Ensemble-Learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Ensemble Learning<a id=\"Top\"></a>\n",
    "\n",
    "<div class=\"alert alert-block alert-info\" style=\"margin-top: 20px\">\n",
    "\n",
    "<font size = 3>\n",
    "Table of Content\n",
    "    \n",
    "<ul>\n",
    "<li>1. <a href=\"#Part_1\">Prelude: Tossing a biased coin</a></li>\n",
    "<li>2. <a href=\"#Part_2\">Ensemble Learning</a></li>\n",
    "    <ul>\n",
    "        <li>2.1 <a href=\"#Part_2_1\">Voting classifiers</a></li>\n",
    "        <li>2.2 <a href=\"#Part_2_2\">Bagging and Pasting</a></li>\n",
    "        <li>2.3 <a href=\"#Part_2_3\">Boosting</a></li>\n",
    "        <li>2.4 <a href=\"#Part_2_4\">Stacking</a></li>\n",
    "    </ul>    \n",
    "</font>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from scipy.stats import binom\n",
    "\n",
    "# Define overall figure size. Use the Golden ratio to compute width and height.\n",
    "height = 6.0\n",
    "width = height*0.5*(1.0+np.sqrt(5.0))\n",
    "\n",
    "plt.rcParams['figure.figsize'] = (width, height)\n",
    "\n",
    "# Instanciate the random number generator\n",
    "np.random.seed(seed=0)\n",
    "rnd = np.random.random"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Prelude: Tossing a biased coin<a id=\"Part_1\"></a>\n",
    "<a href=\"#Top\">Back to page top</a>\n",
    "\n",
    "Fair coin tossing is a classic example in probability theory and statistics. Now instead of a fair coin, let us assume we have a biased one: the coin has a __51%__ chance of coming up heads, and __49%__ chance of coming up tails. Now we want to asking the following question: __what is the probability of getting a majority of heads after $n$ tosses__? \n",
    "\n",
    "Probability theory tells us that the distribution of the number of heads $k$ in a sequence of $n$ tosses is given by the binomial probability mass distribution:\n",
    "\n",
    "$$ \n",
    "    P(k, n, p) = \\left(\\begin{array}{c} n \\\\ k\\end{array}\\right)\\,p^k\\,(1-p)^{(n-k)}.\n",
    "$$\n",
    "\n",
    "Here $p$ and $1-p$ is the probability of coming up heads and tails respectively. In our example, $p=0.51$. The Scipy library `scipy.stats` has a built-in function `binom.pmf(k,n,p)` that returns $P(k, n, p)$. Let's calculate the probability of having $k=0$, 1, 2, $\\ldots$, 6 heads after six tosses:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Probility of having   0 heads:  0.01384\n",
      " Probility of having   1 heads:  0.08644\n",
      " Probility of having   2 heads:  0.22491\n",
      " Probility of having   3 heads:  0.31213\n",
      " Probility of having   4 heads:  0.24365\n",
      " Probility of having   5 heads:  0.10144\n",
      " Probility of having   6 heads:  0.01760\n"
     ]
    },
    {
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\n",
      "text/plain": [
       "<Figure size 698.991x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "p = 51./100.\n",
    "num_toss = 6\n",
    "phead = []\n",
    "for i in range(num_toss+1):\n",
    "    f = binom.pmf(i, num_toss, p)\n",
    "    phead.append(f)\n",
    "    print(' Probility of having {0:3d} heads: {1:8.5f}'.format(i, f))\n",
    "    \n",
    "plt.plot(range(num_toss+1), phead, 'bo-')    \n",
    "plt.xlabel('Number of heads', fontsize=18)\n",
    "plt.ylabel('Probability', fontsize=18)\n",
    "plt.xlim(0,num_toss)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.show()   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The distribution is not symmetric around $n=3$: the probability of having 4 heads is slightly bigger than that of coming up with 2 tails, and so on. This, of course, is the result of having a biased coin.\n",
    "\n",
    "Following this example, we can now answer the question: __what is the probability of getting a majority of heads after $n$ tosses__? This is just the sum of probability mass function $P(k,n,p)$ for $k > n/2$. Now let us plot the answer as a function of the number of tosses up to $n=500$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ProbMajorHead(n, p):\n",
    "    psum = 0.0\n",
    "    for i in np.arange(n/2.+1., n+1., 1.):\n",
    "        psum += binom.pmf(i, n, p)    \n",
