYWteOk0e5WWSW1DNnsZpkzp5rWXMYZzLXsiYz5iwHs5aDWdth\nsWdhZmamrue79GVH4o53nIxBbnaeKfXOWaLwD5gsz9lzLmtuZp/IuazJiDnLwazlYNZ2WOxZGB0d\nrfs5+YEsew5HztJE5uxl+KeNa1lHh8+m1oxMci1rMmPOcjBrOZi1nQx//MqusbGxtJtADcCc6yvL\nc/ZczjrDb3sqXM6aSpizHMxaDmZth8WehfZ2DreUgDnXLrxQSJZ7mFzLmvvsJXMtazJjznIwazmY\ntR0Wexb6+vrSbgI1AHOuXbMUHa5lHVmNM8V2ZJFrWZMZc5aDWcvBrO2w2LMwPj6edhOoAZhz7Zpl\nnz2Xs85wjZ0Kl7OmEuYsB7OWg1nbYbFngX9ZkIE5165Z9tlzLescV+NM5FrWZMac5WDWcjBrOyz2\nLMzPz6fdBGoA5ly7Zpmz51rWkSI7tVZkk2tZkxlzloNZy8Gs7fBzgIXZ2dm0m0ANwJxr1yxz9lzL\nOtqzl147ssi1rMmMOcvBrOVg1nZY7FngPh8yMOfaNcucPZezznKRnQaXs6YS5iwHs5aDWdthsWeB\n+3zIwJxr1yxz9lzLOrIaZ3bf9lS4ljWZMWc5mLUczNoOiz0L+Xw+7SZQAzDnegjN2ctw155rWUeG\ncabXjExyLWsyY85yMGs5mLUdFnsWenp60m4CNQBzrl1kGGd6zajI5ay5GmeUy1lTCXOWg1nLwazt\nZPnzV2bt3bs37SZQAzDn2kWKvQz37LmWdXT4bGrNyCTXsiYz5iwHs5aDWdthsWehv78/7SZQAzDn\n2jVL0eFa1tFhnBl+41PgWtZkxpzlYNZyMGs7LPYscOlXGZhzfWV5gRbXsm6W/Q3T4FrWZMac5WDW\ncjBrOyz2LMzNzaXdBGoA5ly75eW0W1Ad57LmPnuJnMuajJizHMxaDmZth8WeBe7zIQNzrl2T1HrO\nZZ1L+Jrcy5rMmLMczFoOZm2HxZ4F7vMhA3OuXbP07LmWdaTYY9dehGtZkxlzloNZy8Gs7bDYs1Ao\nFNJuAjUAc67dcpP07bmcNefsRbmcNZUwZzmYtRzM2g6LPQudnZ1pN4EagDnXbqk5aj3nso6sxsme\nvQjXsiYz5iwHs5aDWdthsWdh//79aTeBGoA510GTFHvuZR1ajTPFVmSRe1mTCXOWg1nLwazt8HOA\nhcHBwbSbQA3AnGtXbJJJe65l3dFWKvbYsRflWtZkxpzlYNZyMGs7LPYsTE1Npd0EagDmXLtik4zj\ndC3rDV35la85jDPKtazJjDnLwazlYNZ2WOxZmJ+fT7sJ1ADMuXbN0rPnWtbrO9tWvp5dKKbYkuxx\nLWsyY85yMGs5mLUdFnsWuM+HDMy5ds3Ss+da1rlcDi89ugc5AKeMdqfdnExxLWsyY85yMGs5mLUd\nFnsWuM+HDMy5dsXmqPWczPrvX/8CfPPiU3H25vVpNyVTXMyayjFnOZi1HMzaDos9C1z6VQbmXLtm\n6dlzMevWlhz6Cm2VDxTGxaypHHOWg1nLwaztsNizkM/nKx9ETY85165Zij1mLQezloE5y8Gs5WDW\ndljsWZiYmEi7CdQAzLl2zbJAC7OWg1nLwJzlYNZyMGs7LPYsDA0Npd0EagDmXLtm6dlj1nIwaxmY\nsxzMWg5mbYfFngX+ZUEG5ly74lLaLagOs5aDWcvAnOVg1nIwazss9iwsLCyk3QRqAOZcu2YZxsms\n5WDWMjBnOZi1HMzaDos9C9znQwbmXLtmGcbJrOVg1jIwZzmYtRzM2g6LPQvc50MG5ly7ZunZY9Zy\nMGsZmLMczFoOZm2HxZ6Frq6utJtADcCca9csc/aYtRzMWgbmLAezloNZ27HacVcp1Q7gFgCbAXQA\nuBHArwHcCmAZwOMALtdaLymlPgTgAgCLAK7UWj+slDqu2mPtb+3waW1tTbsJ1ADMuXbNMoyTWcvB\nrGVgznIwazmYtR3bnr2LAezVWr8awPkAPgfg0wCu8x/LAXiLUup0AOcAeAWAnQA+779+LcdmzuTk\nZNpNoAZgzrVrlmGczFoOZi0Dc5aDWcvBrO3YFnt3Arje/zoHryfuDAD3+4/dA+BcAGcDuFdrvay1\n/gOANqXU8BqPzZzh4Uw2i+qMOdeuWXr2mLUczFoG5iwHs5aDWduxGsaptZ4GAKVUD4C7AFwH4Cat\ndfDJbgpAH4BeAHtDLw0ez63h2D1J7Thw4AAmJiYwNDSEiYkJLCwsYHR0FGNjY+jq6kJraysmJycx\nPDyMffv2YXl5GcPDw9i1axe6u7sBANPT0xgZGcGePXuQy+UwMDCAPXv2oLe3F8ViETMzMyvnbG9v\nR19fH5566ils3LgR8/PzmJ2dXXk+n8+jp6cHe/fuRX9/P2ZnZzE3N7fyfKFQQGdnJ/bv34/BwUFM\nTU1hfn5+5fnOzk7k8/lU7ml8fBx9fX28p9A9Pf3009iyZYtT99TonK44cwQf+dGzuOz0QYyPj2f2\nnpaWltDe3i42J0n39OSTT2JwcNCpe3Ixp1rv6cknn8SGDRucuicXc6rHPc3NzWHDhg1O3ZOLOdXj\nnnbv3o1CoeDUPdUrp/7+/qRyCblly2FWSqmNAL4N4Ata61uUUs9qrY/2n3sLgPMAPAGgoLX+pP/4\no/7jj1V7rNZ6PKkN+/fvT6Xb4JlnnsHGjRvTuDQ1EHOuj+XlZeRyubSbsSpmLQezloE5y8Gs5WDW\nyfr7+xM/aFkN41RKjQC4F8DVWutb/IcfVUpt87/eAeABAA8C2K6UalFKHQOgxS/e1nJs5rAbWQbm\nXB9ZL/QAZi0Js5aBOcvBrOVg1nZs5+xdA6AfwPVKqfuUUvfBG8p5g1LqIQB5AHdprR+BV8g9BOBu\nAJf7r79qDcdmzq5du9JuAjUAc5aDWcvBrGVgznIwazmYtR3rYZxZkNYwzr1792JwcDCNS1MDMWc5\nmLUczFoG5iwHs5aDWSer+zBOIiIiIiIiyjYWexamp6fTbgI1AHOWg1nLwaxlYM5yMGs5mLUdDuO0\nMDc3h0KhkMalqYGYsxzMWg5mLQNzloNZy8Gsk3EYZ53t2ZO49R85hDnLwazlYNYyMGc5mLUczNoO\niz0LzbCUPNWOOcvBrOVg1jIwZzmYtRzM2g6LPQsDAwNpN4EagDnLwazlYNYyMGc5mLUczNoOiz0L\n7EaWgTnLwazlYNYyMGc5mLUczNoOiz0Lvb29aTeBGoA5y8Gs5WDWMjBnOZi1HMzaDos9C8ViMe0m\nUAMwZzmYtRzMWgbmLAezloNZ22GxZ2FmZibtJlADMGc5mLUczFoG5iwHs5aDWdvhPnsWDh06hI6O\njjQuTQ3EnOVg1nIwaxmYsxzMWg5mnYz77NXZ2NhY2k2gBmDOcjBrOZi1DMxZDmYtB7O2w2LPQnt7\ne9pNoAZgznIwazmYtQzMWQ5mLQeztsNiz0JfX1/aTaAGYM5yMGs5mLUMzFkOZi0Hs7bDYs/C+Ph4\n2k2gBmDOcjBrOZi1DMxZDmYtB7O209QLtBA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with plt.style.context('bmh'): \n", " plt.figure(figsize=(15, 8))\n", " plt.title('Ads watched (hour ticks)')\n", " plt.plot(df.ads);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We have everything you could ask for - trend, seasonality, even some outliers.