{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Майнор по Анализу Данных, Группа ИАД-2\n", "## 15/02/2017 Линейная регрессия, градиентный спуск" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\n", "\n", "plt.style.use('ggplot')\n", "plt.rcParams['figure.figsize'] = (12,8)\n", "\n", "# Для кириллицы на графиках\n", "font = {'family': 'Verdana',\n", " 'weight': 'normal'}\n", "plt.rc('font', **font)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "code_folding": [], "collapsed": false }, "outputs": [], "source": [ "try:\n", " from ipywidgets import interact, IntSlider, fixed\n", " from utils import *\n", "except ImportError:\n", " print u'Так надо'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Постановка задачи" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Дано описание $n$ объектов по $m$ признакам. Обычно оно выражается в виде матрицы размера $n \\times m$: $X = [x^{(i)}_j]^{i=1\\dots n}_{j=1\\dots m} $. ($x^{(i)}_j$ означает $j$-ый признак $i$-го объекта) \n", "Дана **вещественная** зависимая переменная, которая тоже имеет отношение к этим объекам: $y \\in \\mathbb{R}^n$.\n", "\n", "Наша задача, выявить **линейную** зависимость между признаками в $X$ и значениями в $y$:\n", "$$\\hat{y} = X\\beta \\quad \\Leftrightarrow \\quad \\hat{y}^{(i)} = \\beta_0 + \\beta_1x^{(i)}_1 + \\dots$$\n", "То есть необходимо оценить коэффициенты $\\beta_i$.\n", "\n", "В случае линейной регрессии коэффициенты $\\beta_i$ рассчитываются так, чтобы минимизировать сумму квадратов ошибок по всем наблюдениям:\n", "$$ L(\\beta) = \\frac{1}{2n}(\\hat{y} - y)^{\\top}(\\hat{y} - y) = \\frac{1}{2n}(X\\beta - y)^{\\top}(X\\beta - y) \\rightarrow \\min$$ $$ \\Updownarrow $$ $$ L(\\beta_0,\\beta_1,\\dots) = \\frac{1}{2n}\\sum^{n}_{i=1}(\\hat{y}^{(i)} - y^{(i)})^2 = \\frac{1}{2n}\\sum^{n}_{i=1}(\\beta_0 + \\beta_1x^{(i)}_1 + \\dots - y^{(i)})^2 \\rightarrow \\min $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Пример: Стоимость автомобиля" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Загрузите [тренировочные данные](http://bit.ly/1gIQs6C) и [тестовые данные](http://bit.ly/IYPHrK) по характеристикам автомобилей Honda Accord. Названия столбцов говорят сами за себя." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "df_train = pd.read_csv('http://bit.ly/1gIQs6C')\n", "df_test = pd.read_csv('http://bit.ly/IYPHrK')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Выберем одну переменную mileage в качестве предиктора, а переменную price в качестве зависимой переменной" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "
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" ], "text/plain": [ " price mileage year trim engine transmission\n", "0 14995 67697 2006 ex 4 Cyl Manual\n", "1 11988 73738 2006 ex 4 Cyl Manual\n", "2 11999 80313 2006 lx 4 Cyl Automatic\n", "3 12995 86096 2006 lx 4 Cyl Automatic\n", "4 11333 79607 2006 lx 4 Cyl Automatic" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "df_train.head()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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Tk4k7Dw3Kb5m6aVWNNjTR2wkAAOQ3khBAnnEcR4YcWYYkx+G5KJDnQrapR7f3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\nSHd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "df_train.plot(x='mileage', y='price', kind='scatter', s=120)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.linear_model import