    "    return psum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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d73Ir27vfnXuX7rWXz7lJklRVZYa4I4G7awEOIKU0MyLuBI6itRCnTsydC9/8Zg5vzz2Xe5d+5SvwvvfBppuWXTtJktRXZT62vjPwQJPt04EpLZ7jnyJiWUQsiYhbImK//qteNc2YAR/6UB7L7bOfzdNd3XADPPoo/Ou/GuAkSRouymyJGwssbLJ9ATCmheN/APwSeBqYAPwrcEtEHJJSuq2/KlkV06bl59t++tM8+O4JJ8DHPgY77VR2zSRJ0kAoe4iRZj1MW3pKK6V0Qt3bOyLiGnLL3vnAvs2OiYhTgVMBxo8f37OaDlF33AHnngu33AIbbZRb2z7yEdhqq7JrJkmSBlKZt1MXklvjGo2heQtdl1JKLwLXA6/vosylKaWpKaWp48aN6+lHDCl33QWHHAJvehM8+GBuhZs9G770JQOcJEntoMyWuOnk5+IaTQEe7OU5g+ate8PGX/8KZ54Jv/41jBsH//ZvuaepE89LktReymyJuxbYKyIm1TZExERgn2Jfj0TEhsARwD39VL8h5emn4f3vhz32gHvugS9/GWbOhI9+1AAnSVI7KrMl7jLgdOCaiDib3IL2OeBJ6gbwjYgJwAzgvJTSecW2jwOTgVvp6NjwcWAL4PhB/A4D7qWX8q3SCy6AFStyZ4WzzoKNNy67ZpIkqUylhbiU0ksRcRB52q0ryLdCbyZPu7W4rmgAI1i91fBh4B3FshHwAnAn8IGU0h8HofqD4he/yBPQz5kD73pXft5t0qTuj5MkScNfqb1TizlS39lNmVk09FhNKV0HXDdwNSvX7Nk5vF17LeyyS57ndN+m/W0lSVK7KvOZODVYuRIuvBCmTIGbbsozLNx7rwFOkiStqexx4lSYNQve+9487tsRR8DFF8PEiWXXSpIkDVWGuJKlBFdcAaefnt9ffnkOc05ML0mSuuLt1BItXAjHHAMnngi77ZbHgDvxRAOcJEnqniGuJA88AK9/Pfz85/DFL8Jtt8F225VdK0mSVBXeTi3Bz36WW9w22ABuvx323rvsGkmSpKqxJW4QrVwJZ58NRx8Nr31t7nlqgJMkSb1hS9wgWbIEjjsOrrkGPvAB+OY3YdSosmslSZKqyhA3CBYsgLe9De66C77xjdwT1c4LkiSpLwxxA+zZZ+Hgg+HRR+EnP8m3UiVJkvrKEDeAnn4aDjoInnwSfv3r/FqSJKk/GOIGyN/+BgcemIPcDTfAfvuVXSNJkjScGOIGwKJFcNhhMGcO3Hgj7LNP2TWSJEnDjSGun738cu7EMH06XHedAU6SJA0MQ1w/SikPH3LHHfCjH8Ghh5ZdI0mSNFw52G8/+uIX4Yc/hM9/Ho49tuzaSJKk4cwQ109++Us466w8oO+ZZ5ZdG0mSNNwZ4vrBk0/muVB33x2+/W0H8pUkSQPPENdHK1bk1rdXXsmD+b7qVWXXSJIktQM7NvTRF74Av/89/OAHsOOOZddGkiS1C1vi+mD6dDj/fHjPe+D448uujSRJaieGuF5auTIPJ7LRRvD1r5ddG0mS1G68ndpLF18M99wDV14J48aVXRtJktRubInrhXnz4Jxz8mC+73lP2bWRJEntyBDXC5/7HCxeDBde6HAikiSpHIa4Hnr0UfiP/4BTToEpU8qujSRJalc9DnER8duIOCYi1hmICg11Z54J664L555bdk0kSVI7601L3OuAHwJPR8TXImKXfq7TkPXAA/Czn8HHPgZbbFF2bSRJUjvrTYjbAjge+DPwYeAvEXFPRJwSEev3a+2GmAsugNGj4cMfLrsmkiSp3fU4xKWUXkkpXZVSOgSYBJwPbA5cAjwTEd+JiH36uZ6lmz0bfvhDOPlk2GSTsmsjSZLaXZ86NqSUnkgpfQbYDjgMuBU4CfhdRDwYEf8cEev1vZrlu+giSAk++tGyayJJktR/vVN3B44E9gMCmAGsAi4CHouIvfvpc0rxwgtw2WV5TLgJE8qujSRJUh9CXERsHBEfiog/AdOAk4HfAAenlF6dUnotcDCwBPhmJ+fYNiJ+GhGLIuKFiLg6Isb3oi5nRkSKiN/39vt05Sc/gZdegtNPH4izS5Ik9VyPp92KiIOADwDvANYFHgH+L3B5Sml+fdmU0i0R8SWahLiIGA3cAiwDTgQS+fm6WyNi15TSSy3WZxJwFvBcT79Lq777XdhpJ9hzz4H6BEmSpJ7pzdypN5GD19XApSml27sp/xhwZ5Ptp5A7RkxOKT0GEBH3AY8CpwEXtlifbwFXApMZgLlgH3kE/vAH+PKXnZ1BkiQNHb25nfoxYOuU0vEtBDhSSremlA5ssutI4O5agCvKziQHvqNaqUhEHAf8HXBmSzXvhe99D9ZaC044YaA+QZIkqed6E+I2ALbqbGdE7BwR57Rwnp2BB5psnw50O6FVRIwhd5z4vymlBS18Xo+tXAnf/z4cdhhsueVAfIIkSVLv9CbEfQbYtYv9ry3KdGcssLDJ9gXAmBaOv4D8PN7lLZTtlTvugDlz4MQTB+oTJEmSeqc3z5B192TYusCKFs+VenF+ImI/4L3A36WUmp2js+NOBU4FGD+++06w118P66wDhx/e6idIkiQNjpZCXERsCGxct2mTToYCGUuekuvJFk67sCjfaAzNW+jqXQJ8B5gTEbV6jQRGFO+XppSWNR6UUroUuBRg6tSp3Ya/66+H/feH9Yf1ZGKSJKmKWm2J+xeg9pxbAr5WLM0EeciR7kwnPxfXaArwYDfH7lQs/9hk30JyfTurX0tmzoSHHoLTTuvLWSRJkgZGqyHutmId5DD3c+C+hjIJWEzucfqHFs55LfDViJiUUnocICImAvsAn+zm2Ga9Xb8GjAA+TB7WpE+uvz6vjziir2eSJEnqfy2FuGIokdsBImIC8J8ppXv6+NmXAacD10TE2eQQ+DnyrdhLaoWKz5sBnJdSOq+oz22NJ4uI54GRzfb1xvXXw447wg479MfZJEmS+lePe6emlN7XDwGOYkaGg8g9TK8gD9g7EzgopbS4rmiQW9j6a57Xbi1ZArfeaiucJEkaurptiat1YEgpza5/351a+RbKvLObMrNoocdqSumAVurViltvhWXLDHGSJGnoauV26ixgVUSMTim9UrxvZViPEX2oV6l+/3tYe23Yd9+yayJJktRcKyHuPHJoW9Hwftj64x9ht91g3XXLrokkSVJz3Ya4lNK5Xb0fblatgv/5H+dKlSRJQ9ugdRaoiocfhhdfhD33LLsmkiRJnTPENfjjH/PaECdJkoayVnqnrqLnz8CllFJv5mUt3T33wAYbwOTJZddEkiSpc60Ere8zzDsy1PvjH+H1r4e1bKOUJElDWCsdG04ahHoMCS+/DH/9K3z842XXRJIkqWu2N9X5y19gxQqfh5MkSUOfIa6OnRokSVJVtNKxYSawCnhNSml5RDzewnlTSmn7PtdukN13H4wbB1tvXXZNJEmSutZKx4YnyB0bap0bZjNMOzrMmAE77FB2LSRJkrrXSseGA7p6P5zMmAH77192LSRJkrrnM3GFZctgzhzYvnI3gSVJUjvq9YC8ETEKOACYVGx6HLg9pfRyP9Rr0M2cCSkZ4iRJUjX0KsRFxHuBC4ExQBSbE/B8RHwspXR5/1Rv8MyYkdeGOEmSVAU9DnERcQxwObmDw1eBB8lBbgrwj8B3ImJpSunH/VjPAWeIkyRJVdKblrhPAf8L7JVSeqFu+zUR8R/APcBZQOVC3HrrwWablV0TSZKk7vWmY8Nk4LsNAQ6AlNIi4LvAjn2t2GCbMSO3wkV0X1aSJKlsvQlxz9LxHFwzq4C/9a465amFOEmSpCroTYi7HDgpItZv3BERGwLvJ7fGVcaqVbl3qiFOkiRVRSvTbr2pYdPvgLcC9xfPwP0vuWfqFOCfgHnAHf1czwH11FN5nDhDnCRJqopWOjbcxprTbNVup365bl9t2wTgt8CIvlZusNgzVZIkVU0rIe59A16LkhniJElS1bQyd+r3BqMiZZoxA0aOhPHjy66JJElSa5w7lRziJk7MQU6SJKkK+jJ36ubAVPLUW2uEwZTS9/tQr0H17LOw9dZl10KSJKl1vZl2ay3gm8DJdN2SV5kQN38+TJ5cdi0kSZJa15vbqR8HTgN+BJxI7pX6SeBDwKPANOCQ/qrgYFiwAMaOLbsWkiRJretNiDsR+E1K