Checking imbalance effect

imbalance_bdt.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check how imbalance of the training sample affects the performance of a BDT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# imports\n",
    "import numpy as np\n",
    "from collections import OrderedDict\n",
    "\n",
    "from sklearn import datasets\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn.metrics import roc_curve, auc\n",
    "\n",
    "from scikit_learn.general_tools.compare_train_test import compare_train_test\n",
    "from scikit_learn.imbalance.imbalance_base import plot_rocs\n",
    "\n",
    "# functions\n",
    "def build_bdt(min_samples_leaf, max_depth=3,\n",
    "              alg=\"SAMME\", n_estim=100, learn_r=0.1):\n",
    "    from sklearn.tree import DecisionTreeClassifier\n",
    "    from sklearn.ensemble import AdaBoostClassifier\n",
    "    dt = DecisionTreeClassifier(max_depth=max_depth,\n",
    "                                min_samples_leaf=min_samples_leaf)\n",
    "    bdt = AdaBoostClassifier(dt,\n",
    "                             algorithm=alg,\n",
    "                             n_estimators=n_estim,\n",
    "                             learning_rate=learn_r)\n",
    "    return bdt\n",
    "\n",
    "def do_plots(y_test, pred, y_red, pred_red):\n",
    "    # plot bdt outputs\n",
    "    plt = compare_train_test(y_test, pred, y_red, pred_red,\n",
    "                             labels=('full', 'reduced'))\n",
    "    plt.show()\n",
    "\n",
    "    # plot rocs\n",
    "    colors = OrderedDict([('full', 'b'),\n",
    "                          ('reduced', 'r')])\n",
    "\n",
    "    plot_rocs([y_test, y_red],\n",
    "              [pred, pred_red],\n",
    "              colors)\n",
    "\n",
    "def roc_imabalance(n, rdm_state, plots=False):\n",
    "    # create random balanced sample\n",
    "    X, y = datasets.make_classification(n_samples=n,\n",
    "                                        random_state=rdm_state)\n",
    "\n",
    "    # split samples\n",
    "    X_train,X_test,y_train,y_test=train_test_split(X, y,\n",
    "                                                   test_size=0.33,\n",
    "                                                   random_state=rdm_state)\n",
    "\n",
    "    # make samples\n",
    "    n_sig_train = X_train[y_train==1].shape[0]\n",
    "    n_bkg_train = X_train[y_train==0].shape[0]\n",
    "\n",
    "    #as samples are shulfed we just keep the first 1000 sig and bkg\n",
    "    X_sig_red = X_train[y_train==1][:1000,:]\n",
    "    y_sig_red = y_train[y_train==1][:1000]\n",
    "    n_sig_red = X_sig_red.shape[0]\n",
    "    X_bkg_red = X_train[y_train==0][:1000,:]\n",
    "    y_bkg_red = y_train[y_train==0][:1000]\n",
    "    n_bkg_red = X_bkg_red.shape[0]\n",
    "    \n",
    "    X_train_bal = np.concatenate((X_sig_red, X_bkg_red))\n",
    "    y_train_bal = np.concatenate((np.ones(n_sig_red),\n",
    "                                  np.zeros(n_bkg_red)))\n",
    "\n",
    "    X_train_imbal = np.concatenate((X_train[y_train==1], X_bkg_red))\n",
    "    y_train_imbal = np.concatenate((np.ones(n_sig_train),\n",
    "                                    np.zeros(n_bkg_red)))\n",
    "    \n",
    "    if plots:\n",
    "        print \"n sig train balanced is: %s\" %n_sig_red\n",
    "        print \"n bkg train balanced is: %s\" %n_bkg_red\n",
    "        print \"n sig train imbalanced is: %s\" %n_sig_train\n",
    "       \n",
    "    # build bdt, train on full sample and apply\n",
    "    bdt = build_bdt(0.05*len(X_train_bal))\n",
    "    bdt.fit(X_train_bal, y_train_bal)\n",
    "    pred = bdt.predict_proba(X_test)[:,1]\n",
    "    \n",
    "    # train on reduced sample and apply\n",
    "    bdt_imbal = build_bdt(0.05*len(X_train_imbal))\n",
    "    bdt_imbal.fit(X_train_imbal, y_train_imbal)\n",
    "    pred_imbal = bdt_imbal.predict_proba(X_test)[:,1]\n",
    "    \n",
    "    # plots\n",
    "    if plots:\n",
    "        do_plots(y_test, pred, y_test, pred_imbal)\n",
    "    \n",
    "    # get roc area\n",
    "    areas = []\n",
    "    for y, dec in zip([y_test, y_test], [pred, pred_imbal]):\n",
    "        fpr, tpr, thresholds = roc_curve(y, dec)\n",
    "        roc_auc = auc(fpr, tpr)\n",
    "        areas.append(roc_auc)\n",
    "    \n",
    "    return areas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "## Toy 0\n",
      "n sig train balanced is: 1000\n",
      "n bkg train balanced is: 1000\n",
      "n sig train imbalanced is: 100483\n"
     ]
    },
    {
     "data": {