\n", "\n", "In this assignment we will concentrate on methods that have proven to be working in practice and can provide quality, comparable to ARIMA models. Namely, feature engineering, selecting and machine learning\n", "\n", "But before digging into practice - a tiny bit of theory on how to create even more features. In this hometask we will be working with linear models. That means we assume there's a linear dependance between our target variable and the featureset, and we try to model that dependance. Now remember the hour variable we've created in the lecture? That variable showed on which hour a given observation arrived. Naturally, we expect hour plays a huge role, since at night the amount ofactive users who can watch ads drops significantly, at during the day it rises to its peak. However, if we use a single feature with number of an hour, linear models will not be able to model that dependance correctly. Why? Because look at the feature itself. It has values from $0$ to $23$ and even though we know that 0:00 is closer to 23:00 than, say, 20:00 to 23:00, the model will only see the numbers, not the logic behind them. And, of course, number 0 is way further from number 23 than number 20 from 23. \n", "\n", "How will we solve that problem? \n", "\n", "- First possible solution - let's get dummies and make 24 new columns out of one. Clear disadvantages - we explode the dimentionality of our data and lose any trace of the cyclical nature of hours.\n", "\n", "- Second solution - sine/cosine transformation. To fully understand that approach, read [this short article](https://ianlondon.github.io/blog/encoding-cyclical-features-24hour-time/). But in short - we want to encode hour feature with two new columns, which are sine and cosine transformations of \"hour from midnight\"" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use the already familiar prepareData function with some modifications - sine/cosine transformation for hour and dummy transformation for weekday features" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "code_folding": [], "collapsed": true }, "outputs": [], "source": [ "def prepareData(data, lag_start=5, lag_end=14, test_size=0.15):\n", " \"\"\"\n", " series: pd.DataFrame\n", " dataframe with timeseries\n", "\n", " lag_start: int\n", " initial step back in time to slice target variable \n", " example - lag_start = 1 means that the model \n", " will see yesterday's values to predict today\n", "\n", " lag_end: int\n", " final step back in time to slice target variable\n", " example - lag_end = 4 means that the model \n", " will see up to 4 days back in time to predict today\n", "\n", " test_size: float\n", " size of the test dataset after train/test split as percentage of dataset\n", "\n", " \"\"\"\n", " data = pd.DataFrame(data.copy())\n", " data.columns = [\"y\"]\n", " \n", " # calculate test index start position to split data on train test\n", " test_index = int(len(data) * (1 - test_size))\n", " \n", " # adding lags of original time series data as features\n", " for i in range(lag_start, lag_end):\n", " data[\"lag_{}\".format(i)] = data.y.shift(i)\n", " \n", " # transforming df index to datetime