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@cmarinbe
Last active November 15, 2022 15:34
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Checking imbalance effect
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Check how imbalance of the training sample affects the performance of a single DT"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# imports\n",
"from sklearn.cross_validation import train_test_split\n",
"from sklearn import datasets\n",
"\n",
"# functions\n",
"def build_dt(min_samples_leaf, max_depth=3):\n",
" from sklearn.tree import DecisionTreeClassifier\n",
" dt = DecisionTreeClassifier(max_depth=max_depth,\n",
" min_samples_leaf=min_samples_leaf)\n",
" return dt\n",
"\n",
"def compare_train_test(y_train, dec_train,\n",
" y_test , dec_test ,\n",
" labels = ('train', 'test'),\n",
" bins=30, alpha=0.5):\n",
" import numpy as np\n",
" import matplotlib.pyplot as plt\n",
"\n",
" decisions = []\n",
" for dec, y in ((dec_train, y_train), (dec_test, y_test)):\n",
" d1 = (dec[y==1]).ravel()\n",
" d2 = (dec[y==0]).ravel()\n",
" decisions += [d1, d2]\n",
" \n",
" low = min(np.min(d) for d in decisions)\n",
" high = max(np.max(d) for d in decisions)\n",
" low_high = (low,high)\n",
" \n",
" plt.hist(decisions[0],\n",
" color='r', alpha=alpha,\n",
" range=low_high, bins=bins,\n",
" histtype='stepfilled', normed=True,\n",
" label='S (%s)' %labels[0])\n",
" plt.hist(decisions[1],\n",
" color='b', alpha=alpha,\n",
" range=low_high, bins=bins,\n",
" histtype='stepfilled', normed=True,\n",
" label='B (%s)' %labels[0])\n",
" \n",
" hist, bins = np.histogram(decisions[2],\n",
" bins=bins, range=low_high,\n",
" normed=True)\n",
" scale = len(decisions[2]) / sum(hist)\n",
" err = np.sqrt(hist * scale) / scale\n",
" \n",
" width = (bins[1] - bins[0])\n",
" center = (bins[:-1] + bins[1:]) / 2\n",
" plt.errorbar(center, hist, yerr=err, fmt='o', c='r',\n",
" label='S (%s)' %labels[1])\n",
" \n",
" hist, bins = np.histogram(decisions[3],\n",
" bins=bins, range=low_high,\n",
" normed=True)\n",
" scale = len(decisions[2]) / sum(hist)\n",
" err = np.sqrt(hist * scale) / scale\n",
"\n",
" plt.errorbar(center, hist, yerr=err, fmt='o', c='b',\n",
" label='B (%s)' %labels[1])\n",
"\n",
" plt.xlabel(\"BDT output\")\n",
" plt.ylabel(\"Arbitrary units\")\n",
" plt.legend(loc='best')\n",
" return plt\n",
"\n",
"def plot_rocs(y_list, dec_list, colors):\n",
" assert(len(y_list)==len(dec_list))\n",
" assert(len(y_list)==len(colors.keys()))\n",
" \n",
" from sklearn.metrics import roc_curve, auc\n",
" import matplotlib.pyplot as plt\n",
" \n",
" results = {}\n",
" for y, dec, l in zip(y_list, dec_list, colors.keys()):\n",
" fpr, tpr, thresholds = roc_curve(y, dec)\n",
" results[l] = [fpr, tpr, thresholds]\n",
" roc_auc = auc(fpr, tpr)\n",
" plt.plot(fpr, tpr, lw=1, color=colors[l],\n",
" label='%s (area = %0.2f)'%(l, roc_auc))\n",
" plt.xlim([-0.05, 1.05])\n",
" plt.ylim([-0.05, 1.05])\n",
" plt.xlabel('False Positive Rate')\n",
" plt.ylabel('True Positive Rate')\n",
" plt.title('Receiver operating characteristic')\n",
" plt.legend(loc=\"lower right\")\n",
" plt.grid()\n",
" plt.show()\n",
" return results"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# create random problem\n",
"def imbalance_dt(n_samples, sig_w):\n",