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HH1BeXs5HH33E//7v/xIVFcWpp55KcnLycR3C0dHR5OU1fHCYMSbwWkQyKPPQLl8eGRnQ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\njAH+P1X3kzoex0N8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x116ba4050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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p3V9CaUSTkBqGYXiDSAL/chG5CkgWkW4i8jTwRYztihpfzJ1NCd6SekwH9Qbm\nszeIhc+RBP5bgWOBIuB1YA/wu6hbEiN8WoomJcXbDMMwjDpDJBp/P1VdWEv2VGZDtTX+r19fQ9vr\nzqFd4fdRtsowDKNuUxON/zER+U5E7hORWnugGy0CJaUExHr8hmEYQQ4Z+N1pkk8DtgMTROQbERkb\na8OixYJlX3ou8JsO6g3MZ28QL40fVd2sqk8CNwJLgLujbkmMKPUHUI8FfsMwjKqIROPvCVwOXArs\nAN4A3lLVn2NvXsiGamv8s59eTNsxI+myZ3GUrTIMw6jbVGc+/iCvAFNxFkv5KeqWxRgt8VuP3zAM\nI4xINP6TVPWJ+hj0Ab5aOs80fg9gPnsD8zk6VNrjF5E3VfWycqtwBYlkBa46QXJSAD/eCvyGYRhV\nUdWau21VdZOIdATKa0Sqqutjbt0BW6qt8X88bjbtnv0Tx2ybE2WrDMMw6jaHPY5fVTe5uzer6rrw\nDbg5RnZGnUBJqWn8hmEYYUQynPPsCvLOi7YhsWLx2gUEkrw1SZvpoN7AfPYGta3x34TTs+9STudP\nAz6PuiUxQv2lqM96/IZhGEGq0vibAZnAQ8BoDuj8+apaq5Pb10Tjn3nb+7T799P0+nHGoSsbhmEk\nENUZx6+quk5EbgHKRF0RyVLVvGgbGQusx28YhlGWqjT+193XBZVs9YIlGxajPtP4Ex3z2RuYz9Gh\n0oioque7r52iftZaxL/fTyDJWwuxGIZhVEUkc/UMApao6l4RuQboCzxZX8bxT7/iNVrNf4+Tvp8S\nZasMwzDqNjWZj/95oEBE+gB/ANYCr0bZvpiRTAnJDa3HbxiGESSSwO9X1QDwC+BZVX0GZ0hnvWDZ\n5mWek3pMB/UG5rM3qFWNP4x8EbkLuBoYLCJJUI9WLy/1E0iuP+YahmHEmkg0/jbAlcA8VZ0tIkcC\nOapaa3JPTTT+D85/krSfv+fkr5+KslWGYRh1m2pr/Kq6GXgNyBCRC4D9tRn0a4rPX4Jaj98wDCPE\nIQO/iFwOzAUuw1mJa56IXBZrw6LF0m0rUdP4Ex7z2RuYz9EhEo3/z0D/4FKLItIS+Bh4M+rWxIJS\nG8dvGIYRTiQa/zdA76DILiI+nHH9vWrBvqAN1db4Z50yFl9qCkM+rjfrwxuGYUSFmqy5OxP4QESm\n4EzUdgVQb2Y8E38J2qRxvM0wDMOoM0TycPd/cf7E1RvoBUxQ1TtibVi0WLJzrece7poO6g3MZ28Q\nC58rDfws/+OQAAAgAElEQVQi0l1E3haR5TgPdh9T1T+o6r8jbVxEhorIdyKyWkRGV1Gvv4j4ReSS\nwzM/AhsCfs8FfsMwjKqoaj7+OcBkYDYwDBioqhEHZvePXiuBM4GfgK+BEaq6ooJ6HwEFwERV/VcF\nbVVb4/+8903s79aLM/5Vb1aLNAzDiArV0fibquqL7v53IrLoMM85AFjjrtGLiEwFLgJWlKt3K/AW\n0P8w248IX2kJmmI9fsMwjCBVafwNRaSfux0PNArui0i/CNpuB/wYlt7o5oUQkXY4PwbPuVnV69ZX\nwaL8jWBr7iY85rM3MJ+jQ1URcQvwaBXp0w7RdiRB/AngTlVVEREOLO94ECNHjqRTp04AZGRkkJ2d\nTU5ODnDgwlSY1gBLtq0iOTc3svoJkF68eHGdsqc20osXL65T9tRGOkhdscfSsUkfzvc5NzeXSZMm\nAYTiZUUcchx/dRGRk4BxqjrUTf8JCKjq38LqrOVAsG+Bo/P/P1WdXq6tamv8c7tdzd5ThnLGxKur\ndbxhGEZ9pSbj+KvLfKCbiHQCNuGM/x8RXkFVjwozcCLwTvmgX2M0AEmRzD5tGIbhDWIWEVXVD4wC\nPgC+Bd5Q1RUi8hsR+U2szluehfu2ID5vBf7yUoAXMJ+9gfkcHWL61FNVZ1DuX76qOqGSutfGwgbR\nUsR6/IZhGCEimavHB1wFdFbVv7jz8bdW1Xm1YaBrQ7U1/q87DmfvsCs57ZnhUbbKMAyjblOTNXfH\nAwNxFmMB2Ovm1QskELAev2EYRhiRRMQTVfVmoBBAVfOoR0svLtj/