and creating new variables\n", " data.index = pd.to_datetime(data.index)\n", " data[\"hour\"] = data.index.hour\n", " data[\"weekday\"] = data.index.weekday\n", " \n", " # since we will be using only linear models we need to get dummies from weekdays \n", " # to avoid imposing weird algebraic rules on day numbers\n", " data = pd.concat([\n", " data.drop(\"weekday\", axis=1), \n", " pd.get_dummies(data['weekday'], prefix='weekday')\n", " ], axis=1)\n", " \n", " # encode hour with sin/cos transformation\n", " # credits - https://ianlondon.github.io/blog/encoding-cyclical-features-24hour-time/\n", " data['sin_hour'] = np.sin(2*np.pi*data['hour']/24)\n", " data['cos_hour'] = np.cos(2*np.pi*data['hour']/24)\n", " data.drop([\"hour\"], axis=1, inplace=True)\n", " \n", "\n", " data = data.dropna()\n", " data = data.reset_index(drop=True)\n", " \n", " \n", " # splitting whole dataset on train and test\n", " X_train = data.loc[:test_index].drop([\"y\"], axis=1)\n", " y_train = data.loc[:test_index][\"y\"]\n", " X_test = data.loc[test_index:].drop([\"y\"], axis=1)\n", " y_test = data.loc[test_index:][\"y\"]\n", " \n", " return X_train, X_test, y_train, y_test" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Use the functions on original df to prepare datasets necessary for model training. Reserve 30% of data for testing, use initial lag 12 and final lag 48. This way the model will be able to make forecasts twelve steps ahead, having observed data from the previous 1.5 day. \n", "\n", "Scale the resulting datasets with the help of StandardScaler and create new variables - X_train_scaled and X_test_scaled. Don't forget that scaler should be trained on train set only to prevent information about future from leaking." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# You code here\n", "# X_train, X_test, y_train, y_test = " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now train a simple linear regression on scaled data:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# You code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check the quality of the model on the training set via cross-validation. To do so you need to create an object-generator of time series cv folds with the help of TimeSeriesSplit. Set the number of folds to be equal to 5. Then use cross_val_score, feeding it's cv parameter with the created generator. Quality metrics should be neg_mean_absolute_error.\n", "\n", "Don't forget to take an average of the result and multiply it by -1." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "# You code here\n", "# tscv = " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 1. What is the value of MAE on cross-validation?**\n", "\n", "*For discussions, please stick to [ODS Slack](https://opendatascience.slack.com/), channel #mlcourse_ai_news, pinned thread __#a4__*\n", "\n", "- 4876\n", "- 41454725\n", "- 4490\n", "- 0.712" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's have a look at the forecast itself. We'll need plotModelResults function. " ] }, { "cell_type": "code", "execution_count": null, "metadata": { "code_folding": [] }, "outputs": [], "source": [ "def plotModelResults(model, df_train, df_test, y_train, y_test, plot_intervals=False, scale=1.96, cv=tscv):\n", " \"\"\"\n", " Plots modelled vs fact values\n", " \n", " model: fitted model \n", " \n", " df_train, df_test: splitted featuresets\n", " \n", " y_train, y_test: targets\n", " \n", " plot_intervals: bool, if True, plot prediction intervals\n", " \n", " scale: float, sets the width of the