6b3Ar4tt96aU/hN4HbBpsa6ElAxxkiSpenoT4ibREd5WFeu1AVJKL5Fnazi571UbHEuX5oF+DXGSJKlKehPilgLLi9eLyYP9bla3/1lg2z7Wa9AsWJDXhjhJklQlvQlxTwDbA6SUlgOPAYfV7T8Y+FvfqzY45s/P6002KbcekiRJPdGbEHcL8I6691cA74mIWyPiNuBdwE9aOVFEbBsRP42IRRHxQkRcHRHdDrkbERMi4pqIeCIilkbEvIi4LSLe0tMvY0ucJEmqot6ME/dV4MaIGJVSWgZ8kXw79R+AlcClwGe6O0lEjCYHwmXkzhIJOB+4NSJ2LZ6v68z6wDzgbGAOsCFwCvCriHhnSunqVr+MIU6SJFVRj0NcSukZ4Jm69yuBjxRLT5xC7iQxOaX0GEBE3EcepuQ04MIu6jAd+ED9toi4HphJnuvVECdJkoa1MqfdOhK4uxbgAFJKM4E7gaN6erKU0gpgER2dLlpiiJMkSVXUl2m33k1+Nm5Sselx4OcppZaehwN2Bq5psn06+bm6VuqwFjmIbkpu2Xs18M8tfj6QOzasuy6MHt2ToyRJksrVm2m3RpPD10Hk2RqeL9avB94dEacBR3bzTBvAWGBhk+0LyPOxtuIrwMeK14uBY1NKN3dR91OBUwHGj8/9JxzoV5IkVVFvbqd+AXgz8O/AVimlsSmlMcBWxbYDgc+3eK7UZFv0oC5fI4fHt5EHIP5hRLy10w9L6dKU0tSU0tRx48YBhjhJklRNvbmdegzw3ymlM+o3ppSeBc6IiK2LMmc0O7jOQnJrXKMxNG+hW0NKaQ65dyrAL4shTr4K/LKV48EQJ0mSqqk3LXEbArd2sf+Wokx3ppOfi2s0BXiwF/UCmAbs0JMDDHGSJKmKehPi7gN27GL/jsD9LZznWmCviKh1jCAiJgL7FPt6pOjksC8woyfHzZ9viJMkSdXTmxB3NnBKRLytcUdEHAWcDHyqhfNcBswCromIoyLiSHKHiSeBS+rOOSEiVkTEOXXbzo2Ib0TEMRGxf0QcA9wA7EkLAw3XW7DAKbckSVL1dPtMXET8V5PNM4FfRMTDwEPkDgpTgMnkVrjjybdVO5VSeikiDgIuIk/dFcDNwBkppcX1VQBGsHrg/BP5mbtjgY2AZ4G/AvullO7s7jvVLF0KL79sS5wkSaqeVjo2nNTFvtcUS71dgV1omFGhmZTSbOCd3ZSZRUOP1ZTStfTilmsjB/qVJElV1W2ISymVOavDgDLESZKkqhq2Aa0V8+fntSFOkiRVTV+m3QpgD1afduvPKaVmA/gOSbWWODs2SJKkqulViIuIw4D/ACY07JoVER9MKf2mzzUbBN5OlSRJVdWbuVNr47i9BHwDeKDYtTO5E8S1EXFgSukP/VXJgWKIkyRJVdWblrhzyEN6vCGl9Ez9joi4ALinKHNY36s3sBYsgHXWgdGjy66JJElSz/SmY8MbgEsbAxxAse0yYK++Vmww1GZriOi+rCRJ0lDSmxC3DvBiF/tfKMoMec6bKkmSqqo3Ie4h4NiIWONWbLHtmKLMkOeUW5Ikqap6E+K+Rb6lenNEHBER2xXLW8nTZr2B3HN1yLMlTpIkVVWPOzaklL4dETsCHwf2bVLkgpTSd/pcs0Hw/POw8cZl10KSJKnnejVOXErpExHxHeAoYDvy3KYzgGtTSo/0Y/0G1LJlMGpU2bWQJEnquR6FuIgYRb5d+kwR1i4YkFoNkuXLYWSv56yQJEkqT0+fiVtJfu7tLQNQl0G3YgWsvXbZtZAkSeq5HoW4lNIK8kC/w2JkteXLDXGSJKmaetM79b+Bd0dEb44dUgxxkiSpqnrzRNi3gQOB30bE14BHgSWNhVJKs/tYtwG3YoXPxEmSpGrqTYR5oO71AV2UG9GLcw+alPLaljhJklRFvQlx5wGpvysy2AxxkiSpyno6xMg44NfAvJS2PTbXAAAXkklEQVTSjIGp0uAwxEmSpCprqXNCRKwVEf8JPAP8AXgkIn5fhLpKqoU4n4mTJElV1GoP09OBU8nDi1wN3A/sDVwyQPUacLbESZKkKmu1Heq9wEPAXimlFwEi4jLgpIjYOKX0/EBVcKAY4iRJUpW12hI3Gbi8FuAK/07ugfrqfq/VIPJ2qiRJqqJWQ9x6wNMN256u21c5tsRJkqQq68msC43DitTeV3IKLkOcJEmqsp7cTDw8Iraoez+aHOTeFRG7N5RNKaWL+ly7AWSIkyRJVdaTEHdcsTQ6rcm2BFQixPlMnCRJqqJWI8yBA1qLEtgSJ0mSqqylEJdSun2gKzLYDHGSJKnKetKxYVjxdqokSaqytg9xtsRJkqQqKjXERcS2EfHTiFgUES9ExNURMb6F46ZGxKUR8b8RsSQiZkfElRGxXaufbYiTJElVVlqIi4jRwC3Aa4ATgROAHYFbI6K7AYSPBXYGvgG8Bfgk8HfAtIjYtpXPN8RJkqQqK/OJsFOAScDklNJjABFxH/AoediSC7s49ssppbn1GyLiTmBmcd5zuvtwn4mTJElVVubt1COBu2sBDiClNBO4EziqqwMbA1yx7QlgLrB1Kx9uS5wkSaqyMkPczsADTbZPB6b09GQRsROwGfBQK+UNcZIkqcrKDHFjgYVNti8AxvTkRBExEvhPckvcd1o5xtupkiSpysoeYiQ12Ra9OM/FwN7AP6SUmgXDfOKIUyNiWkRMe/HFxYAtcZIkqZrKDHELya1xjcbQvIWuqYj4InAq8P6U0o1dlU0pXZpSmppSmrreeusDhjhJklRNZd5MnE5+Lq7RFODBVk4QEWeRhxf5SErpip58uM/ESZKkKiuzJe5aYK+ImFTbEBETgX2KfV2KiI8A5wNnpZT+vacf7jNxkiSpysoMcZcBs4BrIuKoiDgSuAZ4ErikVigiJkTEiog4p27bscDXgBuAWyJir7qlpZ6ttsRJkqQqK60dKqX0UkQcBFwEXEHu0HAzcEZKaXFd0QBGsHrgPKzYflix1LsdOKD7z89rQ5wkSaqiSKlZB9Hhb8stp6bnnpvGypVl10SSJA1nEXFvSmlqf5+37CFGSuXzcJIkqaraNsSl5K1USZJUXYY4SZKkCmrrEOftVEmSVFVtHeJsiZMkSVVliJMkSaogQ5wkSVIFtXWI85k4SZJUVW0d4myJkyRJVWWIkyRJqqC2DnHeTpUkSVXV1iHOljhJklRVhjhJkqQKMsRJkiRVUFuHOJ+JkyRJVdXWIc6WOEmSVFWGOEmSpApq6xDn7VRJklRVbR3ibImTJElVZYiTJEmqIEOcJElSBbVtiAOfiZMkSdXVtiHOljhJklRlhjhJkqQKMsRJkiRVUFuHOJ+JkyRJVdW2IQ5siZMkSdVliJMkSaqgtg5x3k6VJElV1dYhzpY4SZJUVYY4SZKkCjLESZIkVVCpIS4ito2In0bEooh4ISKujojxLR77hYi4MSLmR0SKiJN6+vk+EydJkqqqtBAXEaOBW4DXACcCJwA7ArdGxHotnOLDwKuAX/a2DrbESZKkqiqzLeoUYBIwOaX0GEBE3Ac8CpwGXNjN8RullFZFxA7Ae3tTAUOcJEmqqjJvpx4J3F0LcAAppZnAncBR3R2cUlrV1wp4O1WSJFVVmSFuZ+CBJtunA1MGowK2xEmSpKoqM8SNBRY22b4AGDMYFTDESZKkqip7iJHUZFsM1IdFxKkRMS0ipoEhTpIkVVeZIW4huTWu0Riat9D1WUrp0pTS1JTSVPCZOEmSVF1lhrjp5OfiGk0BHhyMCtgSJ0mSqqrMEHctsFdETKptiIiJwD7FvgFniJMkSVVVZoi7DJgFXBMRR0XEkcA1wJPAJbVCETEhIlZExDn1B0fE/hFxNHBYsWlqRBxdbGuJt1MlSVJVlRZjUkovRcRBwEXAFeQODTcDZ6SUFtcVDWAEawbOzwL7173/ULHUjumWLXGSJKmqSm2LSinNBt7ZTZlZNAllKaUD+vr5hjhJklRVZQ8xUipDnCRJqqq2DnE+EydJkqqqrUOcLXGSJKmqDHGSJEkVZIiTJEmqoLYOcT4TJ0mSqqqtQ5wtcZIkqaoMcZIkSRXU1iFurbb+9pIkqcraNsZE5EWSJKmK2jrESZIkVZUhTpIkqYLaNsRJkiRVWduGOFviJElSlRniJEmSKsgQJ0mSVEGGOEmSpAoyxEmSJFWQIU6SJKmCDHGSJEkVZIiTJEmqIEOcJElSBRniJEmSKsgQJ0mSVEGGOEmSpAoyxEmSJFWQIU6SJKmCDHGSJEkVZIiTJEmqIEOcJElSBRniJEmSKsgQJ0mSVEGlhriI2DYifhoRiyLihYi4OiLGt3jsuhFxQUQ8ExFLI+KuiHhT65/d+3pLkiSVrbQQFxGjgVuA1wAnAicAOwK3RsR6LZziO8ApwDnAW4FngN9ExO4DU2NJkqShY2SJn30KMAmYnFJ6DCAi7gMeBU4DLuzswIjYDTgOeH9K6bvFttuB6cB5wJHdfbgtcZIkqcrKvJ16JHB3LcABpJRmAncCR7Vw7HLgx3XHrgCuAg6NiFHdfbghTpIkVVmZIW5n4IEm26cDU1o4dmZKaUmTY9cBdujuww1xkiSpysoMcWOBhU22LwDG9OHY2v4uGeIkSVKVlT3ESGqyrZV4Fb05NiJOjYhpETFt2bIXWqmfJEnSkFRmiFtI8xazMTRvZau3oItja/vXkFK6NKU0NaU0dcKEDVuuqCRJ0lBTZoibTn62rdEU4MEWjt2uGKak8dhXgMfWPESSJGn4KDPEXQvsFRGTahsiYiKwT7Gvu2PXBt5Vd+xI4BjgxpTSsv6urCRJ0lBSZoi7DJgFXBMRR0XEkcA1wJPAJbVCETEhIlZExDm1bSmlv5CHF/laRJwcEW8mDy+yHfCZQfwOkiRJpSgtxKWUXgIOAh4BrgCuBGYCB6WUFtcVDWAEa9b1fcB3gfOB64FtgcNSSn8a4KpLkiSVrswZG0gpzQbe2U2ZWTTpdZpSWgp8tFgkSZLaStlDjEiSJKkXDHGSJEkVZIiTJEmqIEOcJElSBRniJEmSKsgQJ0mSVEGGOEmSpAoyxEmSJFVQpJTKrkMpIuJF4OGy66GWbQrMK7sSapnXq3q8ZtXi9aqWySmlDfr7pKXO2FCyh1NKU8uuhFoTEdO8XtXh9aoer1m1eL2qJSKmDcR5vZ0qSZJUQYY4SZKkCmrnEHdp2RVQj3i9qsXrVT1es2rxelXLgFyvtu3YIEmSVGXt3BInSZJUWW0V4iJi24j4aUQsiogXIuLqiBhfdr3aTURsExH/HhF3RcSSiEgRMbFJuXUj4oKIeCYilhbl39Sk3FoRcWZEzIqIlyPirxHxzsH4LsNdRBwdET+LiCeKa/BwRHwxIjZoKDcmIr4dEfMi4qWIuCkidmlyvpauqXovIg6NiFsi4tmIWBYRcyLiJxExpaFcS38PW7226j8RcUPxd/H8hu3+npUsIg4ork3j8nxDuUG5Vm0T4iJiNHAL8BrgROAEYEfg1ohYr8y6taEdgHcDC4E7uij3HeAU4BzgrcAzwG8iYveGcp8DzgUuBt4C3A38d0Qc3r/VbksfB1YCnwIOA74F/BPw24hYCyAiAri22P9h4J3A2uTfrW0aztfqNVXvjQXuBU4H/h44E9gZuDsiJkDrfw97eG3VDyLiPcBuTbb7eza0fAR4Y91ycG3HoF6rlFJbLMA/k/8x2qFu23bACuCjZdevnRZgrbrXJwMJmNhQZrdi+/vqto0kD9B8bd22zYBlwGcbjr8ZuK/s71r1BRjXZNt7i2tzUPH+qOL9gXVlNgIWAN/o6TV1GZDrOLn42X+seN/S38NWr61Lv12njYFngfcUP/fze3ot/D0b8Gt0QPHzPbiLMoN2rdqmJQ44Erg7pfRYbUNKaSZwJ/kHrkGSUlrVQrEjgeXAj+uOWwFcBRwaEaOKzYcC6wA/aDj+B8AuEbFd32vcvlJKc5ts/p9ivXWxPhJ4OqV0a91xi4DrWP13q9Vrqv43v1gvL9at/j1s9dqqf3wFmJ5S+lGTff6eVcegXat2CnE7Aw802T4dmNJku8q1MzAzpbSkYft0cmjboa7cMuCxJuXAazsQ9i/WDxXrrn63xkfE+nXlWrmm6gcRMSIi1omIHYFLyC08VxW7W/172Oq1VR9FxL7kVu4PdlLE37Oh5cqIWBkR8yPihw3Pkw7atWqnEDeW/AxWowXAmEGui7rX1fWq7a+tn09FO3QX5dQPImJr4DzgppRSbRqZ7q7VmBbLea361z3k/8F5BNiVfPv7uWJfq38PW7226oOIWJsctL+aUupsTm9/z4aGRcC/kR8FOoj8TPbBwF0RsVlRZtCuVbvNndpsULwY9FqoFUFr16vVcuqj4v8eryE/N/W++l14rYaiE4ANgUnkDiq/jYh9U0qziv1es6HjE8CrgM93UcbfsyEgpfRn4M91m26PiN8BfyR3djibQbxW7dQSt5DmqXYMzZOwyrWAzq9XbX9tPaboDdRVOfVBRKxL7m01CTg0pTSnbnd312phi+W8Vv0opfRQSume4vmqNwPrA58sdrf697DVa6teKm7DnQV8GhgVERtHxMbF7tr7Efh7NmSllP5EbvF+fbFp0K5VO4W46eT7z42mAA8Ocl3UvenAdsVQCPWmAK/Q8QzcdGAUsH2TcuC17bPiVs/PgD2Bw1NK9zcU6ep3a3ZKaXFduVauqfpZSul58s+39oxNq38PW7226r1JwLrkzlgL6xbILagLgV3w92yoq29VG7Rr1U4h7lpgr4iYVNsQeYDZfYp9GlquJY+r867ahogYCRwD3JhSWlZsvoH8H/vxDcf/A/BA0eNOvVSMBXcluSXnqJTS3U2KXQtsHRH71x23IfA2Vv/davWaqp9FxObkMeFmFJta/XvY6rVV7/0FOLDJAjnYHUj+x9zfsyEqIqYCryY/hwqDeK3aZu7UYgDLvwJLyfesE/mBxA2AXf0/ysEVEUcXL98M/CO5R9ZcYG5K6faizFXkIUT+FZhJHmT2rcDeRfN17VxfAs4gD0j7J/IvwGnk0HHdoHyhYSoivkW+Pp8Hftmwe05KaU4R9H4PbEu+VgvJA8zuCuyWUnqy7nwtXVP1XkT8nPx7cB/wAvkfl38BtgD2TCk90urfw55cW/WviEjA51NKZxfv/T0bAiLiSvLP9E/A88Ae5OuwBPi7lNK8Qb1WZQ+cN5gLMJ58W+gF4EXgFzQMMusyaNcidbLcVlfmVcCF5KERXib/X84BTc41gvwP0RPk3nj3AUeX/R2HwwLM6uJanVtXbizwX+RnOJaQB1vercn5WrqmLn26Zp8gz9jwfHEtHib3fJzYUK6lv4etXluXfr+Oqw3225Nr4e/ZgF6XM4t/YxaRx3h7ErgU2LKMa9U2LXGSJEnDSTs9EydJkjRsGOIkSZIqyBAnSZJUQYY4SZKkCjLESZIkVZAhTpIkqYIMcZKGtIhIEXF52fXojYgYHRHfiIjZEbEyImaVXSdJw4chTmpDEXFAEY5SRJzcSZkUEY2zNKhnPgF8GPgxcBJ5ZpGmionOz42IAwanapKqbmTZFZBUus9GxJUppaVlV2QYOgS4P6X0ry2U3Rj4TPH6tgGrkaRhw5Y4qb1NA7aiixaidhIRIyJidD+ecgvytDuS1O8McVJ7+wl5ns1PRMQm3RXu7Pm0iDip2HdA3bZzi21TIuJrEfFMRLwUETdHxOSizP+JiD9FxNKImBURp3bx2QdHxN0RsSQino2IrxcTuTeW2ygivhwRj0XEsoiYGxE/iohJndT54Ij4dETMIM9d+O5ufgYjI+ITEfFgRLwcEfMj4ucRsUvjuYHtgP3rbl2f28k5DyBPfg3wmbrys3ryuXVl3xsRf4yI54uf+eMRcWVEjKsrs3NE/HdEPFX8nJ6NiFsj4oiGc42KiE9FxPTic5+PiOsiYo+GchERZ0TEfRHxYkS8EBEPR8R3ImLtrn6mknrH26lSe0vk57ZuAs4CPjoAn/E9YDHwBWAc8DHgNxHxaeArwLfIE0V/ALgkIh5MKf2+4Rx/BxwNXAZ8HzgQ+Ajw2og4JKW0CnKAA/5Antz9v4DpwJbAB4F7ImJqSumJhnN/FVi7OPcL5Anju3IlOej9tqj7FsCHgLsiYr+U0p+B3wEnABcB84DPF8fe18k5HwL+pSj/c+DqYvviHn4uEfEP5J/5HcA5wNLi5/EWYDNgbhHYbynO+5/AE8CmwFTgDcD1xbnWBm4A9gauAC4GNgJOAe6MiDellKYV5zkbOA+4rjjnSnKIPRIYRZ4sXFJ/Sim5uLi02QIcQA5wHy/e30huhZpQVyYBv2w4LgGXNznfScW+A+q2nVtsuw6Iuu0fKba/CIyv2z6uqMOPmnxmAt7esP3rxfZjG7YtBXZrKDuBHNAub1Lnh4HRLf7cDimO+XHDd9oVWAHc0VB+FnBbi+eeWJz73L58LjkAvgCM7OKzjizO9+5u6vQvRblDG7ZvCMyu/27An4AHy/5v28WlnRZvp0qC3Bq3DvC5ATj3N1JKqe79HcX6mpTS7NrGlNJccqDasck5Hk4p/aJh25eK9Tsg384Djie3gj0VEZvWFuAl4G7g75uc+1sppSUtfpd3FOvP13+nlNJ9wC+BfetvWfajnnzuImA0cETxM2lmUbF+S0Rs2MXn/gPwv8C9DT/PdcgtgvtGxKvqzrl1ROzb0y8nqXcMcZJI+Vbcj4DjI2LXfj794w3vFxbrmY0Fi33Nns17qHFDSukZ4Hmg9qzbuOLYvwfmNlkOATZvcu5Huq7+arYDVjWrD/BAXZn+1pPP/QL59ugvyLdOfxYRJ0fEBrUDUkq3k29LnwTMi4g7I+KzETGl4dw7Aa+h+c/z/cAI8m1YgE+RW1LvKJ6zuzIijouIdfrwvSV1wWfiJNWcTX7u7Mvk56d6oqu/JSt7uL1Z61Fqsq2xbO31TeTv0KpWW+EaP28wtfy5KaVHizD25mLZn/y832eLZ9hmFOVOjIgLgMOBfcnPKp4VEWeklC6u+9z76fpZybnF+e6KiO2BQ8nPLB4IHAecHRH7ppTspSv1M0OcJABSSjMj4lvAP0fEgZ0UWwCMbbJ9UpNt/amxhYiI2JL8kH2tpW8uuWVuw5TSTQNUjxnkkLITa3ZSqNWxWQtjKzoLqj3+3JTSMuBXxUJEHE7urPBRcmeIWrkHyC15X4mIjYF7gC9FxDeL27aPkls4b0lF55Euv0BKi4GfFQsR8UHgm+ROKxd0d7yknvF2qqR655Mfiu+sJesR4I1RN5ZaRIwB3jfA9ZocEW9v2PaJYv0LgCJkXAnsGRFHNztJRGzWx3rUnss7s/55s4h4LbmzwO+LZ/t6o9YTtVlIbvlzi2fWGv2p/twRMTYiVvv7n1J6nhwERwPrFpu/T+4F27QlLiI2r3vd7edK6l+2xEn6/1JK84pbbJ11cLgY+AFwS0RcQZ5l4BTyM1hbDGDV7gd+EBGXkVuHDiTf+r2d3GOz5ixgH+AnEfETcmeGV8i9Uw8nj4l3Um8rkVL6bXHeY4Exkaclqw318TK5521vzz0/Ih4Djo08Zt3fgJdSStf18HNvjIhF5A4eT5Kv0Unklr4rijLvBf4lIn4OPEYe/mN/cmvfT1LH7B1fJz9LeEFEHEQeluQF8pAlby4+u9Zq+1BE3E1uzXuaPLTLqeSf/1W9/blI6pwhTlKjC8njqm3ZuCOldGVEbAWcXpR7nDw22Cry+GID5U/k1qDPA/9IDhIXA5+qv82XUloUEfuQn+96N3AUeQiOOcDvgW/3Q12OL+pzEvBv5J6vtwOfTind3w/nvojcOWE0ORxf18PP/Rb5u59GbgGbD/wZ+HBK6daizG3AHsBbydd5JbkV7uPknysAKaXlxeC/HySPe/fZYtfTwB/J49HV/Bs5KH+EfJv7OXKI/mJK6a+9+3FI6kqs3vNfkiRJVeAzcZIkSRVkiJMkSaogQ5wkSVIFGeIkSZIqyBAnSZJUQYY4SZKkCjLESZIkVZAhTpIkqYIMcZIkSRVkiJMkSaqg/wdRIFxCpbQUEwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 698.991x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_toss = 500\n",
    "p = 51./100.\n",
    "plist = []\n",
    "for n in np.arange(0., num_toss+1, 2.):\n",
    "    psum = ProbMajorHead(n, p)\n",
    "    plist.append(psum)    \n",
    "    \n",
    "plt.plot(np.arange(0., num_toss+1, 2.), plist, 'b-')    \n",
    "plt.xlabel('Number of tosses', fontsize=18)\n",
    "plt.ylabel('Probability', fontsize=18)\n",
    "plt.xlim(0,num_toss)\n",
    "plt.xticks(fontsize=16)\n",
    "plt.yticks(fontsize=16)\n",
    "plt.show()     "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The probability starts out to be quite small at the beginning. But the more you toss, the higher the probability. For instance, for $n=10000$, the probability reaches 97.6%!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Probability of getting a majority of heads after  10000 tosses is  0.97672\n"
     ]
    }
   ],
   "source": [
    "n = 10000\n",
    "print(' Probability of getting a majority of heads after {0:6d} tosses is {1:8.5f}'.format(n, ProbMajorHead(n, p)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The reason of the 97.6% probability is due to the law of large numbers. As one keeps tossing the coin, the ratio of heads will be getting closer and closer to 51%. The following code snippets plot the head ratio for the first $n=15000$ tosses."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Define the biased coin with 51% probability of coming up heads,  49% of coming up tails.\n",
    "def biased_coin():\n",
    "    if rnd() >= 0.49:\n",
    "        return 1.0\n",
    "    else:\n",
    "        return 0.0\n",
    "\n",
    "def Plot_HeadRatio(num_exp, num_toss):\n",
    "    ratio    = [[0 for x in range(num_toss)] for y in range(num_exp)]\n",
    "    for iexp in range(num_exp):\n",
    "        result = 0.0\n",
    "        for itoss in range(num_toss):\n",
    "            result += biased_coin()\n",
    "            r = result / (itoss+1)\n",
    "            #print(\"%6d   %.4f\"%(i, r))\n",
    "            ratio[iexp][itoss] = r\n",
    "\n",
    "    # Plot the five experiment results\n",
    "    c = ['k', 'b', 'g', 'm', 'y']\n",
    "    for iexp in range(num_exp):\n",
    "        plt.plot(ratio[iexp], ls='-', color=c[iexp])    \n",
    "    plt.xlabel('Number of coin tosses', fontsize=18)\n",
    "    plt.ylabel('Heads ratio', fontsize=18)\n",
    "    plt.xlim(0,num_toss)\n",
    "    plt.ylim(0.42, 0.58)\n",
    "    plt.xticks(fontsize=16)\n",
    "    plt.yticks(fontsize=16)\n",
    "    plt.hlines(0.50, 0, num_toss, colors='k', linestyles='solid', label=\"50%\")\n",
    "    plt.hlines(0.51, 0, num_toss, colors='r', linestyles='dotted', label=\"51%\")\n",