" X, y = datasets.make_classification(n_samples=n_samples,\n",
" weights = [sig_w],\n",
" random_state = 500)\n",
" assert(X.shape[0]==n_samples)\n",
" n_sig_ = X[y==0].shape[0]\n",
" n_bkg_ = X[y==1].shape[0]\n",
" print \"n sig is: %s\" %n_sig_\n",
" print \"n bkg is: %s\" %n_bkg_\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=492)\n",
"\n",
" # build dt\n",
" dt = build_dt(0.05*len(X_train))\n",
"\n",
" # normal train\n",
" dt.fit(X_train, y_train)\n",
" pred = dt.predict_proba(X_test)[:,1]\n",
" \n",
" # balanced train\n",
" dt.class_weight=\"balanced\"\n",
" dt.fit(X_train, y_train)\n",
" pred_b = dt.predict_proba(X_test)[:,1]\n",
"\n",
" # plot bdt outputs\n",
" plt = compare_train_test(y_test, pred, y_test, pred_b,\n",
" labels=('normal', 'balanced'))\n",
" plt.show()\n",
"\n",
" # plot rocs\n",
" from collections import OrderedDict\n",
" colors = OrderedDict([('normal', 'b'),\n",
" ('balanced', 'black')])\n",
" results = plot_rocs([y_test, y_test],\n",
" [pred, pred_b],\n",
" colors)\n",
" for l in colors.keys():\n",
" print \"###\", l\n",
" print 'thresholds:', results[l][-1]\n",
" print 'tpr:', results[l][1]\n",
" print 'fpr:', results[l][0]\n",
" \n",
" return results"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Let's play "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 1:1 proportion"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n sig is: 998\n",
"n bkg is: 1002\n"
]
},
{
"data": {
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OEJG/AD8CfzPG6LSHSinlISVeIzDG9LX9G22MuerSxxWscybWJNIeSAWmlt5c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\nAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x1082ec990>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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YzZVDWY//OaBERAYAvwO+B14Os31NxtatPhIT7aKuYRjeJZTAX6GqVcAFwN9U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\nTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x108224110>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"### normal\n",
"thresholds: [ 1.98995984 0.98995984 0.92537313 0.73529412 0.34848485 0.10738255\n",
" 0.01173709]\n",
"tpr: [ 0. 0.76060606 0.84242424 0.91212121 0.95454545 0.98181818\n",
" 1. ]\n",
"fpr: [ 0. 0.02727273 0.02727273 0.06060606 0.19090909 0.38484848\n",
" 1. ]\n",
"### balanced\n",
"thresholds: [ 1.98990033 0.98990033 0.9249598 0.73413047 0.34713059 0.10681164\n",
" 0.01166804]\n",
"tpr: [ 0. 0.76060606 0.84242424 0.91212121 0.95454545 0.98181818\n",
" 1. ]\n",
"fpr: [ 0. 0.02727273 0.02727273 0.06060606 0.19090909 0.38484848\n",
" 1. ]\n"
]
}
],
"source": [
"n_sig = 1000.\n",
"n_bkg = 1000.\n",
"n_samples = int(n_sig+n_bkg)\n",
"sig_w = n_sig/n_samples\n",
"\n",
"results = imbalance_dt(n_samples, sig_w)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 10:1 proportion"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n sig is: 9941\n",
"n bkg is: 1059\n"
]
},
{
"data": {
"image/png": 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V4lrW3Q54zfmcIAx4Q1WXicg64G/O8YrycPRcNsYYEyCeJIJcHK1+apUIVHUD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\nYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10841c610>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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JUtbGPbJm4JR67IjfGGMgthr/kar6YFtN+kVFRfj93ir1WB3UG6zP3tCsY/WI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\nlxLC1c0zYwAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x107ee66d0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"### normal\n",