LinearRegression" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Обучим модель" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = LinearRegression(fit_intercept=True)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "X = df_train.loc[:, ['mileage']].values\n", "y = df_train.loc[:, 'price'].values" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.fit(X,y)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Модель:\n", "price = 16762.02 + (-0.05)*mileage\n" ] } ], "source": [ "print 'Модель:\\nprice = %.2f + (%.2f)*mileage' % (model.intercept_, model.coef_[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Нарисуйте предсказание модели вместе с данными на плоскости" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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fPn06EP7UanW3Jtc2m83saRMB/wIkDtZVHKyrOFhXcUSjrm63AhaLGlarDHq9AKPR1ecH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\nKu12VVVVv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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = np.linspace(0, max(X), 100)\n", "y_line = model.intercept_ + model.coef_[0]*x\n", "\n", "fig, ax = plt.subplots(1, 1, figsize=(10,5))\n", "ax.scatter(X, y)\n", "\n", "ax.plot(x, y_line, c='red')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Остатки и меры качества" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Давайте взглянем на ошибки (остатки)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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1ffWrX5UkXXXVVQqFQlq9erWCwaCqq6u1ZMmShIVCAQAAJOnll19O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\nnE41DAbA6wVWrRIwf74WjY2RIE6thuQ50movBQtSVVdLl5qwZYsbfX1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OxRJGV8bF2xh0CUqLcHPY8sKfYokqp4YgPAoIqIiIiIiHKAU/+IiIiIiIiIiEgRGFQRERERERER\nEZEicOofERERERENOoGABk6nHi6XCmZzGDabH1ptsNjDIiIa9FhRRUREREREg0ogoIHDIWDSJCum\nTrVi0iQrHA4BgYCm2EMjIhr0GFQREREREdGg4nTqsWiRCT6fCgDg86mwaJEJTqe+yCMjIiIGVURE\nRERENKi4XCoxpIry+VRwuVQy7yAiokJhUEVERERERIOK2RyG0RiOe8xoDMNsDsu8g4iICoVBFRER\nERERDSo2mx/r17vFsEoQwli/3g2bzV/kkREREVf9IyIiIiKiQUWrDaKx0Yu2tgBX/SMiUhgGVURE\nRERENOhotUHY7T7Y7cUeCRERxeLUPyIiIiIiIiIiUgQGVUREREREREREpAgMqoiIiIiIiIiISBEY\nVBERERERERERkSIwqCIiIiIiIiIiIkVgUEVERERERERERIrAoIqIiIiIiIiIiBSBQRURERERERER\nESkCgyoiIiIiIiIiIlIEBlVERERERERERKQI2mIPgIiISptKq4Ou40Jetu3tughdMDjwDRkr0Wes\nHPh2iIiIiIgorxhUERHRwPT2oOeRJcUeRVIVT2wAGFQRERERESkep/4REREREREREZEiMKgiIiIi\nIiIiIiJFYFBFRERERERERESKwKCKiIiIiIiIiIgUgc3UiYio7OVzZcKc4uqERERERDTIMagiIqLy\nVwIrEwJcnZCIiIiIiFP/iIiIiIiIiIhIERhUERERERERERGRIjCoIiIiIiIiIiIiRWCPqhKn6fVB\n43YhHAwW/LM9fz8HXSiU8nUqgwHhAoyHiIiIiIiIiEpb2QdVO3fuxP79++FyuTB8+HDce++9GD9+\nfLGHlTOqQAA9T65E+KJyV7PSjLsOuvuWFXsYREREJeutt97C//zP/+D06dPw+/1YuHAhZsyYIT7/\nxhtvYMeOHTh37hxsNhtmzZqFO+64I24b+/btw8svv4yLFy+i5v+3d+dBUV1pG8CfbtZWQEBAaAmb\nYNS44b4hQhQ1UYJLxLhEcBKjEiexNJX5xliiJm5kYiYGnYprUDMCLgFjNEFFEUTcHRfABURkM7Qj\nq9I03O+PFHfsAEISltv086uySu493D7PS3M4nO57sLPDlClTMGLECK02bX3eRERERNLXpheqjh07\nhqNHj2LhwoVQKpWIj4/Hhg0bsHHjRtja2rZ294iIiIga9MMPP+DHH3/E5MmTMXv2bBgYGMDU1FQ8\nf//+fWzcuBGzZ8+Gp6cnMjIysHnzZlhbW2PYsGEAgEuXLmHnzp2YP38+3N3dcfXqVYSHh8POzg5d\nu3YFwHkTERERSUObXqg6fvw43njjDfTv3x8AMGPGDFy5cgWnTp3Cm2++2cq9IyIi0iYzNILR44bf\nIVtepIJRK9zyDQBQtEelon3rPLYeys/Px8GDB7Fu3TrY2dnV2ebkyZPo3bs3XnvtNQCAg4MDbt++\njbi4OHGh6vjx4/Dx8YGXl5fY5vr16zh+/Li4UMV5ExEREUlBm12oqqysRHZ2Ntzc3LSOv/zyy8jI\nyGilXhEREb1AxTM8+/t7rd2LFzJdvw3gQlWLSUxMhI2NDfbu3Yvbt29Do9HA3d0dwcHB4sJVZmYm\nevbsqfV53bp1w6lTp8SPMzIyMHDgwFptEhISAHDeRERERNLRZheqSkpKAAAKhULruLm5OTIzM3/3\n9QwNpVkqA1MF5JNnQygva/HHlslkEISGt0mX23aC3FQBoy4vt0Cv/jgDhfT7COhGP9nHpqML/WQf\nm44u9NPQVAEYGbV2N+ok1Z/Vf0ZWVhYqKyvRr18/TJo0CaWlpYiOjsbq1auxceNGGBoaori4uM75\nzrNnz6BWq2FsbIzi4mK0a9dOq42ZmRmKiooANP28CWibX4+GyGQyGEn0+6M56WNufcwMMLc+0cfM\ngH7mluLPa+n1qIkZGBg0um1iYiKSkpK0jnXv3h3+/v6wsrJq6q41nZecWrsHjfPV3tbuQcN0oY+A\nbvSTfWw6utBP9rHp6Eo/JSw2Nhapqalax4YPH15r4/DWFB0djf3799d73tbWFl9//TXKy8vRp08f\neHt7i+fs7e0REhKC1NRU9OrVC0Dj5jtyubzBNr9n3gTo8NypGenrfl76mFsfMwPMrU/0MTOgv7ml\nNH9qswtV5ubmAIDS0lKt4yUlJeK53xoxYkSdX4TY2Fj4+/s3fSd13K5duxAUFNTa3ZAk1qZurEvd\nWJf6sTZ1Y13qV/MzW+o/t/39/eHn51fv+ZpFJYVCUWsuY2NjA0NDQ/FdUBYWFigr035ndUlJCUxM\nTGBsbFxvm9LSUlhYWAD4Y/MmgHOn39LX7019zK2PmQHm1if6mBnQ39xSmz81/NKajjIyMoKjoyPS\n0tK0jt+5cweurq6/61q/XVWkXxUUFLR2FySLtakb61I31qV+rE3dWJf66crPbBMTE3To0KHefzWL\nQ126dMHNmzdR9dzm+bm5udBoNFAqlQAAV1fXWvOd9PR0rflOXW1u374ttmnKeROgO1+Hpqav35v6\nmFsfMwPMrU/0MTOgv7ml9nO7zS5UAcDo0aNx+PBhXLx4Ebm5uThw4AAePnyo9fZ5IiIiIqny9fVF\nZWUlvvjiC2RmZiI1NRXh4eHo27cvXFxcAAA+Pj5ITU1FbGws8vLykJycjPj4eIwePVq8zujRo3Hm\nzBmcOnUKeXl5OH78OC5fvlyrDedNRERE1Nra7K1/ADB+/HiUlZVh+/btKC4uRufOnfHxxx/D3t6+\ntbtGRERE1KAOHTpg1apViIiIwOrVqyGTyTB06FDMnj1bbOPq6orFixdj3759iIyMhKWlJd588014\neXmJbQYMGIDg4GAcOHAAjx8/hq2tLRYuXIhu3bqJbThvIiIiIilo0wtVADB16lRMnTq1tbtBRERE\n9IcolUr87W9/e2GbQYMGYdCgQS9sM2bMGIwZM+aFbThvIiIiotZmEBoaGtrandAFTk468pf1Whjr\nUj/Wpm6sS91Yl/qxNnVjXerH2kiDvn4dmFt/6GNmgLn1iT5mBphbCmSCIAit3QkiIiIiIiIiIqI2\nvZk6ERERERERERHpDi5UERERERERERGRJHChioiIiIiIiIiIJIELVUREREREREREJAlcqCIiIiIi\nIiIiIkkwbO0OtKbLly/jxx9/xL1796BWq/HOO+/Ax8dHPH/+/HlERkYiPz8fVlZWGDduHCZMmKB1\njePHjyM2NhYqlQp2dnaYMmUKRowYodVm//79OHHiBIqLi+Ho6IiZM2eid+/eLZLxz9i8eTNOnz6N\nnTt3ol27duJxfazLkydPsGfPHty5cwePHz+GhYUFhg4diunTp8PQ8H/fRvpYm8Zoa3l+6/Llyzhy\n5AgePnyIp0+fonPnzpgyZQoGDBgAANBoNNizZw+SkpLw9OlTuLq6Ijg4GG5ubuI1ysvLsWPHDly6\ndAkajQbdu3fHO++8Azs7O7HN48ePsW3bNty4cQMymQyenp6YO3cuLCwsWjzzH6FSqbBs2TK4u7tj\n6dKlAFgbtVqNw4cP4+zZsygoKICRkRG2bNkCU1NTva2NIAiIiYlBfHw8VCoVOnbsCB8fHwQEBADg\nc0YX6MqYL6Wx++HDh9ixYwdu374NExMTDB48GEFBQTA2Nm7WGrT2uNzSuaUy5rZkbimNqc2ZWxAE\n3L9/H59++ikWLFggfh9LMWNaWhoiIiKQlZUFMzMzeHt7Y8aMGU2e+9SpU4iPj0dOTg40Gg2cnZ3x\n1ltvoVu3bjqd+0WZn5eVlYUVK1bAx8cHc+bM0enMjcldWlqK77//HufPn4dKpYK1tTU2bdqks7kN\nQkNDQ39njdqEH374AZGRkRgzZgymTJkCPz8/dO7cWVyQqXkSBAQEYM6cOXB0dMTOnTvh4OCAl156\nCQBw6dIlbNmyBXPmzMH06dPRvn17bNu2Db1790bHjh0BAMeOHUNMTAzee+89TJkyBU+fPsWuXbvg\n5eWF9u3bt1r+hkRFRSExMRFqtRoBAQEwMjICoL91yc3NRWpqKt544w0EBASgS5cuOHjwIEpLS8XJ\nt77WpiFtLU9dzpw5Azs7OwQEBGD8+PGoqKjArl27MHDgQFhaWmLPnj24ePEiFi1ahAkTJiAnJwdR\nUVHw8/MTFzq/+uorFBQU4IMPPoCfnx+uX7+On3/+GX5+fpDJZACAVatWwdjYGB988AFGjhyJhIQE\nXLt2DV5eXq0Zv1GePn2K1atX4+nTp7CxscGwYcMAQK9rU1lZiZUrV6KkpARTp07FpEmTMHjwYNja\n2kImk+ltbQ4dOoRjx44hODgYkydPhlKpxHfffQdDQ0N07dpVb+uiK3RpzJfK2K1Wq7Fs2TK4uLgg\nJCQEAwcOxOHDh5Gfn4/+/fs3W/7WHpdbOrdUxtyWzi2VMbU5cxcWFmLu3Lk4fvw41Go1hg8fDqVS\nKZ6XUsYnT55g2bJlGDZsGObNm4cePXrg3//+NwRB0FpAaorcx48fx8svv4yAgACMHj0aeXl52Ldv\nH3x8fGBqaqqTuRvKXEOlUmH16tWorq6Gs7Mz+vbtK57TtcyNyV1cXIxPPvkE7du3x9SpUxEQEABP\nT0/x90udzC3ooby8PCE4OFgoKCiot8327duFNWvWaB3bsWOHEBoaKn68bt06YevWrVpt1q9fL4SH\nh4sfL1myRIiJidFqs3TpUiEqKurPRGhWJ0+eFP76178KycnJwrRp04SysjLxnD7X5beio6OFpUuX\nih+zNnVra3kaKyQkRPjhhx+EqqoqISgoSEhOThbPVVVVCcHBwUJ8fLwgCIJQVFQkBAYGCnfv3hXb\nFBcXC4GBgcLNmzcFQRCEe/fuCYGBgcKTJ0/ENhkZGcK0adOER48etUyoP0ij0QirV