    "    plt.legend(fontsize=20)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 698.991x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# number of coin toss experiments   \n",
    "num_exp  = 5 \n",
    "# number of tosses in each experiment\n",
    "num_toss = 15000\n",
    "\n",
    "Plot_HeadRatio(num_exp, num_toss)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As one can see, when $n$ gets large, the heads ratio is consistently above 50% for each sequence, and converges to 51% eventually.\n",
    "\n",
    "__So what does the example of biased coin tossing tell us?__\n",
    "\n",
    "Suppose we have a collection of classifiers that are individually correct 51% of the time. Then the coin toss example basically implies that if we build a majority-vote classifier using these rather weak classifiers, then this voting classifier can achieve a higher accuracy if we collect large enough number of weak classifiers. This of course assumes that the weak classifiers are perfectly independent. Nevertheless, this is the idea behind ensemble learning. Sometimes this is referred to as _**the wisdom of the crowd**_: __if you aggregate the predictions of a group of predictors, you will often end up getting better predictions than with the best individual predictor__."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Ensemble Learning<a id=\"Part_2\"></a>\n",
    "<a href=\"#Top\">Back to page top</a>\n",
    "\n",
    "As just mentioned, one can apply the philosophy of *the wisdom of the crowd* in machine learning. The resulting method is called ensemble learning. The idea is very straightford: train a diverse collection of predictors (can be classifiers, regressors, or neural networks) and aggregate the predictions. Depending on how the training is carried out and the way final prediction is generated, there are a couple different methods that one can choose from. In the following, we will use classifiers as the predictor. The same principle can be applied to other types of predictors. __The key to making ensemble learning work is the *diversity* of the set of predictors__."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Voting classifiers<a id=\"Part_2_1\"></a>\n",
    "<a href=\"#Top\">Back to page top</a>\n",
    "\n",
    "One of the simplest way of aggregating predictions is by voting. In this scenario, suppose we have trained a few classifiers: a Logistic Regression classifier, an SVM classifier, a Random Forrest classifier, and a k-Nearest Neighbors classifier. Then the final outcome will be the one that gets the most votes from the classifiers. This idea is depicted in the following figure:\n",
    "\n",
    "<img src=\"./images/fig_ensemble-01.png\" width='500'>\n",
    "\n",
    "Within this voting method, there are two options __hard voting__ and __soft voting__. \n",
    "\n",
    "1. Hard voting: the prediction is just the one that gets the majority votes.\n",
    "2. Soft voting: the prediction is obtained by averaging over all classifiers' results.\n",
    "\n",
    "Apparently, soft voting works only when the classifier can output class probabilities. It turns out that soft voting usually works better than hard voting.\n",
    "\n",
    "Scikit-Learn provides a class `sklearn.ensemble.VotingClassifier` that can lump together a collection of classifiers (as a list of tuples) and carry out hard or soft voting by srtting the argument `voting='hard'` or `voting='soft'` respectively. The following is a code snippet showing its usage:\n",
    "\n",
    "```python\n",
    "    from sklearn.ensemble import VotingClassifier\n",
    "    \n",
    "    log_clf = LogisticRegression()\n",
    "    rnd_clf = RandomForestClassifier()\n",
    "    svm_clf = SVC()\n",
    "    \n",
    "    voting_clf = VotingClassifier(\n",
    "        estimators=[('Logistic', log_clf), ('RandomForest', rnd_clf), ('SVM', svm_clf)],\n",
    "        voting='soft')\n",
    "        \n",
    "    voting_clf.fit(X_train, y_train)\n",
    "```\n",
    "In additonal to Scikit-Learn's wrapper, one could also implement the voting mechanism by hand.\n",
    "\n",
    "\n",
    "### 2.2 Bagging and Pasting<a id=\"Part_2_2\"></a>\n",
    "<a href=\"#Top\">Back to page top</a>\n",
