bias-variance.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The watermark extension is already loaded. To reload it, use:\n",
      "  %reload_ext watermark\n",
      "CPython 3.6.3\n",
      "IPython 6.2.1\n",
      "\n",
      "torch 0.2.0\n",
      "numpy 1.13.3\n",
      "sklearn 0.19.1\n",
      "\n",
      "compiler   : GCC 7.2.0\n",
      "system     : Linux\n",
      "release    : 4.13.12-1-ARCH\n",
      "machine    : x86_64\n",
      "processor  : \n",
      "CPU cores  : 12\n",
      "interpreter: 64bit\n"
     ]
    }
   ],
   "source": [
    "# 代码运行环境\n",
    "# Author: M. Tong <demon386@gmail.com>\n",
    "%load_ext watermark\n",
    "%watermark -p torch,numpy,sklearn -v -m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$E_{out} (g^{(D)}) = E_x[(g^{(D)} - f(x))^2]$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $f(x)$: real distribution. Here we assume it's $y = x + noise$. $x \\sim Uniform(0, 19)$, assume that noise is fixed so that $f(x)$ is determinisitic"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x + np.random.normal(size=x.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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n57UkjVGbrp73AP8eeDTJQ828/wLsAKiqm4APA7+XZBH4Z+CKavNfDElSawMHf1V9A8hJ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfda36c128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.arange(20)\n",
    "f_x = f(x)\n",
    "plt.plot(x, f_x, '.');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $g^{(D)}$: learned hypothesis from a fixed number dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d_x = np.random.choice(x, 2, replace=True)\n",
    "d_y = f_x[d_x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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42q8G+Jeq+vcBZwJPHzyuC4G7lhrADPCVqrp72JH+5EPA9tH2xl7gfQPPA8BoL/hq4J+G\nnuWIqnogyQ7gQZa2NB5iel6deUeStcDzwAer6sAQQyS5Hfhb4PwkTwK3AJ8Avpbk/Sz9o/j3y7K2\nrxSVpDZM/ZaLJOn0GHRJaoRBl6RGGHRJaoRBl6RGGHRJaoRBl6RGGHRJasT/AvZanKsosJ8RAAAA\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfda5d1080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(d_x, d_y, '.');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$E_{out} (g^{(D)}) = E_x[(g^{(D)} - f(x))^2]$ for this particular dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m = LinearRegression()\n",
    "m.fit(d_x[:, np.newaxis], d_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pred = m.predict(x[:, np.newaxis])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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56/XV7PTHMycP19kzE4Eav4jUeo49t2AnU2ev4LMv93JGZgtmjc7i5I7NanyOxA81fhHx\nBDHHvnlPMXfMXckryzdyQtNG3Dv+dEbr7JkJR41fRI6qIp75t7fyKS03fnF+N35WUzxT4pq+ayJS\nLTNjQd4WbvPHM79zUjt+e1EfnT0zwanxi0hAleOZ3dsez9NXDeCc7jp7ZjJQ4xeRb6kcz2zcII0p\n/nhmfcUzk4Yav4gAXjzzxdxC/uyPZ447I4PJw3vQ6viGsS5NwkyNX0TILdjJtNl5fPrlHnydWzAr\nW/HMZBbMxdYfA0YBW83sZP+yPwOjgRLgc+AKM9sd4LkFwD6gDCg1M1/4SheRUFWOZ7Zr2pC//PA0\nxpzWQfHMJBfMHv8TwP3Ak5WWLQBuMrNS59ydwE3Ab6p5/nlmtj2kKkUkrL4Vzywzrj3vRH4+pBvH\nNdQkQCo46nfZzBY55zKrLJtf6eESYGx4yxKRSDAz3li5lVvn5LFh5wGG9/HimRmtFM9MJeH48X4l\n8EI16wyY75wz4GEzm1ndizjnJgGTADIyMsJQlohUVjme2a3t8Tx1VRaDureJdVkSAyE1fufcLUAp\n8Ew1Qwaa2UbnXFtggXNulZktCjTQ/0NhJoDP57NQ6hKRb+wt9uKZs/7rxTN/P6oPl52leGYqq3Pj\nd85NwPuj71AzC9iozWyj/3arc+5lIAsI2PhFJLzKy40XlxXyp3kV8cx0bhjek9aKZ6a8OjV+59wI\nvD/mnmtmB6oZcxxwjJnt898fDkyvc6UiErRl63cyNceLZ/bv3IInRmdxSifFM8UTTJzzOWAI0No5\nVwRMwUvxNMSbvgFYYmbXOOc6AI+Y2UigHfCyf3094FkzmxeRf4WIALBlbzF3zF3Fyx99SbumDfnr\nuNPI7qt4pnxbMKme8QEWP1rN2I3ASP/9dUDfkKoTkaAcKv3m4uaKZ8rR6FMhksAq4pm3vZrH+h0H\nuKBPO357UW86tzou1qVJHFPjF0lQVeOZT16ZxeAeimfK0anxiySYb8Uz66fxu1F9+InimVILavwi\nCaIinvnn11ez46sSfuhLZ/J3KsUzC5cGfc1cSW1q/CIJoGo88/HLq8QzC5fCrGwoK4G0Bt6F09X8\npRpq/CJxrGo8s9qzZxYs9pq+lXm3BYvV+KVaavwicahqPPPnQ07k2vNqiGdmDvL29Cv2+DMHRbdg\nSShq/CJxxMx4c+VWbvXHM4f1bsfvRgURz0zP8qZ3NMcvQVDjF4kT+Vv3M31OHovWbOPENsfVPp6Z\nnqWGL0FR4xeJsb3Fh7n3jbV8/N58BtZbxcXnjGDEhYMVz5SIUeMXiZHycuOfy4r40+uryDjwGc83\nvJ36lOKWvwJ9O2jvXSJGuxQiMbBs/S6++8C7/N9Ln5DR8lgeOPsADSjFVU7liESI9vhFomjL3mLu\nnLuKf1WNZxbVh+X3KZUjUaHGLxIFh0rLeOydAu5fuJbDgeKZSuVIFKnxi0SQmbFwlXdx8wJ/PPO3\nF/Ums3WAeKZSORIlavwiEfL5tv3cOiePt1d78cxZV2Zxrs6eKXFAjV8kzPYVH+beN9fy+Lve2TN/\ne1FvJpydqXimxA01fpEwKV//Pp+99yr3rG3H2wcyuaS/d/bMNk10cXOJL0E1fufcY8AoYKuZnexf\n1hJ4AcgECoBLzGxXgOdOAH7rf3ibmc0KvWyR+LI69w0y54ynj5XykKtH4djn6db/1FiXJRJQsL97\nPgGMqLLsRuBNM+sOvOl//C3+Hw5TgAFAFjDFOdeiztWKxJmte4v59T+W8