intervals\n", " \n", " cv: cross validation method, needed for intervals\n", " \n", " \"\"\"\n", " # making predictions for test\n", " prediction = model.predict(df_test)\n", " \n", " plt.figure(figsize=(20, 7))\n", " plt.plot(prediction, \"g\", label=\"prediction\", linewidth=2.0)\n", " plt.plot(y_test.values, label=\"actual\", linewidth=2.0)\n", " \n", " if plot_intervals:\n", " # calculate cv scores\n", " cv = cross_val_score(\n", " model, \n", " df_train, \n", " y_train, \n", " cv=cv, \n", " scoring=\"neg_mean_squared_error\"\n", " )\n", "\n", " # calculate cv error deviation\n", " deviation = np.sqrt(cv.std())\n", " \n", " # calculate lower and upper intervals\n", " lower = prediction - (scale * deviation)\n", " upper = prediction + (scale * deviation)\n", " \n", " plt.plot(lower, \"r--\", label=\"upper bond / lower bond\", alpha=0.5)\n", " plt.plot(upper, \"r--\", alpha=0.5)\n", " \n", " # calculate overall quality on test set\n", " mae = mean_absolute_error(prediction, y_test)\n", " mape = mean_absolute_percentage_error(prediction, y_test)\n", " plt.title(\"MAE {}, MAPE {}%\".format(round(mae), round(mape, 2)))\n", " plt.legend(loc=\"best\")\n", " plt.grid(True);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For model coefficients visualization use the following functions:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def getCoefficients(model):\n", " \"\"\"Returns sorted coefficient values of the model\"\"\"\n", " coefs = pd.DataFrame(model.coef_, X_train.columns)\n", " coefs.columns = [\"coef\"]\n", " coefs[\"abs\"] = coefs.coef.apply(np.abs)\n", " return coefs.sort_values(by=\"abs\", ascending=False).drop([\"abs\"], axis=1) \n", " \n", "\n", "def plotCoefficients(model):\n", " \"\"\"Plots sorted coefficient values of the model\"\"\"\n", " coefs = getCoefficients(model)\n", " \n", " plt.figure(figsize=(20, 7))\n", " coefs.coef.plot(kind='bar')\n", " plt.grid(True, axis='y')\n", " plt.hlines(y=0, xmin=0, xmax=len(coefs), linestyles='dashed')\n", " plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Check the model results and plot the coefficients" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# you code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Wonderful, the intervals are plotted, forecast quality is great and everything seems to be fine, but...We might be having too many variables in our model and, possibly, some of them are not that important and can be dropped, reducing the dimentionality of data and reducing the chances of overfit. To make sure we have extra features, plot a heatmape of X_train data correlations with the help of heatmap function from seaborn library:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "# you code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Indeed, features are highly correlated and you can even observe some kind of \"seasonality\" in those correlations on each 24-th lag. Let's try to add regularization to our models and remove some features. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Train Lasso regression on cross-validation (LassoCV) again feeding the cv parameter with the created generator-object. \n", "\n", "Plot the forecast of the model and notice that the error on test dataset has not increased significantly " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# you code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Perfect, we are still having practically the same model quality, while having less features. Use the function getCoefficients and find, how many features are now dropped (coefficient equals zero)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "# you code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 2. How many coefficients of Lasso model equal zero? (with 6 digit precision)?