    "\n",
    "Having a collection of different predictors is one way of achieving diversity in ensemble learning. Another approach is to use the same algorithm for every predictor but train them using different subset of the training set, as shown in the following figure. This way, each model looks at slightly different aspect of the data to make its prediction. \n",
    "\n",
    "<img src=\"./images/fig_ensemble-02.png\" width='680'>\n",
    "\n",
    "Depending on how the data set is sampled, one can implement this training scheme in two different ways:\n",
    "\n",
    "1. __Bagging__: Data sampling is performed __*with*__ replacement.\n",
    "2. __Pasting__: Data sampling is carried out __*without*__ replacement.\n",
    "\n",
    "If we make an analogy between the sampling process and drawing balls from a bag. Bagging is like drawing balls from the bag them putting the ball back. Pasting does not put the drawn balls back. So both bagging and pasting allows training instances to be sampled several times across multiple predictors. __But only bagging allows training instances to be sampled several times for the *same* predictor__.\n",
    "\n",
    "Scikit-Learn has a simple API for bagging and pasting.\n",
    "\n",
    "- `BaggingClassifier()` for classifiers.\n",
    "- `BaggingRegressor()` for regressors.\n",
    "\n",
    "By default, both classes assumes bagging. For pasting, set the argument \n",
    "\n",
    "```python\n",
    "    boostrap = False\n",
    "```\n",
    "\n",
    "However, boostraping introduces a bit more diversity in the data subsets that each predictor is trained on. As such, bagging ends up with a slightly *higher* bias than pasting. However this also means that predictors and up being *less* correlated so the ensemble's variance is *reduced*. So bagging often results in better models.\n",
    "\n",
    "With bagging, some instances may be sampled many times for any given predictor, while others may not be sampled at all. Let's assume the sample size is $m$. Then the chance of _not_ being selected is \n",
    "$ \\left( 1 - \\frac{1}{m} \\right)$. If we perform the drawing $m$ times, then the probability becomes\n",
    "\n",
    "$$ \\left( 1 - \\frac{1}{m} \\right)^m$$\n",
    "\n",
    "When $m$ grows, this becomes\n",
    "\n",
    "$$ \\lim_{m\\rightarrow \\infty} \\left( 1 - \\frac{1}{m} \\right)^m = e^{-1} \\approx 0.36787$$\n",
    "\n",
    "Recall the definition:\n",
    "\n",
    "$$ e^x = \\lim_{m\\rightarrow \\infty} \\left( 1 + \\frac{x}{m} \\right)^m$$.\n",
    "\n",
    "So roughly 36.787% of the training instances will not be sampled in the bagging scheme. These are called __out-of-bag__ (OOB) instances. Note that they are not the same 36.787% for all predictors. Since a predictor never sees the OOB instances during training, it can be evaluated on the OOB instances without the need of a separate validation set. This is called __out-of-bag evaluations__. The ensemble can then be evaluated by averaging out the OOB evaluations. In Scikit-Learn bagging API, the OOB evaluation can be turned on by setting\n",
    "\n",
    "```python\n",
    "    oob_score = True\n",
    "```\n",
    "\n",
    "### 2.3 Boosting<a id=\"Part_2_3\"></a>\n",
    "<a href=\"#Top\">Back to page top</a>\n",
    "\n",
    "Boosting refers to any ensemble method that can combine several weak learners into a strong learner. In most boosting schemes, one trains predictors sequentially, each trying to correcet its predecessor. \n",
    "\n",
    "1. __Adaptive Boosting (Adaboost)__: \n",
    "   In Adaboost, a new predictor corrects its predecessor by paying attention to the training instances \n",
    "   that the predecessor underfitted. This results in new predictors focusing more and more on the hard cases. \n",
    "   The following figure shows decision boundaries of consecutive predictors. It clearly demonstrates how \n",
    "   each new predictor improves the boundary. \n",
    "\n",
    "   <img src=\"./images/fig_ensemble-04.png\" width='780'>\n",
    "\n",
    "   Under the hood, each training instance is assigned a weight. The first predictor is trained and used to \n",
    "   make predictions on the training set. The weights of missclassified training instances will be increased. \n",