68Wdu7cKYSH\nhwthYWGCIAh6X5uoqChh7dq1dZ7T59osX75ciIiI0Dq2ZcsWYf369XpdF12h62N+a4zdycnJQlBQ\nkKDRaMQ2KSkpwqxZs4SKiopmySmFcbmlc0tlzG3p3FIZU5szt0ajEXJycoScnBxh2rRpwoULF7Ty\nSCnj4cOHhcWLF2v1//Dhw8LChQubNHd97d966y0hJSVFZ3M3JnNZWZmwdOlS4ciRI0JoaKiwa9cu\n8ZwuZm5M7vDwcGHbtm31fr4u5tbLPaoSExNhY2ODvXv3YsGCBXj33Xexfv16PHr0SGyTmZmp9XZQ\nAOjWrRsyMjLEjzMyMl7YprKyEtnZ2bXavPzyy1rXkZJr165h3759+Pvf/17n7Q/6Wpe6FBUVwczM\nTPyYtamtreVprKqqKpSVlcHMzAwFBQUoLy+Hq6ureF4ul8PDw0OsQWZmJgRB0Gpjbm4OpVIptsnI\nyICVlRU6dOggtnF1dYWxsbHka7llyxYoFAoEBQVpHdf32pw+fRpmZmZYtmwZ5s6di0WLFiEyMhKC\nIOh1bTw8PJCUlISbN28C+PWWjXv37qFPnz56XRddoOtjfmuN3ZmZmXBycoKBgYHYplu3blCr1Xj4\n8GGzZJXCuNzSuaUy5rZ0bqmMqc2Z28DAAEqlss531kgtY32/CxQWFqK0tLTJctelrKwMVVVV4u8v\n9+/f17ncDWWuqqrCP/7xD/Ts2ROvvfZarfO6mLmh3BqNBmfPnoUgCPj4448RHByMxYsX4+jRozqd\nWy/3qMrKykJlZSX69euHSZMmobS0FNHR0Vi9ejU2btwIQ0NDFBcXQ6FQaH2eubk5nj17BrVaDWNj\nYxQXF2vt3QQAZmZmKCoqAgCUlJQAQJ3XyczMbMaEf8z9+/cRHh6Ojz76CJ06dYJKparVRh/rUpf8\n/HwkJCTg3XffFY+xNrW1tTyNdfjwYcjlcgwcOBDZ2dkA6q5BcXExgF/rZGxsDLlcXqtNzXOjrucO\noP38kaKaPdvqusu8Jr8+1ubZs2f45Zdf4OHhgWnTpsHKygr37t3Dt99+C0EQ4OnpCUA/azNz5kwU\nFhZi1apV6Ny5M0xMTNC3b1+MHTsW6enpAPSzLrpA18f81hq765o/1PwiWfNYTQnqii0AABR2SURB\nVEkq43JL5pbSmNvSX2+pjKktnbuG1J7TxcXFcHBwqPU4QO0XwZtaZGQkHBwc0L17d7EvbS33v/71\nL7Rr105rT6rntcXMubm5qKyshFwux9tvvw0zMzNcv34du3fvhomJCXx9fXUyd5taqIqOjsb+/fvr\nPW9ra4uvv/4a5eXl6NOnD7y9vcVz9vb2CAkJQWpqKnr16gUAWiuF9fntF7sujblOc2pMXb788kts\n2LABf/nLX+Dh4QHg1w3b6tJW6gI0/jnzvMePH2Pt2rUYPHhwrU3Q21JtmlJby/MiZ8+exYEDB/DR\nRx9pDfYN1aCpnjtScvHiRSQlJeGzzz7T+qMDv6WPtSkvLwcAvPHGG3BxcQEAODk5QaVS4cSJE+Iv\nTfpYm/j4eBQWFmLLli3Izs7G8ePHERcXh549e4p7auhjXXSJLo75rT12t9TzUWrjckvlltqY25Lj\nj5TG1NYcd6WUsTXGyNjYWJw9exYrV64U9yNqbF90JfexY8eQl5eHFStW/Ol+6Epm4H/jW2BgoLgX\npLOzMx48eIBTp07B19e30X2RUu42tVDl7+8PPz+/es/XFFWhUNR625mNjQ0MDQ3FVwMtLCxQVlam\n1aakpAQmJibijvZ1tSktLRVvmatZOfztY5WUlIjnWkJj6qJWq6FSqbBp0yZ89dVXAP63UDVv3jyM\nGzcOs2bNalN1ARr/nKmRn5+PtWvXonv37njvvfe0zrW12jSFtpanISdPnkRERASWLFkibrJf87Ut\nKyvT2ki4pKQEnTp1EttUVFSgurpa6zlXUlIifn5dzx1A+/kjNY8ePUJhYSHmz58vHquqqgIAzJo1\nC2vWrAGgn7WpeTXqt98b9vb2KC4uFt92rW+1qaysxLfffoulS5fC2toa1tbW6NOnD3bt2oWtW7di\n2bJlAPSvLrpCV8f81h67LSwskJubW+v88/1oKlIal1syt5TG3JbMLaUxtSVzP09q38sWFhZ1jpHP\nt2lq+/fvx7Fjx7B8+XI4OTmJx9ta7vz8fGRmZmrd0qzRaJCWloa4uDhs3bq1zWUGIL64UlpaqvUc\nd3BwwJ07d8TH07XcberlRBMTE3To0KHefzWTpC5duuDmzZviD2bg17fMaTQa8b5PV1dXpKWlaV0/\nPT1d677Outrcvn1bbGNkZARHR8dabe7cuaN1nebWmLooFAps3LgRGzZsQFhYGMLCwsRJzKpVq+Dv\n7w+gbdUFaPxzBvg15/LlyzF06FDMnz9f69UIoO3Vpim0tTwvsm/fPnz33XdYtmyZ1l8W6dSpE9q1\na6dVA0EQcPfuXfFVXRcXF1RXV4tvwQd+HfRzc3PFOrm5uUGlUqGwsFBsc//+fajVasnWctSoUfj8\n88/FMSUsLAwDBgxAz549ERYWBqVSqbe1USgUsLe3x7Vr17SOP3jwAEqlEnZ2dnpZG41Gg4qKClRU\nVGgdt7a2RmlpqV5/P+kCXRzzpTB2u7q6IiMjA5WVlWKb9PR0sZ5NSUrjckvmltKY25K5pTSmtmTu\n50kto6urq9bjAL/+LmBtbd3kC/oajQabN2/G6dOn8emnn9baN6it5Z48ebLW2BYWFoYuXbrAy8sL\nYWFhUCgUbS4zACiVSpiamtYa37Kzs8Vb8HQxt0FoXTeot3FKpRJHjx7FnTt3oFQqkZ+fj+3bt8PJ\nyQkTJ04EAFhaWiIyMhLGxsawsLDAjRs3sH//fkydOhXOzs4AAFNTU0RGRqJjx44wMTFBSkoKfvzx\nRwQHB8PGxgYAUF1djYMHD+Kll14CAPz8889ISUnBvHnzmvUe5N9LJpPB3Nxc619ZWRlOnz6NWbNm\niX3Vt7rUuHz5MtatW4fXXnsNvr6+KC8vF/8ZGBjA0NBQb2vTkLaWpy6bNm3CuXPn8OGHH8LGxkbr\n+WFmZobi4mIcPXoUbm5uUKvViIqKwsOHDzFv3jwYGRnBxMQEWVlZSExMhJubG0pKSrB7924IgoBZ\ns2ZBJpPBysoKly9fxrVr1+Ds7AyVSoWIiAjY29vXuVmkFBgZGdUaV65evQpBEDB27FjI5XK9rQ3w\n60J5VFQUFAoFFAoFLl68iAMHDmDWrFlwcnLSy9oYGRkhMzMTp0+fho2NDeRyOa5fv47IyEh4e3vD\n09NTL+uiS3RpzJfK2G1nZ4eTJ08iIyMDjo6OyMnJQUREBDw9PTF48OAmzSylcbklcwPSGXNb+ust\nlTG1OXMLgoCnT59CrVYjJiYG/fv3h42NDWQyGQwMDCSV0c7ODjExMSgqKoKdnR3u3buHvXv3ws/P\nT9w7qilyy+VyhIaGIicnBx988AEUCoU4vlVUVEChUOhk7hdlVigUtca3xMRE2NnZidu16GLmhnIb\nGhpCrVbj+++/h7W1NQwMDJCQkIBjx45h/vz54u+dupZbJtS3EVEbl5ubi4iICNy+fRsymQxDhw7F\n7NmzYWJiIrY5f/489u3bh4KCAlhaWmL8+PGYMGGC1nXi4uIQGxuLx48fw9bWFlOnTq21b9H+/ftx\n4sQJFBcXo3Pnzpg1a5b41nIpu3XrFlauXImdO3dq7degj3V50V5WCxcuFPc708faNEZby/NbISEh\nWq8+PC8yMhIajQa7d+/G2bNn8fTpU7i6uiI4OFjrla3y8nLs2LEDly5dgkajQY8ePTB37lzxbekA\noFKpsH37dvEv93h6emLu3Lk6davS5s2bUV5ejqVLlwKA3tcmISEBsbGxKCgogI2NDaZMmSKOB/pa\nm2fPniE6Ohrnz5/HkydPYGtri9GjR2P8+PGQyWR6WxddoitjvpTG7uzsbOzYsQN3796FsbExBg8e\njKCgIHHrgObUmuNyS+eWypjbkrmlNKY2V+5ffvkF77//fq3jNXN0qWVMTU1FREQEHjx4ADMzM3h7\ne+Ott96qdbfGn80dGBhY5+c9vwevruVuKPNvrVy5Ei4uLlqbq+ta5sbkFgQBR44cQVxcHFQqFTp3\n7oyZM2dq/ezVtdx6u1BFRERERERERETS0qb2qCIiIiIiIiIiIt3FhSoiIiIiIiIiIpIELlQRERER\nEREREZEkcKGKiIiIiIiIiIgkgQtVREREREREREQkCVyoIiIiIiIiIiIiSeBCFRERERERERERSQIX\nqoiIiIiIiIiISBK4UEVERERERERERJLAhSoi0jvnzp1DYGAgbt261WyPcevWLQQGBiIlJaXZHoOI\niIjozwoJCcH69etbuxtERCIuVBFRmxEaGorAwMDW7gYRERGRJEVHRzf7i3VERH+WYWt3gIioqUyc\nOBEjRoxo7W4QERERSVL//v1hZWUFpVLZ2l0hIqoXF6qIqM3o379/a3eBiIiISLLc3Nzg5ubW2t0g\nInohLlQRUYuIiorCgQMHEBYWhqNHj+L8+fOoqKjAunXrYG1tjaioKKSkpKCoqAi2trbw8/PD66+/\nrnWNn3/+GfHx8cjNzYWpqSmcnJzg5eWFkSNHAgDWrVuH7OxshIeHi59TXV2N/fv3Iz4+HqWlpVAq\nlejUqVOt/oWEhMDJyQkff/yx1vElS5bAwsICK1asEK/3+eef4+HDh/jvf/+L6upqKJVKjBs3Dq++\n+uoLa6BWq7Fv3z5cuXIFhYWFsLKygqurK15//XV07dr1D9WViIiI9EvNnGrt2rWIjY3FlStXIJfL\nMXz4cAQFBeHGjRs4d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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 2, figsize=(14, 5))\n", "\n", "y_hat = model.predict(X)\n", "res = y - y_hat\n", "ax[0].hist(res)\n", "ax[0].set_xlabel('residuals')\n", "ax[0].set_ylabel('counts')\n", "\n", "ax[1].scatter(X, res)\n", "ax[1].set_xlabel('mileage')\n", "ax[1].set_ylabel('residuals')\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Важно смотреть на остатки.
\n", "Во-первых, они должны быть нормально распределены (Теорема Гаусса-Маркова).
\n", "Во-вторых, не должно быть ярких зависимостей между значениями признака и остатками.
\n", "Ну и там на самом деле много условий\n", "\n", "Посмотрим на меры качества" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from sklearn.metrics import mean_absolute_error\n", "from sklearn.metrics import median_absolute_error\n", "from sklearn.metrics import mean_squared_error\n", "from sklearn.metrics import r2_score" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Можно посчитать простые варианты агрегирования остатков, например:\n", "\n", "* $\\frac{1}{n} \\sum_i |\\hat{y}^{(i)}-y^{(i)}|$ - средняя абсолютная ошибка\n", "* $\\frac{1}{n} \\sum_i (\\hat{y}^{(i)}-y^{(i)})^2$ - средняя квадратичная ошибка" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Средняя абсолютная ошибка 1182.21\n", "Средняя квадратичная ошибка 2412292.55\n" ] } ], "source": [ "print 'Средняя абсолютная ошибка %.2f' % mean_absolute_error(y, y_hat)\n", "print 'Средняя квадратичная ошибка %.2f' % mean_squared_error(y, y_hat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Можно рассмотреть более сложную меру: коэффициент детерминации $R^2$:\n", "\n", "* $TSS = \\sum_i (y^{(i)}-\\bar{y})^2$ - общая сумма квадратов (total sum of squares)\n", "* $RSS = \\sum_i (\\hat{y}^{(i)}-y^{(i)})^2$ - сумма