s+cCv+mg3sB89gax8DmSiFjs\nTqsAhObjD0TdklhhPX7DMIwyRKLxX42z8tbxOHP3XAr8WVX/L/bmhWyotsa/sM157Bs5isF/PS/K\nVhmGYdRtqj2OX1X/KSILgDPcrIvKT7RWlzGN3zAMoyyRrLl7JLAPeMfd9rl59YIFRds9F/hNB/UG\n5rM3iNc4/vc5MO9OQ6AzznTLx0bdmlig6rnAbxiGURWHPVePOzPnLap6fWxMqvCc1db4lzY/jX1/\nGMvAMadH2SrDMIy6TU3G8ZdBVRcCJ0bFqlpANIAkJx26omEYhkeIROP/Y9j2vyLyOs6KWvWC+cV5\nSLK3pB7TQb2B+ewN4qXxNw3b9wPvAgctj1h3MY3fMAwjnCo1fvePWw+r6h9rz6QK7ai2xr+82UAK\n7n+M/rcOjLJVhmEYdZvD1vhFJFlVS4FB7upY9RKfluKzHr9hGEaIqiJicPbNxcDbInKNiAx3t0tq\nwbao8HXJbs893DUd1BuYz96gtjX+YC+/IbADKD8eclrUrYkJAXwee7hrGIZRFZVq/CKyEXiMShZA\nV9VHK8qPBTXR+Fc1yaZw/CT6/Do7ylYZhmHUbaozV08SkBY7k2oHn63AZRiGUYaqIuIWVb23sq3W\nLKwhc/35+FJM4090zGdvYD5Hh4TvCvtM4zcMwyhDVRp/c1XdUcv2VEhNNP51qUdT+MZ0evzi6Chb\nZRiGUbc57HH8dSXo1xSxHr9hGEYZEj4izi3d67mHu6aDegPz2RuYxl8NRNVzD3cNwzCq4rDn448H\nNdH4N6Ucyf6P5nBUTr1ZNMwwDCMqRG0+/vqGqK25axiGEU7CR8QvtZCklIR3swymg3oD89kbmMZf\nDXzW4zcMwyhDwmv8O5Jasn/Bt7TLbhllqwzDMOo2ntb4bRy/YRjGARI+In6hRZ4L/KaDegPz2RuY\nxl8NbK4ewzCMssRc4xeRocATONM8v6SqfytXfhVwB868//nATaq6tFydamv8e6UpReu20Lxj00NX\nNgzDSCDiovG7i7U/AwwFegIjRKRHuWprgVNVtTdwH/BCNG2wHr9hGEZZYh0RBwBrVHWdqpYAU4GL\nwiuo6pequttNzgXaR9OAOfg9F/hNB/UG5rM3qI8afzvgx7D0RjevMq4H3o+mAULAc3/gMgzDqIqq\nll6MBhEL8yJyGnAdMKii8pEjR9KpUycAMjIyyM7OJicnBzjwi1hR+nSUj76cTcMmSRHVT4R0MK+u\n2FNb6XDf64I9lo5+Oicnp07ZUxvpYF4k9XNzc5k0aRJAKF5WREwf7orIScA4VR3qpv8EBCp4wNsb\nmAYMVdU1FbRT7Ye7iFBUGCC1YYVrxhuGYSQs8foD13ygm4h0EpEGwBXA9HKGHYkT9K+uKOjXCFVy\nAV+St4J++R6wFzCfvYH5HB1iKvWoql9ERgEf4AznfFlVV4jIb9zyCcDdQCbwnIgAlKjqgKgYEAhQ\niuAzid8TuJ8fw/Akh6OKJPRcPVpcgj+1McmBEiwmJD7ubW28zTCMWqeyz74n5+pRfykBfBb0DcMw\nwkjowF9aEmBWvI2IA6aDGoZRFQkd+AP+AJrYLhqGYRw2Ca3xF2zZg79Ne9J1TwysMuoapvEbXsU0\n/jACJY7GbxjxZuXKlWRnZ5Oens4zzzxzyPo+n4+1a9cCzp8Xx44dW2ndbdu20aNHD4qKiqJmr3Ew\nRUVF9OjRg+3bt8fblBqT0FFRSwN8RiDeZtQ6XtS767rPDz/8MGeccQZ79uxh1KhRh3WsiFQ5VPWh\nhx7i2muvJTU1taZmxo28vDwuvvhimjZtSqdOnXj99dcrrVtUVMTvf/972rVrR1ZWFrfccgt+vz9U\nvnHjRoYNG0bz5s1p06YNt956K6WlpQCsW7cOn89HWlpaaHvggQdCx/r9fm699VbatGlD8+bNufDC\nC9m0aRMAqampXHfddTz00EMxugq1R0IH/tKSAIoN6THiz/r16+nZs2e1j69MwioqKuLVV1/l6quv\nrla74QEzntxyyy00bNiQn3/+mddee42bbrqJb7/9tsK6Dz30EAsXLmT58uWsWrWKhQsXcv/994fK\nb7vtNlq0aMHmzZtZvHgxn376KePHjy/Txp49e8jPzyc/P58xY8aE8sePH8/s2bNZunQpmzZtIjMz\nk1tvvTVUPmLECCZPnkxJSUmUr0DtktCBP+APMFAaxtuMWid8jg+vUJd9Pv3008nNzWXUqFGkp6ez\nevVqcnJyePnll0N1Jk2axODBgw+77blz55KRkUHbtm1DeRMnTqRnz56kp6fTpUsXXnjhwEznubm5\ntG/fnocffpg2bdpw/fXXo6o89NBDdO3alRYtWnDFFVewc+fO0DGXXXYZbdq0ISMjgyFDhlQakKvL\nvn37mDZtGvfddx+NGzdm0KBBXHTRRfzjH/+osP67777LrbfeSkZGBi1atOC2227jlVdeCZUvX76c\nK664ggYNGnDEEUcwdOhQli9fXqaNQKBiJWD58uWcc845tGzZktTUVC6//PIyx7Zv357MzEy+/PLL\nKHgePxI68Gupjeox4s8nn3zC4MGDefbZZ9mzZw/dunU7pHwTKd988w1HH310mbwjjjiC9957jz17\n9jBx4kR+//vfs2jRolD51q1b2blzJxs2bGDChAk89dRTTJ8+nc8++4zNmzeTmZnJLbfcEqp//vnn\ns2bNGrZt20a/fv246qqrKrXn5ptvJjMzs8ItOzu7wmNWrVpFcnIyXbt2DeX16dPnoGAdTvgdUCAQ\nYOPGjeTn5wNwzjnnMGXKFAoLC/npp5+YMWMG5557bpnjO3bsSIcOHbjuuuvYsWNHKP/ss89mxowZ\nbN68mYKCAl577TXOO++8Msf26NGDJUuWVGpbfSCho2JpcSlzqN+3ZNWhruvdsSASn0Wis1WXWIw4\n2rVrF2lpaWXyzjvvPDp37gzAqaeeytlnn83s2bND5T6fj3vvvZeUlBQaNmzIhAkTuP/++2nbti0p\nKSncc889vPXWW6Fe8ciRI2nSpEmobMmSJaEgW57x48ezc+fOCrfFixdXeMzevXtJT08vk5eWllbp\nOYYOHcqTTz7J9u3b2bJlC0899RQiQkFBAQDjxo1j2bJlpKen06FDB/r3789FFznLgLRs2ZL58+ez\nYcMGFixYQH5+fpkfsuHDh9O3b1/atWtHs2bNWLly5UEP1tPS0ti1a1eFttUXEjrwa2nARvUYIVSj\ns1WXWMwllJWVdVCAnDFjBieddBLNmzcnMzOT999/v0yvtmXLljRo0CCUXrduHRdffHGoZ96zZ0+S\nk5PZunUrpaWl3HnnnXTt2pVmzZrRuXNnRCSqI1uaNm3Knj1lh1zv3r37oB+0IGPGjKFv375kZ2dz\nyimncPHFF5OcnMwRRxyBqnLOOedw2WWXUVBQwPbt28nLy2P06NEANGnShH79+uHz+WjVqhXPPPMM\nH374Ifv27QPg9ttvJz8/n7y8PPbt28fFF1980N1Cfn4+mZmZUfM/HiR0VAz4A5zkaxxvM2qduqx3\nx4r65nOTJk1CwQZgy5Yt1Wqnd+/erFq1KpQuKipi+PDh3HHHHfz888/s3LmT8847r8zdRvkfoCOP\nPJKZM2eW6Z0XFBTQpk0bpkyZwvTp0/n444/ZvXs3P/zwA6pa6d3LjTfeWGbETPjWq1evCo/p3r07\nfr+fNWsOTM67ZMkSjjvuuArrN2zYkKeffpqNGzeyZs0asrKyOOGEEwDYvn07CxYsYNSoUaSkpJCV\nlcXIkSN5//2q13cK3t3MnDmTa6+9loyMDBo0aMCoUaOYN28eeXl5oborVqygT58+VbZX10n4wG8a\nv1FXCA+W2dnZTJs2jcLCQtasWVPmQW9Vx5Wnf//+7Nq1KzTksLi4mOLiYlq0aIHP52PGjBl8+OGH\nVdp14403ctddd7FhwwbA+V/A9OnO7Ol79+4lNTWVrKws9u3bx1133VVlW88//3xotEz57Ztvvqnw\nmCZNmnDJJZdw9913U1BQwJw5c3jnnXe45pprKqy/adMmNm3ahKry1Vdfcf/993PvvfcC0KJFC9q0\nacNzzz1HaWkpu3btYvLkyaFAPW/ePFauXEkgEGDHjh3cdtttnHbaaaG7i969ezN58mT27NlDSUkJ\n48ePDw0bBfjpp5/Iy8vjpJNOqvI61HUSOioG/AG+UO/9qcU0/rpJeE/797//fWjUybXXXsvVV19d\nprz8fmUyUYMGDRg5ciT//Oc/AUd/fuqpp7j88svJysri9ddfD+nbFbUN8Nvf/pYLL7yQs88+m/T0\ndAYOHMi8efMA+NWvfkXHjh1p164dxx13HAMHDoyJZDV+/HgKCwtp1aoVV199Nc8//zw9evQAYMOG\nDaSlpbFx40YAvv/+ewYNGkTTpk259tpr+dvf/saZZ54Z8m3atGm88847tGjRgm7dupGamsrjjz8O\nwNq1azn33HNJT0+nV69eNGrUqMx/Bh5//HF8Ph9dunShVatWzJw5k3//+9+h8ilTpjBy5EhSUlKi\nfg1qk4SesmH9hyv54rwzGOHfGAOr6i7hy7R5hdzcXE477TRPTtmwfft2Bg8ezOLFi+v1n7jqOkVF\nRWRnZzN79mxatGgRb3PKcLhTNiR04F83YwWlF11Cl+IVMbDKqGvYXD2GV7G5esII+AMEJKFdNAzD\nOGwSOioG/AG+0oJ4m1Hr1Ae9O9p40WfDqC4JHfjVX2qjegzDMMqR0FFRSwP0T2oWbzNqHa892AVv\n+mwY1SWhA3/AH0BN4zcMwyhDQkdFLQ0wN7A33mbUOl7Uu73os2FUl4QO/NbjNwzDOJiEjorqL+WE\n5Ix4m1HreFHvTnSfx40bV+kUBrEikjUCBg0aVO+nKK4PXHrppcycOTNq7SV24C8NoJIUbzMMo8bE\nYpqEmvLOO+/QrFmzej9h2ejRo2nRogUtWrTgzjvvrLLuSy+9RLdu3UhLS+Pcc89l8+bNobJzzz23\nzKR0qamp9O7dO1T+xRdfMGDAANLT0+nTpw+ff/55mbYfeOABOnbsSLNmzRgxYkSZWVdHjx7Nn//8\n5yh5nOCBP+AP8HXpnkNXTDC8qHfXJ5/rynKHNeX555+v9l1IXbkGEyZM4O2332bp0qUsXbqUd955\nhwkTJlRYNzc3lzFjxjB9+nTy8vLo3LkzI0aMCJXPmDGjzKR0J598MpdffjngrCk8bNgwRo8eze7d\nu7njjjsYNmxYaF7/yZMn889//pMvvviCTZs2UVhYWGbJx/79+7Nnzx4WLFgQFb8TOvA7Pf6611My\nvEenTp14+OGH6d27N2lpaQQCAb766itOPvnk0OpUn376aaj+Dz/8wJAhQ0hPT+fss88uM/99bm4u\nHTp0OKj9jz/+GIDS0lIefPBBunbtSnp6OieccEJogrPvvvuOs846i+bNm3PMMcfw5ptvhtrYsWMH\nF154Ic2aNePEE0/k+++/r9Sf4uJiZs2axZAhQ0J58+bNY+DAgWRmZtK2bVtuvfXWMmvT+nw+xo8f\nT7du3UKrhr377rtkZ2eTmZnJoEGDyszgGVwOMj09nWOPPZb//Oc/h3XNI2Hy5MncfvvttG3blrZt\n23L77bczadKkCuu+++67XHbZZfTo0YOUlBTGjh3LZ599xg8//HBQ3XXr1jF79mx+9atfAU5vv3Xr\n1gwfPhwR4aqrrqJly5ZMmzYNcO6err/+etq1a0eTJk0YPXo0b7zxBvv37w+1mZOTw3vvvRcVvxM+\n8B+f0jzeZtQ6ia53V0R98Hnq1KnMmDGDXbt2sXnzZi644ALuvvtudu7cySOPPMLw4cNDC6ZceeWV\n9O/fnx07djB27FgmT55cpdwTPoPnY489FjpXcPnFxo0bs2/fPs466yyuvvpqtm3bxtSpU7n55ptZ\nscKZy+qWW26hcePGbNmyhVdeeYWJEydWes7Vq1fj8/nKrPWbnJzMk08+yY4dO/jyyy/5+OOPD1rk\n/O233+brr7/m22+/ZdGiRVx//fW8+OKL5OXl8Zvf/IYLL7ww9GPRtWtX5syZw549e7jnnnu4+uqr\nK123YMqUKZUu+ZiVlRX64SvPt99+W0aq6t27d6VLPpafDyc4h/+yZcsOqvvqq69y6qmncuSRR1bY\nVvD44LkqaruoqIjVq1eH8qK65GNwUYW6vDlmHj7zH/xA52edWa1jjfrHIT8n0VqEqxp06tRJJ06c\nGEo/9NBDes0115Spc8455+jkyZN1/fr1mpycrAUFBaGyK6+8MlR/1qxZ2r59+4Pa//jjj1VVtXv3\n7jp9+vSDbJg6daoOHjy4TN4NN9yg9957r/r9fk1JSdGVK1eGyu666y495ZRTKvRnzpw52rp16yp9\nfvzxx/Xiiy8OpUVEZ82aFUrfeOONOnbs2DLHHH300frpp59W2F52dra+/fbbVZ7zcElKSirj86pV\nq9SdFPIg/vvf/2rLli116dKlWlBQoDfccIP6fD6dOnXqQXW7dOmikydPDqW3b9+umZmZOnXqVC0u\nLtZJkyapz+fTG2+8UVVVX3rpJe3evbuuW7dOd+3apcOGDVMR0a+++irUxgsvvKCnn356hbZV9tl3\n8w+KqQnd4ycQYL5/d7ytqHXqk94dLSLyOc5rL4bLM+vXr+fNN98s0zP9/PPP2bJlC5s2bSIzM5NG\njRqF6nfs2DHimUc3btxIly5dDspfv349c+fOLXPOKVOmsHXrVrZv347f7y9jY1W91czMzIOWfFy1\nahUXXHABbdq0oVmzZowZM6bMko8VXYNHH320jD0bN24MPTB99dVX6du3b6hs2bJlB7VXU8ov+7h7\n926aNm1aYd0zzjiDcePGMXz4cDp37kznzp1JS0ujffv2ZerNmTOHrVu3cumll4bymjdvzn/+8x8e\nffRRWrduzQcffMCZZ54ZOva6665jxIgR5OTk0KtXL04//XSAMm3n5+eTkRGdUYoJHfi1NIBiGr9R\nNwiXTY488kiuueaaMssd5ufnc8cdd9CmTZvQ8odB1q9fHzq+SZMmZcpKS0vZtm1bKN2hQ4cyyxiG\nn3PIkCEHnfPZZ5+lRYsWJCcnh1bhAsrsl6dr166oaplRLTfddBM9e/ZkzZo17N69mwceeCAkh1R2\nDcaMGVPGnr1793LFFVewfv16brjhBp599lny8vLYuXMnxx13XKU/fq+99lqlSz6mp6dXKvUce+yx\nZRaBr2rJR4Cbb76ZVatWsWXLFi655BL8fv9B9SdPnszw4cNp3Ljssq+nnnoq8+bNY8eOHbz66qt8\n9913DBgwIHRdxo0bxw8//MCGDRvo2bMn7du3p127dqHjV6xYQXZ2dqW2HRYV3QZEawOGAt8Bq4HR\nldR5yi1fAvStpE6FtzGHYu7Yd3Ruy/OrdaxR/6ju56Q2CJdiVFV//PFHbd26tX7wwQfq9/u1sLBQ\nZ82apRs3blRV1ZNOOklvv/12LS4u1tmzZ2t6enpI6tm1a5c2btxY33vvPS0uLtZx48ZpcnJyqP2/\n//3v2rt3b129erUGAgFdsmSJ7tixQ/Pz87Vjx476j3/8Q4uLi7W4uFjnzZunK1asUFXVK664Qn/5\ny19qQUGBLl++XNu1a3eQNBTOhRdeqFOmTAmlBwwYoH/5y180EAjoihUrtHv37mWkIhHR77//PpSe\nP3++dujQQefOnauBQED37t2r7777rub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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1165ec850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "## Toy 1\n",
      "## Toy 2\n",
      "## Toy 3\n",
      "## Toy 4\n",
      "## Toy 5\n",
      "## Toy 6\n",
      "## Toy 7\n",
      "## Toy 8\n",
      "## Toy 9\n",
      "## Toy 10\n",
      "## Toy 11\n",
      "## Toy 12\n",
      "## Toy 13\n",
      "## Toy 14\n",
      "## Toy 15\n",
      "## Toy 16\n",
      "## Toy 17\n",
      "## Toy 18\n",
      "## Toy 19\n",
      "## Toy 20\n",
      "## Toy 21\n",
      "## Toy 22\n",
      "## Toy 23\n",
      "## Toy 24\n",
      "## Toy 25\n",
      "## Toy 26\n",
      "## Toy 27\n",
      "## Toy 28\n",
      "## Toy 29\n",
      "## Toy 30\n",
      "## Toy 31\n",
      "## Toy 32\n",
      "## Toy 33\n",
      "## Toy 34\n",
      "## Toy 35\n",
      "## Toy 36\n",
      "## Toy 37\n",
      "## Toy 38\n",
      "## Toy 39\n",
      "## Toy 40\n",
      "## Toy 41\n",
      "## Toy 42\n",
      "## Toy 43\n",
      "## Toy 44\n",
      "## Toy 45\n",
      "## Toy 46\n",
      "## Toy 47\n",
      "## Toy 48\n",
      "## Toy 49\n",
      "## Toy 50\n",
      "## Toy 51\n",
      "## Toy 52\n",
      "## Toy 53\n",
      "## Toy 54\n",
      "## Toy 55\n",
      "## Toy 56\n",
      "## Toy 57\n",
      "## Toy 58\n",
      "## Toy 59\n",
      "## Toy 60\n",
      "## Toy 61\n",
      "## Toy 62\n",
      "## Toy 63\n",
      "## Toy 64\n",
      "## Toy 65\n",
      "## Toy 66\n",
      "## Toy 67\n",
      "## Toy 68\n",
      "## Toy 69\n",
      "## Toy 70\n",