    "   The second predictor is then trained using the updated weights and, again, is used to make its own \n",
    "   predictions. The process goes on until all predictors are trained. Then the ensemble makes predictions \n",
    "   by taking into accounts their weights.\n",
    "\n",
    "\n",
    "2. __Gradient Boosting__:\n",
    "   Gradient boosting also adds predictors sequentially to an ensemble, each one correcting its predessor. \n",
    "   However, instead of tweaking the instance weights at every iteration like AdaBoost does, this method \n",
    "   tries to fit the new predictor to the *residual errors* made by the previous predictor. The following \n",
    "   figure shows Gradient Boosting in action:\n",
    "\n",
    "   <img src=\"./images/fig_ensemble-05.png\" width='780'>\n",
    " \n",
    "   The left column shows data residuals and predictions. The right column shows the ensemble's predictions. \n",
    "   In the first row, the ensemble has only one predictor so it has the same prediction as the first predictor. \n",
    "   In the second row, a new predictor is trained on the reidual errors of the first predictor. On the right, \n",
    "   one can see the second regressor's predictions are added back to the first one's results. Tn the third row \n",
    "   another regressor is trained on the residual errors of the second regressor. It can be seen that the \n",
    "   ensemble’s predictions gradually get better as regressors are added to the ensemble.\n",
    " \n",
    "   For the decision tree algorithm, Scikit-Learn provides __Gradient Boosted Regression Trees (GRBT)__ \n",
    "   class that does all the labor for us. For other predictors, one can update the training lable as the \n",
    "   following pseudocode\n",
    " \n",
    "   ```python\n",
    "   y[0] = y_train\n",
    "   predictor[0].fit(X_train, y_train)\n",
    "   for i in range(1, num_of_predictors+1):\n",
    "       y[i] = y[i-1] - predictor[i-1].pred(X_train)\n",
    "       predictor[i].fit(X_train, y[i])\n",
    "   ```\n",
    "\n",
    "### 2.4 Stacking<a id=\"Part_2_4\"></a>\n",
    "<a href=\"#Top\">Back to page top</a>\n",
    "\n",
    "Stacking is liks a more sophisticated voting ensemble: instead of using trivial functions (such as hard voting) to aggregate the predictions of all predictors in an ensemble, stacking scheme trains a model to perform this aggregation, as depicted by the following figure.\n",
    "\n",
    "<img src=\"./images/fig_ensemble-06.png\" width='400'>\n",
    "\n",
    "The question is: how do we train the blender? An approach is to use a *hold-out* set. First, the training set is splitted into two subsets. The first subset is used to trained the predictors at the bottom layer.\n",
    "\n",
    "<img src=\"./images/fig_ensemble-07.png\" width='460'>\n",
    "\n",
    "Next, the bottom layer predictor are used to make predictions on the second subset (hold-out set). In the example shown in the figure, each instance in the hold-out set will have three predicted values. A separate training set can be created using these predicted values. This training set will have an extra dimension: the number of predictors in the bottom layer. Using the same traget values, the blender can be trained on the new training set. At then end, the blender learns to predict the target values using the bottom layer's predictions.\n",
    "\n",
    "<img src=\"./images/fig_ensemble-08.png\" width='520'>\n",
    "\n",
    "Using this method, it is possible to train, say, three blenders. The trick is to split the training set into three subsets. The first one is used to train the first layer, the second one is used to create the training set used to trained the second layer, and the third set is used to create the training set used to trained the third layer. After the training is done, one can make a prediction for a new instance by going through each layer sequentially."
   ]
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    "---\n",
    "\n",
    "__Figure Credits__: The PNG figures displayed this notebook are taken from __A. Géron: Hands-On Machine Learning__."
   ]
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