квадратов остатков (residual sum of squares)\n", "* $ESS = \\sum_i (\\hat{y}^{(i)}-\\bar{y})^2$ - объясненная сумма квадратов (explained sum of squares)\n", "\n", "Для простоты будем считать, что\n", "$$TSS = ESS + RSS$$\n", "\n", "Тогда Коэффициент детерминации $R^2=1-\\frac{RSS}{TSS}$\n", "\n", "Рассчитайте его для нашей модели\n" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.43096955626446265" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "r2_score(y, y_hat)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Преобразование переменных" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Нормализация" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Как мы с вами убедились из ДЗ2, может решить всё)\n", "Переход к близким или единым шкалам улучшает сходимость градиентного спуска, уменьшает риск переполнения разрядности чисел, однако приходится жертвовать прямой интерпретируемостью..\n", "\n", "Нормализацию обычно проделывают для вещественных признаков.\n", "\n", "Нормализация z-score:\n", "1. Вычитаем среднее: $x - \\bar{x}$\n", "2. Делим на стандартное отклонение: $\\frac{x - \\bar{x}}{std(x)}$\n", "\n", "Можно проделать вручную, можно с помошью метода ниже" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/andrey.shestakov/anaconda2/lib/python2.7/site-packages/sklearn/utils/validation.py:429: DataConversionWarning: Data with input dtype int64 was converted to float64 by StandardScaler.\n", " warnings.warn(msg, _DataConversionWarning)\n" ] }, { "data": { "text/plain": [ "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.preprocessing import StandardScaler\n", "\n", "scaler = StandardScaler()\n", "X = scaler.fit_transform(X)\n", "\n", "model = LinearRegression(fit_intercept=True)\n", "model.fit(X, y)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Модель:\n", "price = 12084.24 + (-1351.67)*mileage`\n" ] } ], "source": [ "print 'Модель:\\nprice = %.2f + (%.2f)*mileage`' % (model.intercept_, model.coef_[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Природа зависимости" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Далеко не всегда переменные зависят друг от друга именно в том виде, в котором они даны. Никто не запрещает зависимость вида\n", "$$\\log(y) = \\beta_0 + \\beta_1\\log(x_1)$$\n", "или\n", "$$y = \\beta_0 + \\beta_1\\frac{1}{x_1}$$\n", "или\n", "$$y = \\beta_0 + \\beta_1\\log(x_1)$$\n", "или\n", "$$y = \\beta_0 + \\beta_1 x_1^2 + \\beta_2 x_2^2 + \\beta_3 x_1x_2 $$\n", "и т.д.\n", "\n", "Не смотря на то, что могут возникать какие-то нелинейные функции - всё это сводится к **линейной** регрессии (например, о втором пункте, произведите замену $z_1 = \\frac{1}{x_1}$)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Пример: Вес тела - мозгов" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Загрузите [данные](https://www.dropbox.com/s/837utfb6yh4x8xb/weights.csv?dl=0) и информацией о весах мозга и тел различных биологических видов. Вес тела задан в килограммах, вес могза в граммах." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "df = pd.read_csv('weights.csv', sep=';', index_col=0)\n", "df.head()" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "df.plot(x = 'body_w', y='brain_w', kind='scatter')\n", "for k, v in df.iterrows():\n", " plt.annotate(k, v[:2])\n", "# Должно получится что-то несуразное.." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Теперь давайте возьмем логарифм от обеих переменных и сонова нарисуем их на графике" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Your Code Here\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Как обучать линейную регрессию?\n", "Попробуем разобраться без всяких `.predict()` и `.fit()`" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Рассмотрим случай с одним признаком и свободным членом" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$X$ - признаковое описание наблюдений, $y$ - прогнозируемая величина\n", "\n", "Пусть задана функция ошибки (функция потерь) $L(\\cdot)$. \n", "Нам надо построить такой функционал $f(X)$, который будет выдавать значение наиболее близкие к $y$, иначе говоря: $$L\\left(f(X) - y\\right) \\rightarrow\\min $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Определим функцию потерь, как сумму квадратов разности выдаваемого ответа функционала и реального значения: \n", "$$ L(\\cdot) = \\frac{1}{2n}\\sum_{i=1}^n(f(x^{(i)}) - y^{(i)})^2$$\n", "\n", "Так как среди всего множества моделей мы выбрали линейную регрессию, то $$f(X) = \\beta_0 + \\beta_1x_1$$\n", "Подставляем это выражение в $L(\\cdot)$ и находим $\\beta_0$,\n", "$\\beta_1$!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ L(\\beta_0,\\beta_1) = \\frac{1}{2n}\\sum^{n}_{i=1}(f(x^{(i)}) - y^{(i)})^2 = \\frac{1}{2n}\\sum^{n}_{i=1}(\\beta_0 + \\beta_1x^{(i)}_1 - y^{(i)})^2 \\rightarrow \\min\\limits_{\\beta_0, \\beta_1} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Задание\n", "\n", "Избразите функцию потерь на трехмерном графике в зависимости от $\\beta_0$ и $\\beta_1$ для задачи с автомобилем" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "beta0 = np.linspace(-5, 5, 100)\n", "beta1 = np.linspace(-5, 5, 100)\n", "\n", "B0, B1= np.meshgrid(x,y)\n", "\n", "# Your Code Here\n", "L = ..\n", "\n", "fig = plt.figure(figsize=(14, 7))\n", "ax = fig.add_subplot(1, 2, 1, projection='3d')\n", "ax.view_init(40, 25)\n", "ax.plot_surface(B0, B1, L, alpha=0.3,)\n", "ax.set_xlabel('$\\beta_0$')\n", "ax.set_ylabel('$\\beta_1$')\n", "\n", "ax = fig.add_subplot(1, 2, 2)\n", "contour = ax.contour(B0, B1, L)\n", "plt.clabel(contour, inline=1, fontsize=10)\n", "ax.set_xlabel('$\\beta_0$')\n", "ax.set_ylabel('$\\beta_1$')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Градиентный спуск" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Градиентый спуск - это итеративный метод оптимизации функции. Он заключается в постепенном перемещении к точке экспетмума в направлении антиградиента этой функции в точке." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Посчитаем, чему равен градиент функции потерь $L(\\beta_0, \\beta_1):$\n", "$$ \\frac{\\partial L}{\\partial \\beta_0} = \\frac{1}{n}\\sum^{n}_{i=1}(\\beta_0 + \\beta_1x^{(i)}_1 - y^{(i)})$$\n", "$$ \\frac{\\partial L}{\\partial \\beta_1} = \\frac{1}{n}\\sum^{n}_{i=1}(\\beta_0 + \\beta_1x^{(i)}_1 - y^{(i)})x_1^{(i)}$$\n", "\n", "Иногда проще это записать в виде матриц:\n", "$$ \\frac{\\partial L}{\\partial \\beta} = X^\\top(X\\beta - y)$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Метод градиентного спуска заключается в итеративном и **одновременном(!!!)