"thresholds: [ 1.92520325 0.92520325 0.17297297 0.04197531 0.009699 ]\n",
"tpr: [ 0. 0.80626781 0.89173789 0.91452991 1. ]\n",
"fpr: [ 0. 0.01036901 0.05519976 0.11314425 1. ]\n",
"### balanced\n",
"thresholds: [ 1.99131315 0.99131315 0.66028261 0.29192335 0.12077592 0.05365891]\n",
"tpr: [ 0. 0.80626781 0.89173789 0.91452991 0.95441595 1. ]\n",
"fpr: [ 0. 0.00914913 0.05519976 0.11314425 0.50045746 1. ]\n"
]
}
],
"source": [
"n_sig = 10000.\n",
"n_bkg = 1000.\n",
"n_samples = int(n_sig+n_bkg)\n",
"sig_w = n_sig/n_samples\n",
"\n",
"results = imbalance_dt(n_samples, sig_w)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 100:1 proportion"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n sig is: 99466\n",
"n bkg is: 1534\n"
]
},
{
"data": {
"image/png": 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gwThw8Xx7Yj9RVpe4qATfcl2rz7cnvyY+PoH6dRtSeOxrooiNiOXY\nqHrkH86jjtWrUpzHT+4iOqpxpeOJijnKz351PQ9OGc/vpvyeF//7/zhZHBf2/VOZ5bzDH9OgzkVB\n+7kibV+VF8+R47toVr97RPxewr1c1b+R6vodRQIzwzlnFV7RORcRL+A24KUS7+8EZp1Rx426d5xr\nwDAHzsEyBxPO0+W7q7Cu55UYc4e7sc9tLjHmjgj6uSqz/IMg/lyRtq/OFc/kCPq9hHu5Kn8j1fM7\nemryNBcJPIf6ShyXK7NSMF7A4EASRNtG15X4JUw8j5evrsK6p18x1Ib9OTmIP1ek7atzxTM5gn4v\n4V6uyt9I9fyOGsf0dmvXrq3Wg31lVDZBRNIppl7AFHf6FNPDwEnn3O9K1ImMYEVEahhXiVNMkZQg\nYoBNwHXALmAVcLtzbkNYAxMROU9FzJPUzrliM/sVsBiIBuYoOYiIhE/E9CBERCSyRMxzECUF8sCc\nmc30fr7OzC4JdYyhcq59YWZ3ePfBp2b2gZl1C0ecoRDog5RmdoWZFZvZD0MZXygF+DeSamZrzWy9\nmWWHOMSQCeBvpImZvWdmn3j3xd1hCDPozOzPZpZnZp+VU6dix83KXNkO5gvP6aUtQAegDvAJ0PmM\nOjcC73qXrwT+He64w7gvegONvMsDzud9UaLeP4F3gMHhjjuM/y8Sgf8Abbzvm4Q77jDuiynAb0/t\nB2A/EBPu2IOwL64GLgE+K+PzCh83I7EH0RPY4pzb5pw7DrwB3HxGnZuAVwCccyuBRDNrHtowQ+Kc\n+8I596FzrsD7diXQJsQxhkog/y8ARgFvAV+HMrgQC2Rf/Bj4H+fcDgDn3L4QxxgqgeyL3UBD73JD\nYL9zzv/E0TWYc24FkF9OlQofNyMxQbQGvirxfoe37Fx1auOBMZB9UdII4N2gRhQ+59wXZtYaz8Hh\nBW9Rbb3AFsj/i4uAZDP7l5l9ZGZ3hSy60ApkX7wEdDWzXcA6YEyIYos0FT5uRsxdTCUE+kd95j29\ntfFgEPDPZGbXAPcA3w9eOGEVyL54DnjIOefMzDj7/0htEci+qANciue28XrAh2b2b+fc50GNLPQC\n2RcTgE+cc6lmlgIsMbPuzrnCIMcWiSp03IzEBLETaFvifVs8ma68Om28ZbVNIPsC74Xpl4ABzrny\nupg1WSD74jLgDU9uoAlwg5kdd879PTQhhkwg++IrYJ9z7ghwxMyWA92B2pYgAtkXVwEZAM65XDPb\nCnQEPgpJhJGjwsfNSDzF9BFwkZl1MLO6wFDgzD/wvwM/Ad8T2Aecc3mhDTMkzrkvzKwd8DfgTufc\nljDEGCrn3BfOuQudcxc45y7Acx3iF7UwOUBgfyMLgR+YWbSZ1cNzUTInxHGGQiD7YiNwPYD3nHtH\n4IuQRhkZKnzcjLgehCvjgTkz+5n38xedc++a2Y1mtgU4DPw0jCEHTSD7AngUSAJe8H5zPu6c6xmu\nmIMlwH1xXgjwb2Sjmb0HfAqcxDPOWa1LEAH+v3gSmGtm6/B8KX7AOfdN2IIOEjObD/QFmpjZV8Bk\nPKcaK33c1INyIiLiVySeYhIRkQigBCEiIn4pQYiIiF9KECIi4pcShIiI+KUEISIifilBSK1mZie8\nQ15/YmYfm1lvb3kHMztiZmvMLMfMVprZcO9nP/Wus9bMjnmHUl9rZk9WQzwTqrh+31M/g0iw6TkI\nqdXMrNA5l+Bd7g9M8I7J0wH4h3PuYu9nF+B5In2Gc+7lEutvBS6rrgerSsZTyfWnAIXOuenVEY9I\nedSDkPNJI8Dvgd45txX4NTA60MbMLM7M5np7GGvMLNVbfreZzSpR7x3vN/+ngHhvb+Q1M2vvnejm\ndW8vZoGZxXvX2WZmyd7ly72jsrYHfgaM87bxg0ruB5GARNxQGyLVLN7M1gJxQEvg2nLqrgU6VaDt\n+4ETzrluZtYRyDKz73L2CJkOcM65h8zsfufcJeA5zQV8F/ipc+5DM5sD/BKY7qcNnHNfmtkf8fQg\nnqlAnCKVoh6E1HZHnHOXOOc645lx79Vy6lZ0ePDvA68DOOc2AV/iOeBXxFfOuQ+9y68DgfQKausw\n5hJhlCDkvOGc+zeegcyalFHlEio+4qm/8fWLKf23FVdeWGe0dep9yTbKW18kaJQg5LxhZp3wjPi5\n389nHYBpwKwzPyvHCuAO7/rfBdoBm4BtQA/zaItnWsxTjptZyVO77bxDL4NnmtAV3uVtwOXe5cEl\n6hcClb7ILVIRShBS2526KLwWz3zFP3Gnb91LOXWbK/AmnjuYXjlj/fJu83seiDKzT71tD3fOHXfO\nfQBsxdMbmQF8XGKd2cCnZvaat+1NwP3eGBpxerrUx4AZZrYaT2/iVBz/AG71/ky1dfZAiRC6zVUk\nTM681VYk0qgHIRJe+oYmEUs9CBER8Us9CBER8UsJQkRE/FKCEBERv5QgRETELyUIERHxSwlCRET8\n+v9bhuHv61lz1QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x108594350>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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txzp3AFNVdZu70zOSfrhZtMhJ+oMGwVNPnWTo0IdYvHgxP/zwA9HR0cEOzxgT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\nNe/jjz/OGlawa9eu2WKPj49XEck18Zc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"text/plain": [
"<matplotlib.figure.Figure at 0x108580bd0>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"### normal\n",
"thresholds: [ 1.15522828 0.15522828 0.02576531 0.01758392 0.01271061 0.00549503]\n",
"tpr: [ 0. 0.47887324 0.54929577 0.6277666 0.68410463 1. ]\n",
"fpr: [ 0. 0.04108671 0.10075229 0.16717936 0.21554534 1. ]\n",
"### balanced\n",
"thresholds: [ 1.90109528 0.90109528 0.58568491 0.47842507 0.4154359 0.25582487]\n",
"tpr: [ 0. 0.51307847 0.56740443 0.64386318 0.69215292 1. ]\n",
"fpr: [ 0. 0.05902598 0.12919928 0.19063138 0.24466238 1. ]\n"
]
}
],
"source": [
"n_sig = 100000.\n",
"n_bkg = 1000.\n",
"n_samples = int(n_sig+n_bkg)\n",
"sig_w = n_sig/n_samples\n",
"prop = int(n_sig/n_bkg)\n",
"\n",
"results = imbalance_dt(n_samples, sig_w)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### 1:100 proportion"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"n sig is: 1531\n",
"n bkg is: 99469\n"
]
},
{
"data": {
"image/png": 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5grmKCTNrA7T3L++cq9yUarAd2O6cW+l9/h7wGLDbzFo653abWStgT6CdM723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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x114b32490>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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ec/WIyM3AG0AZIE5EmgB9VTXPB7yq+jXwdba8UdnSg4HBJyPayJsRI6BRI7j0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\nBP4gCIKcEYE/CIIgZ3wHqYB5WYGjK78AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10859d990>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"### normal\n",
"thresholds: [ 1.99404849 0.99404849 0.98563892 0.97917691 0.85042861]\n",
"tpr: [ 0. 0.81653306 0.86652239 0.95878928 1. ]\n",
"fpr: [ 0. 0.29254302 0.3499044 0.49139579 1. ]\n",
"### balanced\n",
"thresholds: [ 1.73112138 0.73112138 0.62984651 0.58795114 0.45301293 0.1057869 ]\n",
"tpr: [ 0. 0.67799555 0.76044747 0.86652239 0.93662938 1. ]\n",
"fpr: [ 0. 0.26003824 0.29636711 0.3499044 0.45124283 1. ]\n"
]
}
],
"source": [
"n_sig = 1000.\n",
"n_bkg = 100000.\n",
"n_samples = int(n_sig+n_bkg)\n",
"sig_w = n_sig/n_samples\n",
"\n",
"results = imbalance_dt(n_samples, sig_w)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This shows that a single `dt` is indeed affected by imbalance. And in this case, gaining statistics does not compensate for this imbalance. \n",
"\n",
"Using the option ```class_weight='balanced'``` does not seem to help much."
]
}
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