++X/0EapdRz5TRwZXQ7\nsDzWpYlUK6jGb2aLgJ1VFo8BKvbeZwHfDfDU7wALzGyn/7eBBRz5A0Qk4RwqLeOh/3zOeXe9zZyP\nN9H+tAtIq9cQXBpOOXyJc6HM8bczs00AZrbJOdc2wJiOQGGlx0X+ZSIJa+GqLUyfXRHPbMtvL+rj\nxTMLOyuHLwkh0n/cdQGWWcCBzk0CJgFkZGREsiaROqkcz+za5jieuOIMhvSstL+jHL4kiFAa/xbn\nXHv/3n57YGuAMUXAkEqPOwFvB3oxM5sJzATw+XwBfziIxMK+4sPctzCfx9/9gkb1vHjmT87KpEE9\nxTMlMYXS+HOACcAd/tt/BxjzOvDHSn/QHQ7cFMI2RaKmvNx46cMi7py3mu37D3GJrxP/+51eimdK\nwgs2zvkc3p57a+dcEV5S5w7gH865q4ANwMX+sT7gGjO72sx2OuduBT7wv9R0M6v6R2KRuPPRhl1M\nnZ3Hx4W7OT2jOY9O8NE3vXmsyxIJC2cWf7MqPp/PcnNzY12GpKCte4u5c95qXvqwiDZNGnLThb34\n7mkdOeaYQH+uEokfzrllZuYLZqyO3JXkUbi0zqmaktJyHn/3C+59cy0lZeVcc+6JXHd+N46v7uLm\nIglMn2pJDoVLYVb2N+ezn5ATdPN/a9VWps/J44vtX3F+r7b8blQfugQ6e6ZIklDjl+RQsNhr+pWv\nYHWUxr/OH898a/U2urY+jsevOIPzegY6HEUkuajxS3LIHOTt6QdxBat9xYe5f2E+j737BQ3rpXHL\nSO/smYpnSqpQ45fkEMQVrMrLjX999CV3zF3F9v2HuLh/J/53RE/aNmkUg4JFYkeNX5JHDUfOLi/c\nzZScFXxcuJvT0pvzyAQfpymeKSlKjV+S2tZ9xfxp3mr+ucyLZ864uC/fO13xTEltavySlCrimfct\nzOdQaRk/Pbcrvzi/u+KZIqjxSxJ6y39x83WKZ4oEpMYvSeOL7V9x65w8Fq7a6sUzLz+D83opnilS\nlRq/JLyq8cybR/bi8rO71D6eGcKRvyKJRI1fElZFPPPOeavYtu8QY/t34v/qGs8M4chfkUSjxi8J\naXnhbqbmrGC5P57595+EGM+sw5G/IolKjV8SytZ9xfx53mpe9Mcz77q4L98PRzyzFkf+iiQ6NX5J\nCCWl5Tzx3y+4981v4pnXndeNJo3qh2cDQRz5K5Is1Pgl7r21eiu3zv4mnvnbi3rTtc3x4d+Qrpkr\nKUKNX+JW5XhmF8UzRcJGjV/izv5Dpdy3cC2PvRNiPFNEAqpz43fO9QReqLSoK/B7M/tLpTFD8C7C\n/oV/0b/MbHpdtynJrbzcePmjL7kjHPFMEalWnRu/ma0GTgNwzqUBXwIvBxi62MxG1XU7kho+LtzN\n1Nkr+GjDbvqmN2fmZf05PaNFrMsSSUrhmuoZCnxuZuvD9HqSIrbtO8Sf5q3ixWVFtD6+IX8eeyo/\n6NdJZ88UiaBwNf5xwHPVrDvLOfcxsBGYbGYrwrRNCbdQT1lQi+eXlJYz678F3PvmWopLy/jp4K5c\nd34Y45kiUq2QG79zrgGQDdwUYPWHQGcz2++cGwm8AnSv5nUmAZMAMjIyQi1LaivUUxbU4vlvr/Yu\nbr5u21ec17MNvxvVJzLxTBEJKBwxiQuBD81sS9UVZrbXzPb7778G1HfOtQ70ImY208x8ZuZr06ZN\nGMqSWgl0yoIwP79g+1dcPesDLn/8A8zgsct9PH5Flpq+SJSFY6pnPNVM8zjnTgC2mJk557LwftDs\nCMM2JdxCPWVBDc/ff6jUO3vmO19QP81x04W9uGKg4pkisRJS43fOHQtcAPy00rJrAMzsIWAs8DPn\nXClwEBhnZhbKNiVCQj1lQYDnmxmvLP+S219bxdZ9h/hBv078ZkRP2jZVPFMkllw89mGfz2e5ubmx\nLkNC8EmRd/bMDzfspm+nZkzNPknxTJEIcs4tMzNfMGN15K6E1fb9h/jzvNX8Y1khrY5TPFMkHqnx\nS1gcLvPimX99w4tnThzUlV8onikSl9T4JWT/WbON6bNX8Pm2rxjij2eeqKSOSNxS45c6W7/jK26d\ns5I3Vm6hS+vjeOxyH+f3alf3F9Q1b0WiQo1fau2rQ6X87a18HlnsxTNvvLAXVwzMpGG9tLq/qK55\nKxI1avwStIp45h1zV7Flb5jjmbrmrUjUqPFLUKrGMx/8cX/6hTOeqWveikSNGr/U6NvxzAb8aeyp\njI1EPFPXvBWJGjV+CejreOabazlYUsbV53ThF0O70zSS8Uxd81YkKtT45QiL1mxjmj+eeW4PL57Z\nra3imSLJQo1fvlY5ntm51bE8OsHH+b3a4pyOuhVJJmr88q14Zr00x29G9OLKc0KMZ4pI3FLjT2Fm\nxr+Xb+T2uSvZsvcQ3z+9I7+5sBftdPZMkaSmxp+iPi3aw9TZK1i2fhendmrGA5f2p39nnT1TJBWo\n8aeY7fsPcdfrq3kh1x/P/MGpjO2vs2eKpBI1/hRxuKycJ99bz1/eWMPBkjKuGtiFXw6LcDxTROKS\nGn8KWLRmG9Pn5JG/dT+De7Th94pniqQ0Nf4ktn7HV9z26koW5HnxzEd+4mNob8UzRVKdGn8S+upQ\nKQ+8nc/fF3nxzP8b0ZOrzumieKaIAGFo/M65AmAfUAaUVr3mo/N2L/8KjAQOAJeb2YehbleOVDWe\n+b3TO3Kj4pkiUkW49vjPM7Pt1ay7EOju/xoAPOi/lTD67Ms9TM1ZQe76XZzSUfFMEaleNKZ6xgBP\nmpkBS5xzzZ1z7c1sUxS2nfR27D/EXfNX8/wHhbQ8tgF3/uAULu6frnimiFQrHI3fgPnOOQMeNrOZ\nVdZ3BAorPS7yL/tW43fOTQImAWRkZIShrORWNZ555cAu/HJod5o1VjxTRGoWjsY/0Mw2OufaAguc\nc6vMbFGl9YF2Pe2IBd4PjJkAPp/viPXyjcVrtzFtduV4Zm+6tW0S67JEJEGE3PjNbKP/dqtz7mUg\nC6jc+IuA9EqPOwEbQ91uKtqw4wC3vprHgrwtZLRUPFNE6iakxu+cOw44xsz2+e8PB6ZXGZYDXOec\nex7vj7p7NL9fO1/HMxd/Qb1jHP/7HS+e2ai+4pkiUnuh7vG3A17273HWA541s3nOuWsAzOwh4DW8\nKGc+XpzzihC3mTLMjJyPN3L7a6vYvLeY753ekd+M6MUJzRTPFJG6C6nxm9k6oG+A5Q9Vum/AtaFs\nJxVVjWf+7dLT6d+5ZazLEpEkoCN340zVeOYd3z+Fi33ppCmeKSJhosYfJw6XlfPUe+u5R/FMEYkw\nNf44sHjtNqbPzmPt1v0M6t6aKaP7KJ4pIhGjxh9DG3Yc4LZX85jvj2fOvKw/F/Rpp3imiESUGn8M\nHCgp5YG3Pmfm4nWkOcUzRSS61PijqGo887undeDGC3srnikiUaXGHyWffbmHabNX8EHBLk7u2JT7\nf3Q6vswwxzMLl0LBYsgcBOlZ4X1tEUkaavwR5sUz1/D8BxsiG88sXAqzsqGsBNIawIQcNX8RCUiN\nP0IOl5Xz9JL13LNgDV+VlHHF2V341bAIxjMLFntN38q824LFavwiEpAafwS8m7+dabNXsGaLF8/8\n/ag+dG8X4Xhm5iBvT79ijz9zUGS3JyIJS40/jAp3HuAPr65k3orN0Y9npmd50zua4xeRo1DjD4MD\nJaU8+PbnPLwoxvHM9Cw1fBE5KjX+EJgZsz/ZxO2vrWTTnmJ+1XMXV3X6kqbdWkL9brEuT0QkIDX+\nOlqxcQ/TcvJYWrCTkzs25bGhRu/5k2FDCbx/j1I1IhK31PhraedXJd7ZM5duoPmxDbj9+6dwiS+d\ntHfvVqpGRBKCGn+QSv3xzLv98cwJZ2dy/dAeNDvWH89UqkZEEoQafxAqxzPP6eadPfOIeKZSNSKS\nINT4a1A5npnesjEPX9af4TXFM5WqEZEEUOfG75xLB54ETgDKgZlm9tcqY4YA/wa+8C/6l5lVvRh7\n3DlQUspDb3/OQ/545uThPbh6UNfIxzN1rh0RiYJQ9vhLgRvM7EPnXBNgmXNugZnlVRm32MxGhbCd\nqDEz5nyyiT/645nZfTtw08hetG/WOPIb17l2RCRK6tz4zWwTsMl/f59zbiXQEaja+BPCio17mDY7\nj6Vf7KRP+6b8ddzpZHWJ4sXNda4dEYmSsMzxO+cygdOB9wOsPss59zGwEZhsZivCsc1w2flVCTPm\nr+a5pRto1rg+f/jeyYw7IyP6FzdXKkhEoiTkxu+cOx54CbjezPZWWf0h0NnM9jvnRgKvAN2reZ1J\nwCSAjIyMUMs6qtKycp55fwMz5q/mq5IyfnJWJv8zrFI8M9qUChKRKHFmVvcnO1cfmAO8bmZ3BzG+\nAPCZ2faaxvl8PsvNza1zXUfz3/ztTJudx+ot+xjYrRVTRp9Ej0ifPVNEJIKcc8vMzBfM2FBSPQ54\nFFhZXdN3zp0AbDEzc85lAcf1/f60AAAII0lEQVQAO+q6zVAV7jzAH19bydzPNtOpRWMe+nF/vnOS\nLm4uIqkllKmegcBlwKfOueX+ZTcDGQBm9hAwFviZc64UOAiMs1B+xaijgyVlPPh2Pg8vWscxznHD\nBT2YODgK8UwRkTgUSqrnHaDGXWUzux+4v67bCFVFPPP211aycU8xo/t24KYLe9GheRTimSIicSpp\nj9zN27iXqbNXsPSLnfRu35R7fngaA7q2inVZIiIxl3SNP27imSIicSppGn9FPPPuBWvYf6g09vFM\nEZE4lTSNv7i0nPvfyuekDk2ZMvokep6geKaISCBJ0/iPb1iPnOsGckLTRopniojUIGkaPxCdk6mJ\niCS4Y2JdgIiIRJcav4hIilHjFxFJMWr8IiIpRo1fRCTFqPGLiKQYNX4RkRSjxi8ikmLU+EVEUowa\nv4hIilHjFxFJMWr8IiIpJqTG75wb4Zxb7ZzLd87dGGB9Q+fcC/717zvnMkPZXsQVLoXFM7xbEZEk\nVeezczrn0oC/ARcARcAHzrkcM8urNOwqYJeZdXPOjQPuBH4YSsERU7gUZmVDWQmkNYAJOZCeFeuq\nRETCLpQ9/iwg38zWmVkJ8DwwpsqYMcAs//1/AkNdvJ4sv2Cx1/StzLstWBzrikREIiKUxt8RKKz0\nuMi/LOAYMysF9gCRu+J5KFM1mYO8PX2X5t1mDgp/fSIicSCUC7EE2nO3OozxBjo3CZgEkJGRUftq\nQp2qSc/ynlOw2Gv6muYRkSQVyh5/EZBe6XEnYGN1Y5xz9YBmwM5AL2ZmM83MZ2a+Nm3a1L6acEzV\npGfBoBvU9EUkqYXS+D8AujvnujjnGgDjgJwqY3KACf77Y4GFZhZwjz9kmqoREQlKnad6zKzUOXcd\n8DqQBjxmZiucc9OBXDPLAR4FnnLO5ePt6Y8LR9EBaapGRCQoLlI74KHw+XyWm5sb6zJERBKGc26Z\nmfmCGasjd0VEUowav4hIilHjFxFJMWr8IiIpRo1fRCTFqPGLiKSYuIxzOue2Aevr+PTWwPYwlhNu\nqi80qi80qi808VxfZzML6rQHcdn4Q+Gcyw02yxoLqi80qi80qi808V5fsDTVIyKSYtT4RURSTDI2\n/pmxLuAoVF9oVF9oVF9o4r2+oCTdHL+IiNQsGff4RUSkBgnb+J1zI5xzq51z+c65GwOsb+ice8G/\n/n3nXGYUa0t3zr3lnFvpnFvhnPtVgDFDnHN7nHPL/V+/j1Z9/u0XOOc+9W/7iFOhOs+9/vfvE+dc\nvyjW1rPS+7LcObfXOXd9lTFRff+cc48557Y65z6rtKylc26Bc26t/7ZFNc+d4B+z1jk3IdCYCNX3\nZ+fcKv/372XnXPNqnlvjZyGC9U11zn1Z6Xs4sprn1vh/PYL1vVCptgLn3PJqnhvx9y/szCzhvvDO\n//850BVoAHwM9Kky5ufAQ/7744AXolhfe6Cf/34TYE2A+oYAc2L4HhYArWtYPxKYi3f5zDOB92P4\nvd6Ml1GO2fsHDAb6AZ9VWvYn4Eb//RuBOwM8ryWwzn/bwn+/RZTqGw7U89+/M1B9wXwWIljfVGBy\nEN//Gv+vR6q+KutnAL+P1fsX7q9E3ePPAvLNbJ2ZlQDPA2OqjBkDzPLf/ycw1DkX6BrAYWdmm8zs\nQ//9fcBKjrwQfbwbAzxpniVAc+dc+xjUMRT43MzqekBfWJjZIo68bGjlz9gs4LsBnvodYIGZ7TSz\nXcACYEQ06jOz+WZW6n+4BO/yqDFRzfsXjGD+r4espvr8feMS4LlwbzdWErXxdwQKKz0u4sjG+vUY\n/4d/D9AqKtVV4p9iOh14P8Dqs5xzHzvn5jrnTopqYd5F7+c755b5L3RfVTDvcTSMo/r/cLF8/wDa\nmdkm8H7YA20DjImX9/FKvN/gAjnaZyGSrvNPRT1WzVRZPLx/g4AtZra2mvWxfP/qJFEbf6A996rx\npGDGRJRz7njgJeB6M9tbZfWHeNMXfYH7gFeiWRsw0Mz6ARcC1zrnBldZHw/vXwMgG3gxwOpYv3/B\niof38RagFHimmiFH+yxEyoPAicBpwCa86ZSqYv7+AeOpeW8/Vu9fnSVq4y8C0is97gRsrG6Mc64e\n0Iy6/apZJ865+nhN/xkz+1fV9Wa218z2+++/BtR3zrWOVn1mttF/uxV4Ge9X6sqCeY8j7ULgQzPb\nUnVFrN8/vy0V01/+260BxsT0ffT/MXkUcKn5J6SrCuKzEBFmtsXMysysHPh7NduN9ftXD/g+8EJ1\nY2L1/oUiURv/B0B351wX/17hOCCnypgcoCJBMRZYWN0HP9z8c4KPAivN7O5qxpxQ8TcH51wW3vdi\nR5TqO84516TiPt4fAT+rMiwH+Ik/3XMmsKdiWiOKqt3TiuX7V0nlz9gE4N8BxrwODHfOtfBPZQz3\nL4s459wI4DdAtpkdqGZMMJ+FSNVX+W9G36tmu8H8X4+kYcAqMysKtDKW719IYv3X5bp+4aVO1uD9\nxf8W/7LpeB9ygEZ4UwT5wFKgaxRrOwfv19FPgOX+r5HANcA1/jHXASvwUgpLgLOjWF9X/3Y/9tdQ\n8f5Vrs8Bf/O/v58Cvih/f4/Fa+TNKi2L2fuH9wNoE3AYby/0Kry/Gb0JrPXftvSP9QGPVHrulf7P\nYT5wRRTry8ebH6/4DFak3DoAr9X0WYhSfU/5P1uf4DXz9lXr8z8+4v96NOrzL3+i4jNXaWzU379w\nf+nIXRGRFJOoUz0iIlJHavwiIilGjV9EJMWo8YuIpBg1fhGRFKPGLyKSYtT4RURSjBq/iEiK+X88\ntcXJ7yUhZQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfda4c0d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, pred, x, f_x, '.')\n",
    "plt.legend(['g(x)', 'f(x)']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$E_{out} (g^{(D)}) = E_x[(g^{(D)} - f(x))^2]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1264579178828598"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((pred - f_x) ** 2).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$E_{out}$ is the out-of-sample error for this particular hypothesis, and we want to evaluate the learning algorithm's overall performance on $D$, thus\n",
    "\n",
    "$E_D[E_{out} (g^{(D)})] = E_D[E_x[(g^{(D)} - f(x))^2]]$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def error_over_D(model, data_num):\n",
    "    mean_square_over_D = []\n",
    "    # We use simulation to approximate expectation over D\n",
    "    for i in range(10000):\n",
    "        d_x = np.random.choice(x, data_num, replace=True)\n",
    "        d_y = f_x[d_x]\n",
    "        model.fit(d_x[:, np.newaxis], d_y)\n",
    "        pred = model.predict(x[:, np.newaxis])\n",
    "        mean_square = ((pred - f_x) ** 2).mean()\n",
    "        mean_square_over_D.append(mean_square)\n",