** обновлении значений $\\beta$ в направлении, противоположному градиенту:\n", "$$ \\beta := \\beta - \\alpha\\frac{\\partial L}{\\partial \\beta}$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Теперь к шагам алгоритма:\n", "\n", "* Задаем случайное начальное значение для $\\beta$\n", "* Пока не будет достигнуто правило останова:\n", " * Считаем ошибку и значение функции потерь\n", " * Считаем градиент\n", " * Обновляем коэффициенты" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def gradient_descent(X, y, iters, alpha):\n", " n = y.shape[0] \n", " Beta = np.random.rand(2)\n", " for i in xrange(iters):\n", " y_hat = X.dot(Beta)\n", " \n", " # считаем ошибку и значение функции потерь\n", " #...\n", " \n", " # считаем градиент\n", " #...\n", "\n", " # обновляем коэффициенты\n", " # ...\n", " return Beta" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "Beta = gradient_descent(X, y, 1000, 0.05)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Переобучение\\недообучение, мультиколлинеарность и регуляризация" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Одна из важнейших характеристик моделей, будь то линейная регрессия, наивные Байес и др. - их **обобщающая способность**.\n", "Наша задача не построить \"идеальную\" модель, на имеющихся у нас наблюдениях, которая идеально их будет предсказывать, но и применять эту модель для новых данных.\n", "\n", "Ниже приводятся примеры 3х моделей." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "[Andrew's Ng Machine Learning Class - Stanford]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Второй момент, который важен для линейных моделей - **мультиколлинеарность**. Этот эффект возникает, когда пара предикторов близка к взаимной линейной зависимости (коэффициент корреляции по модулю близок к 1). Из-за этого:\n", "\n", "* Матрица $X^{\\top} X$ становится плохо обусловленной или необратимой\n", "* Зависимость $y = \\beta_0 + \\beta_1x_1 + \\beta_2x_2$ перестаёт быть одназначной\n", "\n", "С этим эффектом можно бороться несколькими способами\n", "\n", "* Последовательно добавлять переменные в модель\n", "* Исключать коррелируемые предикторы" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Регуляризация" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "В обоих случаях может помочь **регуляризация** - добавление штрафного слагаемого за сложность модели в функцию потерь. В случае линейной регрессии было:\n", "$$ L(\\beta_0,\\beta_1,\\dots) = \\frac{1}{2n}\\sum^{n}_{i=1}(\\hat{y}^{(i)} - y^{(i)})^2 $$\n", "Стало (Ridge Regularization)\n", "$$ L(\\beta_0,\\beta_1,\\dots) = \\frac{1}{2n}\\left[ \\sum^{n}_{i=1}(\\hat{y}^{(i)} - y^{(i)})^2\\right] + \\lambda\\sum_{j=1}^{m}\\beta_j^2$$\n", "или (Lasso Regularization)\n", "$$ L(\\beta_0,\\beta_1,\\dots) = \\frac{1}{2n}\\left[ \\sum^{n}_{i=1}(\\hat{y}^{(i)} - y^{(i)})^2\\right] + \\lambda\\sum_{j=1}^{m}|\\beta_j|$$\n", "\n", "Но об этом, вероятно, в следующий раз" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# В sklearn эти методы называются так\n", "from sklearn.linear_model import Lasso\n", "from sklearn.linear_model import Ridge" ] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [conda root]", "language": "python", "name": "conda-root-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" }, "nav_menu": {}, "toc": { "navigate_menu": true, "number_sections": false, "sideBar": false, "threshold": 6, "toc_cell": false, "toc_section_display": "block", "toc_window_display": true }, "toc_position": { "height": "116px", "left": "49px", "right": "674.333px", "top": "173px", "width": "170px" } }, "nbformat": 4, "nbformat_minor": 2 }