      "## Toy 71\n",
      "## Toy 72\n",
      "## Toy 73\n",
      "## Toy 74\n",
      "## Toy 75\n",
      "## Toy 76\n",
      "## Toy 77\n",
      "## Toy 78\n",
      "## Toy 79\n",
      "## Toy 80\n",
      "## Toy 81\n",
      "## Toy 82\n",
      "## Toy 83\n",
      "## Toy 84\n",
      "## Toy 85\n",
      "## Toy 86\n",
      "## Toy 87\n",
      "## Toy 88\n",
      "## Toy 89\n",
      "## Toy 90\n",
      "## Toy 91\n",
      "## Toy 92\n",
      "## Toy 93\n",
      "## Toy 94\n",
      "## Toy 95\n",
      "## Toy 96\n",
      "## Toy 97\n",
      "## Toy 98\n",
      "## Toy 99\n",
      "### Results\n",
      "Mean area with full set is: 0.9729 +- 0.0142\n",
      "Mean area with redu set is: 0.9694 +- 0.0142\n"
     ]
    }
   ],
   "source": [
    "# run toys\n",
    "n_toys = 100\n",
    "n_samples = 300000\n",
    "rdm_state = 500\n",
    "plots = True\n",
    "\n",
    "areas = {'balanced': [], 'imbalanced': []}\n",
    "for i in range(n_toys):\n",
    "    print \"## Toy %s\" %i\n",
    "    if i>0: plots = False\n",
    "    a_bal, a_imbal = roc_imabalance(n_samples, rdm_state, plots)\n",
    "    areas['balanced'].append(a_bal)\n",
    "    areas['imbalanced'].append(a_imbal)\n",
    "    rdm_state += 1\n",
    "\n",
    "print \"### Results\"\n",
    "print \"Mean area with balanced set is: %0.4f +- %0.4f\" %(np.mean(areas['balanced']), np.std(areas['balanced']))\n",
    "print \"Mean area with imbalanced set is: %0.4f +- %0.4f\" %(np.mean(areas['imbalanced']), np.std(areas['imbalanced']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "### Results\n",
      "Mean area with balanced set is: 0.9729 +- 0.0142\n",
      "Mean area with imbalanced set is: 0.9694 +- 0.0142\n"
     ]
    }
   ],
   "source": [
    "print \"### Results\"\n",
    "print \"Mean area with balanced set is: %0.4f +- %0.4f\" %(np.mean(areas['balanced']), np.std(areas['balanced']))\n",
    "print \"Mean area with imbalanced set is: %0.4f +- %0.4f\" %(np.mean(areas['imbalanced']), np.std(areas['imbalanced']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This shows that a factor 1:100 of imbalance in the training sample does not degrade (or at least, not significantly) the performance of a BDT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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imbalance_dt.ipynb

ROC_imbalance.ipynb