    "    return np.mean(mean_square_over_D)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.svm import SVR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error over D for linear regression: 19.418551\n",
      "Error over D for SVM Regression: 12.310735\n"
     ]
    }
   ],
   "source": [
    "data_num = 2\n",
    "print(\"Error over D for linear regression: %f\" % error_over_D(LinearRegression(), data_num))\n",
    "print(\"Error over D for SVM Regression: %f\" % error_over_D(SVR(kernel='linear'), data_num))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So SVM outperforms when seeing sampling only two data points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error over D for linear regression: 1.135086\n",
      "Error over D for SVM Regression: 1.372207\n"
     ]
    }
   ],
   "source": [
    "data_num = 8\n",
    "print(\"Error over D for linear regression: %f\" % error_over_D(LinearRegression(), data_num))\n",
    "print(\"Error over D for SVM Regression: %f\" % error_over_D(SVR(kernel='linear'), data_num))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "When seeing more data points, the error decreases and Linear regression seems to outperform.\n",
    "\n",
    "Conclusion: $E_D[E_{out} (g^{(D)})]$ is influenced by number of samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import scipy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(-1, 1, 0.01)\n",
    "y = scipy.sin(np.pi * x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 139,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fdfd395ea58>]"
      ]
     },
     "execution_count": 139,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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KE6UV/OvrDEYkdWRiahe74ygXpg5PpHfnCB7/Ygdllf57+qrbhcEYUwncjuMP+nZgvjFm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\nJI1waQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfd2bebb70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 140,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:7: RankWarning: Polyfit may be poorly conditioned\n",
      "  import sys\n"
     ]
    }
   ],
   "source": [
    "h0_all = []\n",
    "h1_all = []\n",
    "for i in range(2000):\n",
    "    d_x = np.random.choice(x, 2, replace=True)\n",
    "    d_y = scipy.sin(np.pi * d_x)\n",
    "    h0 = np.polyfit(d_x, d_y, deg=0)\n",
    "    h1 = np.polyfit(d_x, d_y, deg=1)\n",
    "    h0_all.append(h0)\n",
    "    h1_all.append(h1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "h0_bar = np.mean(h0_all)\n",
    "h1_bar = np.mean(h1_all, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.2473868431336183e-05"
      ]
     },
     "execution_count": 142,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h0_bar"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.77713148, -0.00563103])"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "h1_bar"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bias"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Bias of H0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.50000000525246124"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((np.repeat(h0_bar, len(x)) - y) ** 2).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Bias of H1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.20670007189530804"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "((h1_bar[0] * x + h1_bar[1] - y)**2).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fdfda429470>"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Rq4H8qSveCXmHtX3X8kHLD1RSMJBALxd6NKzCwt0XSLqdrXU49zBEYvACYgo8\nj9Vve5hXgPUFntsJIcKEEPuFEA+dQUsIMUrfLyw+Pr5kESuKifh2SyQWFoLXO5hGtXAj/QYzDs6g\n+8rufLTvIxIyEgB4oc4LeDmWzcn8tDSpc20ycvKYu8O0lgA1xHB4YffsFzoZiBDiRSAYaFtgs6+U\n8qoQogawVQhxUkr5wG9JSjkPmAcQHBxs+pONKMpjXE5MZ9XRKwxt4UcVFztNY7mZeZN5J+ax/Nxy\ncnW59KrZi1cbvVou5jHSUoCnE70aV+OnfZcY1aYG7o62WocEGKZiiAV8Cjz3Bq7e30kI0Ql4D+gl\npcy6s11KeVX/PRrYDjxlgJgUxeR9vy0KSwvBaxou2XlnptM8mcefUX/SvXp3/nr+L6a1noaPk89j\n9lYMYXyHWmTl5jFvV7TWodxliMRwCKglhKguhLABBgL3XF0khHgKmEt+UrhRYLurEMJW/9gDaA0U\nHLRWlDIpJimdlUdiGRTiQ2Vn41cLCRkJfHboM0ZvGo2UEg97D/7p9w8ft/5YJQQjC/B0zK8a9l4i\nIS3r8TsYQYkTg5QyFxgPbATOAMuklKeFENOEEL303T4HHIHl912WWg8IE0IcB7YBM+67mklRyqTv\nt0VhIQRjjFwtJGQk8Pmhz+m+sju/nfkNTwdPsvLy34ycbcxnTeKy5vWO+VXD/J2mUTUY5JY7KeU6\nYN192/5T4HGnh+y3F2hoiBgUxVzEJKWz4nAsg5r5UtXF3mjHPRR3iLGbx5Kty+bZGs8yutFofJ19\njXZ85eFqVnKkd5AXP+27xKttauCh8ViDuvNZUYzsh+3nsRDGGVtIzEjkVMIpAAI9Aukd0Js1fdYw\n/enpKimYmPEdAkymalCJQVGM6MqtDFYcjuGFEG+qVSy9aiEpM4mZYTPpvqo77+56Fykl9lb2vN/i\nffyc/R7/AorRFawatB5rUIlBUYzoh21RALzWLqBUXj8pM4mZh2fSbWU3loQvoYNvB77p8I3ZrwRX\nXphK1WB60/opShl19VYGy8Ji6B/sg1cpVQsH4w6y+NRiulfvzujGo6nhUqNUjqOUDlMZa1CJQVGM\nZPb2/Ps2xxpwbOFW5i2WhC/B1daVlxq8RBe/LtTtUxd/F3+DHUMxrvEdAlh97Arzdkbzrx71NIlB\nnUpSFCO4lpzB0kMx9GvqjbdryedEupV5i2+PfEvXlV1ZeHIhl1PzF32xEBYqKZi5/6saLmo21qAS\ng6IYwZzt59FJyVgDjC38df4vuq3qxoKTC3jG+xlW9VrF+y3eN0CUiql4vUMA2bk65mk01qBOJSlK\nKYtLzuT3QzGENvF+4hlUk7O8qXaSAAAgAElEQVSSyZN5uNm54ePkQ+tqrRnTeAy1XE1j8j3FsGpU\ncqSPvmoYpcFYg6oYFKWUzdlxnjydZFz74lcLyVnJzDo6i24ru/Hd0e8ACPIM4st2X6qkUMaN17Bq\nUBWDopSi6ymZ/HbwMqFNvPB1L3q1kJKdws/hP/NL+C+k5aTR2a8zg+oOKsVIFVNTsGp49ZkaVHIy\nXtWgKgZFKUV3qoXx7Yv36f7bI98y5/gcWlRtwYrnVjCz3Uxqu5r2etCK4d2pGhYYeeZVVTEoSim5\nkZLJbwcu8/xTj68WUrNT+fXMrzzj9QwNPBowsuFI+tXuR123ukaKVjFFNSo5arJeg6oYFKWUzN0Z\nTa5OMv4RYwup2anMOT6Hriu78v2x79lzdQ8AVSpUUUlBAfKrhszcPBbsvmC0Y6qKQVFKQXxqFr8e\nuETvoGr4e1QotM/P4T8z5/gcUrJTaO/Tntcav0Y9d21uaFJMV4CnEz0bVuWnvRcZ9UwNXCvYlPox\nVcWgKKVg3s7zZOfqHljL+XbObXRSB+RXC00qN2Hps0v5tsO3KikoDzWhYy1uZ+exaI9xqgaDJAYh\nRDchRIQQIkoIMbWQdlshxFJ9+wEhhH+Btnf12yOEEF0NEY+iaCkhLYuf91+id5AX1fXVwu2c28w/\nMZ+uK7uy7fI2AF5r/BrfdfiO+u71tQxXMQO1KzvRo2EVFu+5SHJ6Tqkfr8SnkoQQlsD3QGfy138+\nJIRYc99KbK8AN6WUAUKIgcD/AwYIIeqTvxRoA6AasFkIUVtKmVfSuBRFK/N3RpOdq2N8hwBu59zm\n97O/s/j0YpKzkmnj3QZvJ28ANeOpUiyvd6hFfGoWibezcHGwLtVjGWKMoRkQJaWMBhBC/AH05t61\nm3sDH+ofrwBmifz/it7AH1LKLOCCECJK/3r7DBCXohhdYloWP+27xHONq1GzkiOD1g7iVOIpnvF6\nhrFBYwn0CNQ6RMVM1avqzPIxrYxyLEMkBi8gpsDzWKD5w/pIKXOFEMmAu377/vv29TJATIWavf08\nPQ+PxPf+aQka9IFmr0J2Ovza/8EdgwbDU0PgdiIse+nB9pCXITAUkmNh1egH21uNhzrdISES/nrj\nwfY2k6Fme7h2Aja8+2B7x/+Ab3O4fAC2THuwvdt/oWojOL8Ndn7xYPtzX4NHLYhYD3tnPdjedy64\neMOplXBo0YPtL/wEFdzh6K9w7LcH24csBxsHODgfTv/vwfYRf+d/3/MtnNt4b5u1Hby4Mv/xjs8g\nese97Q6uMOCX/MebP4SYQ/e2O1eD0Pn5j9dPhbiT97a714Re3+Y/XjMBEs/f216lIXSfkf945auQ\ncvXedp8Q6PRh/uOlL0L6zXvba7SFtu/kP/4llPjrCQypmMa4FA/40YrxXvVx6vEujSo1gh978gD1\nt6f+9qDof3t3fp5SZojEUFg9LIvYpyj75r+AEKOAUQC+vk+2JGHszXSuJWdQ2dkWWyvLJ3oNRSlM\nek46v+Ylssg1iTRLaKHLphNWtK7gA5UaaR2eohSLkLLQ9+Giv4AQLYEPpZRd9c/fBZBS/rdAn436\nPvuEEFZAHFAJmFqwb8F+jzpmcHCwDAsLK3asV25l0O7zbQwI8eGTPg2Lvb+i3C9Xl8sv4b/w4+kf\nScpMIjetNl90mkzPOi21Dk1RHiCEOCylDH5cP0NclXQIqCWEqC6EsCF/MHnNfX3WAMP0j/sBW2V+\nRloDDNRftVQdqAUcNEBMhfKqaE+/pj4sOxTLteSM0jqMUg7cueTUUliy+fJmarrURhc7jo6u76mk\noJi9EicGKWUuMB7YCJwBlkkpTwshpgkheum7LQTc9YPLk/i/SuE0sIz8geoNwLjSviJpXPua6KS8\nu5qWohRHRm4GS04voeeqniRmJCKEYF7nedQTb5Ge5sOEjmrGU8X8GeTOZynlOmDdfdv+U+BxJlDI\nyBpIKacD0w0RR1F4uzrQP9ibPw7G8Fq7mlR1KZ21d5WyJTM3k2URy1h0ahGJmYk0r9qctJw03O3d\nyc6xYsneS/QIrErtyk5ah6ooJVYu73we2y4AnZTMUVWDUgRp2Wn0XNWTz8M+J8A1gMXdFrOgywL8\nnP0AWLj7AmlZubzeseSrsymKKSiXcyX5uDkQ2sSb3w/FMLZ9AJWd7bQOSTExmbmZHIw7SBvvNjja\nODKw7kCe8nyK4Cr3jtslp+eweM9FugdWoW4VZ42iVRTDKpcVA8C49gHk6dRYg3KvrLwsfj3zKz1W\n9WD8lvHEpObfovNqo1cfSAoAC/dcIDUrV40tKGVKuU0Mvu4O9H3Ki98PXuZGSqbW4Sgay8rL4rcz\nv9FjZQ9mHJyBr7MvC7suxMfJ56H7JGfk8OOeC3RrUIV6VVW1oJQd5TYxQP4857k6yZwdxl9TVTEt\nqdmpzDw8E28nbxZ2WcjibosJqRLyyH0W7b5AaqYaW1DKnnI5xnCHn3sF+gR58euBS4xpVwNPJzXW\nUF5k52WzKnIVYdfD+LzN53jYe/Bnrz/xdvIu0uR2yRk5LNpzga4NKtOgmosRIlYU4ynXFQPkVw05\neTrmqaqhXMjOy2bp2aX0WNWD6QemcyP9Bqk5qQD4OPsUecbTO9WCGltQyqJyXTEAVPfIrxp+OXCJ\n0W1rUsnJOGuqKsYXkRTB+K3jibsdR1ClID5u/TEtqrYo9vTXqlpQyrpyXzFAftWQnatj/i5VNZQ1\nOXk5XEy+CICvsy913eoyt/Ncfur+Ey2rtXyiNRHuVAsTO9Y2cLSKYhpUYgBqVHKkV+Nq/LTvIglp\nWVqHoxhATl4Oy88tp+efPXlt82vk6nKxt7Lnuw7f0apaqydeJOdOtdCtQRXqV1NXIillk0oMeuM7\n1MqvGnaqqsGc5eTlsOLcCp7981mm7ZtGJftKvNfiPSyFYaZZV2MLSnmgEoNegKcjzzWuxk/7LpGo\nqgaztfPKTj7a9xHu9u780PEHfunxC097PW2QZTST03NYtFtVC0rZpxJDAa93CCAzN4/5uy5oHYpS\nRDm6HP6M/JNlEcsAaO/TngVdFvBrj195xvsZg66rrO5yVsoLlRgKCPB04tlG+WMNSbeztQ5HeYRc\nXS5/Rv5Jrz978Z+9/2Hzpc1IKbEQFjSv2tygCQHyq4UfVbWglBMqMdxnQocAMnLyWKCuUDJZ+67u\no9f/8hOCs60zszrMYm7nuQZPBgXdqRYmdlLVglL2lfv7GO5Xq7ITPRpWZcnei7z6TA1cK9hoHZJC\nfoWQkZuBk40T9lb2OFo78l2H72jr3bZUEwL8X7XQPVDNiaSUDyWqGIQQbkKITUKISP1310L6BAkh\n9gkhTgshTgghBhRoWyyEuCCEOKb/CipJPIYyoUMt0nPyWLBbVQ1ay9Xlsub8Gnr/rzdfhn0JQJBn\nEEufXUo7n3alnhRAjS0o5U9JTyVNBbZIKWsBW/TP75cOvCSlbAB0A74WQlQs0P62lDJI/3WshPEY\nRJ0qTvRsWJUf91xUVyhpJFeXy1/n/6LP6j68t/s97K3saevd9m67MRICqGpBKZ9Kmhh6A0v0j5cA\nfe7vIKU8J6WM1D++CtwAKpXwuKXujU61yczJY84OtV6DFr4/9j3/2v0vbC1t+brd1yx7bhntfdsb\nPQ5VLSjlUUnHGCpLKa8BSCmvCSE8H9VZCNEMsAEKvttOF0L8B33FIaU0iY/oAZ6O9Any4qd9l3j1\nmRp4qlXeSlWeLo8NFzdQ3aU69d3r0692PwLdA2nv2x4Loc01ErfSs1W1oJRLj/2PE0JsFkKcKuSr\nd3EOJISoCvwMjJBS6vSb3wXqAiGAGzDlEfuPEkKECSHC4uPji3PoJzaxUy1ydZLvt0UZ5XjlUZ4u\nj3XR63h