**\n", "\n", "*For discussions, please stick to [ODS Slack](https://opendatascience.slack.com/), channel #mlcourse_ai_news, pinned thread __#a4__*\n", "\n", "- 11\n", "- 12\n", "- 15\n", "- 17" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alright, we have some features dropped. But what if we want to go further and transform our linear-dependant features into more compact representation? To do so we'll use principal component analysis." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "code_folding": [], "collapsed": true }, "outputs": [], "source": [ "from sklearn.decomposition import PCA\n", "from sklearn.pipeline import make_pipeline\n", "\n", "def plotPCA(pca):\n", " \"\"\"\n", " Plots accumulated percentage of explained variance by component\n", " \n", " pca: fitted PCA object\n", " \"\"\"\n", " components = range(1, pca.n_components_ + 1)\n", " variance = np.cumsum(np.round(pca.explained_variance_ratio_, decimals=4)*100)\n", " plt.figure(figsize=(20, 10))\n", " plt.bar(components, variance)\n", " \n", " # additionally mark the level of 95% of explained variance \n", " plt.hlines(y = 95, xmin=0, xmax=len(components), linestyles='dashed', colors='red')\n", " \n", " plt.xlabel('PCA components')\n", " plt.ylabel('variance')\n", " plt.xticks(components)\n", " plt.show()" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "# Create PCA object: pca\n", "\n", "# Train PCA on scaled data\n", "\n", "# plot explained variance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 3. What is the minimal number of components needed to explain at least 95% of variance of the train dataset?**\n", "\n", "*For discussions, please stick to [ODS Slack](https://opendatascience.slack.com/), channel #mlcourse_ai_news, pinned thread __#a4__*\n", "\n", "- 5\n", "- 7\n", "- 9\n", "- 12" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Create the pca object once again, this time setting inside it the optimal number of components (explaining at least 95% of variance). After that create two new variables - pca_features_train and pca_features_test, assigning to them pca-transformed scaled datasets." ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# you code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now train linear regression on pca features and plot its forecast." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "# you code here" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 4. What is the MAE of linear regression, trained on pca-transformed features? **\n", "\n", "*For discussions, please stick to [ODS Slack](https://opendatascience.slack.com/), channel #mlcourse_ai_news, pinned thread __#a4__*\n", "\n", "- 5140\n", "- 4917\n", "- 6719\n", "- 4663" ] } ], "metadata": { "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": "3.7.1" }, "varInspector": { "cols": { "lenName": 16, "lenType": 16, "lenVar": 40 }, "kernels_config": { "python": { "delete_cmd_postfix": "", "delete_cmd_prefix": "del ", "library": "var_list.py", "varRefreshCmd": "print(var_dic_list())" }, "r": { "delete_cmd_postfix": ") ", "delete_cmd_prefix": "rm(", "library": "var_list.r", "varRefreshCmd": "cat(var_dic_list()) " } }, "types_to_exclude": [ "module", "function", "builtin_function_or_method", "instance", "_Feature" ], "window_display": false } }, "nbformat": 4, "nbformat_minor": 2 }