+zfNM3TWVVZGrAPBy9KKjX0fNkgLA3J3RpGXn8kYnNSeSUr48tmKQUnZ6WJsQ4roQoqq+\nWqhK/mmiwvo5A38D70sp9xd47Wv6h1lCiB+ByY+IYx4wDyA4OFg+Lm5D8HOvQP+m3vx+MIZRbWvi\nVdHeGIctN7Zc2sI3R7/hQvIFAioG8GXbL+nk99A/N6O6kZrJ4j0X6dW4GnWqOGkdjqIYVUk/jq0B\nhukfDwNW399BCGED/An8JKVcfl9bVf13Qf74xKkSxmNwr+vPLc/aqqoGQ9BJHTp9wXju5jkshSVf\ntP2Clb1W0sW/i6YVQkE/bDtPdp5OVQtKuVTS/8IZQGchRCTQWf8cIUSwEGKBvs8LQBtgeCGXpf4q\nhDgJnAQ8gE9KGI/BeVW0Z2AzH5aHxXA5MV3rcMyWTurYcHEDfVf3ZcvlLQC80vAVVvZaSVf/riaT\nEACu3MrgtwOX6dfEm+oeFbQOR1GMrkSDz1LKRKBjIdvDgJH6x78Avzxk/w4lOb6xjGsfwNJDMXyz\nJZIvX2isdThmRSd1bLq0iTnH5xB1K4oaLjVwsHIAwMbSNG8enLU1EoAJ6i5npZxSdz4XQWVnO4a2\n8GPRngu81q4mAZ6OWodkNiZum8j2mO1Ud6nOZ20+o4tfFywtDDMFdmm4mHCbZWGxDG3hp8aUlHLL\ndOp3EzemXU3srC35Zkuk1qGYNJ3UseXSFjJzMwHoE9CHGc/M4M9ef9K9eneTTgoAX28+h7WlYGz7\nmlqHoiiaUYmhiDwcbRneyp+1J65yNi5F63BMjk7q2HxpM/3/6s8b299gbfRaADr6dqRnjZ4mnxAA\nzl1PZfXxqwxr5Y+nk7pvRSm/VGIohlFtauBoY8WX/5zTOhSTIaVky+UtvPDXC7y5/U2y8rL49OlP\n6RPwwE3wJm/mP+eoYGPFmDaqWlDKNzXGUAwVHWwY1aYGX246x+FLSTT1c9M6JJOw+NRiMvMy+fTp\nT+levTtWFub3Z3UyNpkNp+OY2LGWmlFXKfdUxVBMrzxTHQ9HW/7f+gikNMp9diZFSsm2y9sYtn4Y\nCRkJCCH4st2X/K/3/3iu5nNmmRQAvtwUQUUHa155prrWoSiK5lRiKCYHGysmdqrFwYtJbD1b6I3e\nZZKUku0x2xmwdgATtk0gPiOea2n5N657OniabUIAOHghie0R8YxuUxNnO2utw1EUzZnvf7OGBob4\nsHBXNJ9tiKBdHU8sLYwzBbRWsvOyGbZ+GKcST+Ht6M3HrT/m2RrPmnUyuENKyX/Xn6Gyc/7FBYqi\nqIrhiVhbWjC5ax0irqfy59ErWodTKqSUhCeGA/k3ojWt3JRpraax5vk19AnoUyaSAsDG03EcvXyL\nNzvVxt7G9K+cUhRjUInhCfUIrEojbxe+2nSOzJw8rcMxGCklO2N3MvjvwQxcO5Dzt/JnSJ8cMpnn\naz2PtUXZOdWSk6fjsw0RBHg60q+pt9bhKIrJUInhCVlYCKZ0q8uVWxn8sv+S1uGUmJSSXbG7GLJu\nCOO2jONm1k0+bPUhvs6+WodWapaFxRCdcJsp3epiZan+FRTljrJxPkAjrQM8eKaWB7O2RfFCiI9Z\nD1zeyrrFpO2TcLNz48OWH9KrZi+sLc3353mc9Oxcvt4cSbCfK53qPXJ9KUUpd9THpBKa0q0ut9Jz\nmGtmS4BKKdl7ZS+f7P8EKSWudq4s6LqAtc+vJbR2aJlOCgALd10gPjWLd3vUNdr60YpiLlRiKKFA\nLxd6Na7Gwt0XuJGSqXU4jyWlZO/Vvby0/iVGbx7NjtgdJGQkANC4UuMynxAAEtOymLszmi71K6ub\nFBWlECoxGMDkLnXI00m+NvEJ9q6kXWHYhmGM3jSaa7ev8e8W/+bv5/+mkkMlrUMzqu+2RpGencs7\n3epqHYqimCQ1xmAAvu4ODGnux0/7LjKspb9JLQUppSQpMwl3e3fc7dzJ1eXyfvP3eb7W8ya7HkJp\nOh+fxi/7LzEgxFdNn64oD1GiikEI4SaE2CSEiNR/d31Iv7wCq7etKbC9uhDigH7/pfplQM3SxI61\ncLKz5pO/w01iqgwpJQeuHWD4huEMWTeEHF0OdlZ2/NrjVwbUHVAukwLAp3+fwc7akre6qCU7FeVh\nSnoqaSqwRUpZC9iif16YDCllkP6rV4Ht/w/4Sr//TeCVEsajGdcKNkzsWItdkQlsi9B2qoxDcYcY\nsXEEI/8ZSWxqLC/Vfwn0uao8D7Tujkxgy9kbjO8QgIejrdbhKIrJKmli6A0s0T9eAhR5rmWR/w7V\nAVjxJPuboqEt/ajhUYFP/j5DTp5OkxgOXDvAyxtf5nLKZaY2m8q60HUMrje4XAwqP0qeTvLJ3+H4\nuNkzorW/1uEoikkraWKoLKW8BqD//rALwu2EEGFCiP1CiDtv/u7ALSllrv55LOD1sAMJIUbpXyMs\nPj6+hGGXDmtLC/7Vox7R8beNetNbWFzY3YVxQqqE8HHrj1kfup4h9YZga6k+GQMsPRTD2bhU3u1e\nD1srNfWFojzKYwefhRCbgSqFNL1XjOP4SimvCiFqAFuFECeBwpZBe+jJeSnlPGAeQHBwsPYn8R+i\nYz1PWge48/XmSJ5/youKDqV3Lv/w9cP8cOwHDsYdpIZLDXpU74GFsDDLRXJKU0pmDl/+E0Ezfze6\nBxb2p6woSkGPrRiklJ2klIGFfK0GrgshqgLovxd6cl1KeVX/PRrYDjwFJAAVhRB3kpM3cLXEP5HG\nhBC837M+qZk5pbY+dERSBCP/GcnwDcM5f+s874S8w9Jnl2Ih1NXHhfl+WxRJ6dn8+9n65XqMRVGK\nqqTvJGuAYfrHw4DV93cQQrgKIWz1jz2A1kC4zL90ZxvQ71H7m6N6VZ0ZEOLLz/suEXUjzWCvm6PL\nASAzL5Oom1G8Hfw260PXM7T+UOys1BrFhbmcmM6Puy/S9ylvGnq7aB2OopiFkiaGGUBnIUQk0Fn/\nHCFEsBBigb5PPSBMCHGc/EQwQ0oZrm+bAkwSQkSRP+awsITxmIy3uuRP4/zRX6dLfPnqsRvHGPXP\nKKbvnw7k36H8T79/eKnBS9hb2Rsi3DJr2trTWFkK3u5aR+tQFMVslOgGNyllItCxkO1hwEj9471A\nw4fsHw00K0kMpsrD0Za3Otfmw7/CWX8qjh4Nqxb7NY7dOMbs47PZe3UvbnZutPFuc7etvN6HUByb\nw6+z+cwN/tWjLlVcVEWlKEWl7nwuRS+28GNZWCwfrw2nbe1KVLAt+q/75/Cf+ezQZ7jZufFW07d4\noc4LOFg7lGK0ZUtmTh4frT1NLU9HRrRW6zgrSnGoxFCKrCwt+LhPA0Jn7+O7rVFM7f7ouXlOxJ/A\nzsqO2q616eDbgRxdDgPrDFQJ4Qn8sP08MUkZ/P5qC6zVWguKUizqP6aUNfVzo39TbxbsiibqRmqh\nfU7Gn+S1za8xZN0Q5h6fC4CXoxcvB76sksITuJhwmzk7ztM7qBota7prHY6imB2VGIxgSve6ONhY\n8sGaeweiTyeeZtyWcQxeN5hTCaeY2GQiH7f+WMNIzZ+Ukg//Oo2N/mZDRVGKTyUGI/BwtOXtbnXZ\nE5XI3yev3d2+K3YXx+OPM7HJRDaEbmBkw5GqQiihTeHX2R4RzxudalHZWQ04K8qTEKYwE2hxBQcH\ny7CwMK3DKJY8naTb7N+It/yLjzoOo3et7qTnpKOTOhxt1PTPhnA7K5cuX+3E0daKtROeVmMLinIf\nIcRhKWXw4/qpwWcjCE8MZ/bx2cQ5bkfm2bHsSBS9a6GqAwP7fGMEV5MzWD66pUoKilICKjGUshkH\nZ/DrmV9xsnFifNB44mKC+XF3HHuDE2hV00Pr8MqMsItJLNmXv1BSsL9arlNRSkIlhlIQkRSBr7Mv\n9lb2NK7UmIq2FRlSbwhONk5k1Mtj25mdvLvqJBsmtsHeRs30WVKZOXlMWXmCai726g5nRTEAVW8b\nUERSBG9se4N+f/Vj5bmVAHSv3p0xjcfgZJO/3Ke9jSX/7duIS4npfLX5nJbhlhmztkZxPv42n/Zt\nWKybCBVFKZz6LzKAiKQI5hyfw+bLm3G0duS1xq/RK6DXQ/u3rOnO4Oa+LNgVTc+GVWnsU9GI0ZYt\n4VdTmLPjPKFNvGlbu5LW4ShKmaAqBgP49MCn7L+2nzGNx7AhdANjg8bibOP8yH2mdq+Lp5MdU1ae\nIDtXm9XezF1uno4pK09Q0cGafz+r7llQFENRieEJRN6MZMrOKSRkJADwUauP2BC6gXFB43CxLdrU\nzs521nzSJ5Czcal8vy2qNMMts+btiubklWSm9Q4s1QWRFKW8UYmhGKJuRjF5x2RC14SyI3YHZxLP\nAODv4l/khFBQp/qV6fuUF7O2RXEs5pahwy3TTl1J5qtN5+jRsIpalU1RDEwlhiLI0+Xxzs536Lum\nL7tidzGy4Ug2hm7kGe9nSvzaH/ZuQBVnO95ceoz07NzH76CQmZPHm0uP4epgw/Q+DdWqbIpiYCox\nPMKN9PyVSi0tLHGwcuCVhq+wMXQjE5pMeKIKoTDOdtZ80b8xFxNv8+m6MwZ5zbLusw0RRN5I4/P+\njXGtoE4hKYqhlSgxCCHchBCbhBCR+u+uhfRpL4Q4VuArUwjRR9+2WAhxoUBbUEniMZToW9G8s+Md\nuqzoQuTN/HWbP2z1IRObTKSineGvIGpZ052RT1fnl/2X2Xa20GWzFb3dkQks2nOBYS391FVIilJK\nSloxTAW2SClrAVv0z+8hpdwmpQySUgYBHYB04J8CXd6+0y6lPFbCeEokOjmaKTun0Gd1H7bHbmdY\ng2F42Bvn7uTJXetQt4oTby0/TlxyplGOaW7iU7N4c9kxalaqwNTu6iokRSktJU0MvYEl+sdLgD6P\n6d8PWC+lTC/hcQ0uPSedwX8PZlvMNoYHDmdD6AbebPomrnYPFEGlwtbKklmDm5CZk8eEP46Sm6cu\nYS0oTyd5c+kxUjJy+H5IE3XHuKKUopImhspSymsA+u+ej+k/EPj9vm3ThRAnhBBfCSFsH7ajEGKU\nECJMCBEWHx9fsqj1LiZfZPax2UgpcbB24LM2n7EhdAOTmk7Czc748+0EeDrySZ9ADl5I4tstkUY/\nvimbvT2K3VEJfNSrAXWrPPoeEUVRSuaxdz4LITYDhV0P+F5xDiSEqAo0BDYW2PwuEAfYAPOAKcC0\nwvaXUs7T9yE4OLhEc4VfSrnEvBPzWBu9FhsLG3rU6IGfsx9tvNuU5GUNom8Tb/aeT+S7bVE0q+7O\n07XURHsHohOZuekcvRpXY0CIj9bhKEqZ99jEIKXs9LA2IcR1IURVKeU1/Rv/o0ZOXwD+lFLmFHjt\nO6vWZAkhfgQmFzHuJ3Iz8yZfhH1xNyEMrTeU4YHDjTaOUFTTejfgeMwtXv/9CGvGP42PW/mdnvta\ncgbjfjuKn3sFPu2rLk1VFGMo6amkNcAw/eNhwOpH9B3EfaeR9MkEkf/f3gc4VcJ4Hsneyp6jN47y\nYr0XWR+6nskhk00uKQA42Fgxd2hTcnWS0T8fJiM7T+uQNJGZk8eYnw+TkZ3LvKFNcVQT5CmKUZQ0\nMcwAOgshIoHO+ucIIYKFEAvudBJC+AM+wI779v9VCHESOAl4AJ+UMJ5HsrOyY3Wf1bwd8rZJJoSC\nalRy5NuBT3EmLoUpK09gjivtlYSUkvf+PMXx2GRmDgiiVmUnrUNSlHKjRB/BpJSJQMdCtocBIws8\nvwh4FdKvQ0mO/ySsLayNfcgn1r6uJ5O71OHzjRHUr+bMmLY1tQ7JaH7cc5GVR2KZ2LEWXRuoKS8U\nxZhUbW7ixrarSfi1FGasP4uPqwM9G1XVOqRS98/pOD75O5wu9SszsWMtrcNRlHJHJQYTJ4Tgy/6N\nuZ6cyZvLjuHpbEtIGV668ujlm0z44ygNvSvyzcCnsLBQg82KYmxqriQzYGdtyfyXgvGuaM/IJWGc\nj0/TOqRScSnxNiOXhOHpZMfCYcHqJjZF0YhKDGbCtYINi0c0w9pSMHTBAWKSTO7m8RK5lpzB0IUH\n0UnJ4hEheDg+9F5HRVFKmUoMZsTX3YHFI5qRlpXLkAUHuJacoXVIBnEjNZMh8w+QdDubH0c0o0Yl\nR61DUpRyTSUGMxPo5cJPrzQn6XY2Q+Yf4EaqeU+4l5iWxZD5B4hLyWTxiBCC1PrXiqI5lRjMUJBP\nRX4cEcK15EwGzdvP1VvmWTncSMlkyIIDXE5KZ+GwEILL8KC6opgTlRjMVIi/G4tHhHAjJYt+s/ea\n3YD0pcTbhM7Zy+WkdBYND6FlTXetQ1IURU8lBjPWvIY7v49qQXaejv5z9nEyNlnrkIok/GoKobP3\nkZaZy2+vtqB1gGnfha4o5Y1KDGYu0MuF5WNaYW9tyQtz9/H3iWuP30lDG0/H0X/OXqwtBcvHtFRj\nCopiglRiKAOqe1Tgz7GtqFfViXG/HeGzDWfJ05nW3Eo6neSrTecY/fNhAjwdWTW2FQGeav4jRTFF\nKjGUEZ7Odvw+qgWDmvnww/bzjFh8yGSuWEpMy2LUz2F8syWS0CbeLB3dkqou9lqHpSjKQ6jEUIbY\nWlny376NmP58IAeiE+n61U7WndT21NI/p+Po8tVOdp5L4IPn6vNF/0bYWas7mhXFlKnEUAYNae7H\n3xOewcfNgbG/HuH1348Sl2zc6uFGSiaTlh5j1M+Hqexsx1+vP82I1tXVQjuKYgaEOc7zHxwcLMPC\nwrQOw+Tl5On4Ydt5vt8WhaWFYHTbGoxuU7NU5yDKzMljwa5ofth+npw8HaPb1GRCx1rYWKnPIIqi\nNSHEYSll8GP7lSQxCCH6Ax8C9YBm+nUYCuvXDfgGsAQWSCnvLOhTHfgDcAOOAEOllNmPO65KDMUT\nk5TOjPVn+fvkNTydbBne2p/BzXyp6GBjsGMkZ+Twx8HL/LjnInEpmXSpX5l3e9SjukcFgx1DUZSS\nMVZiqAfogLnA5MISgxDCEjhH/gpvscAhYJCUMlwIsQxYJaX8QwgxBzgupZz9uOOqxPBkDl1M4tst\nkeyKTMDe2pLnm3jxbKOqNPN3w8qy+J/o83SSQxeT+PvENVYeiSU9O4+WNdx5vWMArWqqexMUxdQU\nNTGUdAW3M/qDPapbM3IwzgcAAAhFSURBVCBKShmt7/sH0FsIcQboAAzW91tCfvXx2MSgPJkQfzd+\nfqU5Z+NSWLT7AisPx/Lbgcu4OljTvq4nQT4VaVDNmbpVnKlQyPrK6dm5nLmWSvjVZI7HJrPt7A0S\nb2djY2XBc42q8fLT/jSo5qLBT6YoiiEZY6EeLyCmwPNYoDngDtySUuYW2P7A8p+K4dWt4sxn/Rrz\nYa8G7DwXz8bT19keEc+qI1fu9rG1ssDZ3poKNpbczs4jJSOHrFzd3faKDta0qVWJboFVaFu7UqGJ\nRFEU8/TY/2YhxGagsEV335NSri7CMQorJ+Qjtj8sjlHAKABfX98iHFZ5HAcbK7oFVqVbYFWklMSl\nZHL6SgrnbqSSnJFDSkYOaVl5ONpa4mxnjbO9NbU8HWng5UI1Fzt1hZGilFGPTQxSyk4lPEYs4FPg\nuTdwFUgAKgohrPRVw53tD4tjHjAP8scYShiTch8hBFVd7KnqYk+n+pW1DkdRFA0Z4xrCQ/+/vbML\ntaM6w/DzVklESvUkWpvUqicQYwUhkSC2hVp/UOtFEmmqR5AeNV4k/bkRoZH0QgqltTdCacFaq7YK\n8SdFOEVDiCbBG2PrhRqjJDmJSGNSI1qVUnoa9OvF+rasfTJ779lnz0x2cr4HNnvmWz/znnfWnjWz\nZuYsYLGkUUlzgDFgwtJd7+3Aas83DpS5AgmCIAhqZKCOQdKNkg4C3wCelbTF4wslPQfgVwM/BrYA\nbwFPmdlur+KnwF2SJkn3HP44iJ4gCIJgcOIFtyAIgllC2cdV43XUIAiCoI3oGIIgCII2omMIgiAI\n2oiOIQiCIGgjOoYgCIKgjRPyqSRJ7wPvzLD4WaSX64aNYdUFw6stdPVH6OqfYdU2U13nm9nZvTKd\nkB3DIEh6pczjWk0zrLpgeLWFrv4IXf0zrNrq1hVDSUEQBEEb0TEEQRAEbczGjuHB4y2gA8OqC4ZX\nW+jqj9DVP8OqrVZds+4eQxAEQdCd2XjFEARBEHThpOwYJH1f0m5Jn0nqeOde0vWS9kialLQ+i49K\nelnSPklP+r8Lr0LXPElbvd6tkkYK8lwp6dXs819JqzztUUlvZ2lLm9Ll+T7Ntj2RxWvxq6w2SUsl\nveT7/HVJN2dplXrWqc1k6XPdg0n35IIs7R6P75F03SA6ZqDrLklvuj8vSDo/Syvcrw3puk3S+9n2\n78zSxn2/75M03rCu+zNNeyV9lKXV6dfDko5IeqNDuiT9xnW/LunSLK06v8zspPsAXweWADuA5R3y\nnALsBxYBc4DXgIs97SlgzJcfANZVpOvXwHpfXg/c1yP/POBD4HRffxRYXYNfpXQB/+4Qr8WvstqA\nC4HFvrwQOAycWbVn3dpMlueHwAO+PAY86csXe/65wKjXc0qDuq7M2tG6lq5u+7UhXbcBvy0oOw84\n4N8jvjzSlK5p+X8CPFy3X173t4FLgTc6pN8AbCbNgHk58HIdfp2UVwxm9paZ7emR7TJg0swOmNn/\ngCeAlZIEXAVs8nx/AlZVJG2l11e23tXAZjP7T0Xb70S/uj6nZr9KaTOzvWa2z5cPAUeAni/xzIDC\nNtNF7ybgavdoJfCEmU2Z2dvApNfXiC4z2561o52kGRPrpoxfnbgO2GpmH5rZv4CtwPXHSdctwMaK\ntt0VM3uRdDLYiZXAny2xkzQL5gIq9uuk7BhK8lXgH9n6QY/NBz6yNMFQHq+Cc8zsMIB/f7lH/jGO\nbZC/8EvI+yXNbVjXaZJekbSzNbxFvX71ow0ASZeRzgL3Z+GqPOvUZgrzuCcfkzwqU7ZOXTlrSGed\nLYr2a5O6vuf7Z5Ok1jTAQ+GXD7mNAtuycF1+laGT9kr96jnn87Ai6XngKwVJG8yszBShRTPZW5f4\nwLrK1uH1LAAuIc181+Ie4J+kA9+DpBnwft6grvPM7JCkRcA2SbuATwry9fWoW8WePQaMm9lnHp6x\nZ0WbKIhN/1traVc9KF23pFuB5cAVWfiY/Wpm+4vK16Drr8BGM5uStJZ0tXVVybJ16moxBmwys0+z\nWF1+laGR9nXCdgxmds2AVRwEvpatnwscIv3/kTMlnepnfK34wLokvSdpgZkd9oPYkS5V3QQ8Y2ZH\ns7oP++KUpEeAu5vU5cM0mNkBSTuAZcBfGMCvqrRJ+hLwLPAzv8Ru1T1jzwro1GaK8hyUdCpwBmlo\noEzZOnUh6RpSZ3uFmU214h32axUHup66zOyDbPUPwH1Z2e9MK7ujAk2ldGWMAT/KAzX6VYZO2iv1\nazYPJf0dWKz0RM0cUgOYsHQnZztpfB9gHChzBVKGCa+vTL3HjGv6gbE1rr8KKHxyoQ5dkkZawzCS\nzgK+BbxZs19ltc0BniGNvT49La1KzwrbTBe9q4Ft7tEEMKb01NIosBj42wBa+tIlaRnwe2CFmR3J\n4oX7tUFdC7LVFaR54SFdKV/r+kaAa2m/eq5Vl2tbQrqR+1IWq9OvMkwAP/Cnky4HPvaTn2r9quvu\n+vH8ADeSetAp4D1gi8cXAs9l+W4A9pJ6+w1ZfBHpRzsJPA3MrUjXfOAFYJ9/z/P4cuChLN8FwLvA\nF6aV3wbsIh3cHge+2JQu4Ju+7df8e03dfvWh7VbgKPBq9llah2dFbYY0NLXCl09zDybdk0VZ2Q1e\nbg/w3YrbfC9dz/tvoeXPRK/92pCuXwK7ffvbgYuysne4j5PA7U3q8vV7gV9NK1e3XxtJT9UdJR3D\n1gBrgbWeLuB3rnsX2VOXVfoVbz4HQRAEbczmoaQgCIKggOgYgiAIgjaiYwiCIAjaiI4hCIIgaCM6\nhiAIgqCN6BiCIAiCNqJjCIIgCNqIjiEIgiBo4/+CiLVtthTlkgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfda429588>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y, x, np.repeat(h0_bar, len(x)), '--', x, h1_bar[0] * x + h1_bar[1], '--')\n",
    "plt.legend(['Sin(pi x)', 'H_0', 'H_1'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Variance of H0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 153,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.226105840895\n"
     ]
    },
    {
     "data": {
      "image/png": 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635B8hm0ArgauTrcLuCmN+xEyd13meb785LOZmdXp5ktJZmbWgBODmZnVcWIw\nM7M6TgxmZlbHicHMzOo4MZiZWR0nBjMzq+PEYGZmdf4fbTJj5ryCuIQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfd1cab4a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var = []\n",
    "for i in range(500):\n",
    "    d_x = np.random.choice(x, 2, replace=True)\n",
    "    d_y = scipy.sin(np.pi * d_x)\n",
    "    h0 = np.polyfit(d_x, d_y, deg=0)\n",
    "    plt.plot(x, np.repeat(h0, len(x)), 'b', alpha=0.06)\n",
    "    var.append((h0 - h0_bar) ** 2)\n",
    "plt.plot(x, np.repeat(h0_bar, len(x)), 'b')\n",
    "print(np.mean(var))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Variance of H1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 154,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:5: RankWarning: Polyfit may be poorly conditioned\n",
      "  \"\"\"\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:5: RankWarning: Polyfit may be poorly conditioned\n",
      "  \"\"\"\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:5: RankWarning: Polyfit may be poorly conditioned\n",
      "  \"\"\"\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:5: RankWarning: Polyfit may be poorly conditioned\n",
      "  \"\"\"\n",
      "/usr/lib/python3.6/site-packages/ipykernel_launcher.py:5: RankWarning: Polyfit may be poorly conditioned\n",
      "  \"\"\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.7825423886\n"
     ]
    },
    {
     "data": {
      "image/png": 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O1nOYHRp5zpKOqMBu6zJHjOQoE841pwjgyOecsFkBmP+3c/Q4J2wGfSuGfN0M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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdfd32c3470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "var = []\n",
    "for i in range(500):\n",
    "    d_x = np.random.choice(x, 2, replace=True)\n",
    "    d_y = scipy.sin(np.pi * d_x)\n",
    "    h1 = np.polyfit(d_x, d_y, deg=1)\n",
    "    plt.plot(x, h1[0] * x + h1[1], 'b', alpha=0.06)\n",
    "    pred = h1[0] * x + h1[1]\n",
    "    var.append((pred - y) ** 2)\n",
    "plt.plot(x, h1_bar[0] * x + h1_bar[1], 'b')\n",
    "print(np.mean(var))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## bias + variance of H0 and H1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- H0: 0.5 (bias) + 0.226 (variance) = 0.726\n",
    "- H1: 0.2 (bias) + 1.783 (variance) = 1.983"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}