01-01-2016-rrfd-netflix-churn-alaysis.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Netflix Churn Analysis "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How good is our model? Well we need to express, test, and cycle. So a constant upgrading of what we're doing and data we're using is necessary. but remember is the new version of our data better than the last?\n",
    "\n",
    "Let's use cross validation to test this out.\n",
    "\n",
    "This attempts to avoid over fitting )training on and predicting the same datapoints) while still producing a prediction for each observation dataset. So you hide subsets in the data while training a set of models.\n",
    "\n",
    "After training each model predicts on the subset that has been hidden to it, emulating multipule train-test splits. When done correctly, every observation will have a 'fair' corresponding prediction.\n",
    "\n",
    "Let's use scikit-learn!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a replication of (http://nbviewer.ipython.org/github/donnemartin/data-science-ipython-notebooks/blob/master/analyses/churn.ipynb) inorder to learn how to create some data analysis tools as well as learn iPython notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import json\n",
    "\n",
    "from sklearn.cross_validation import KFold\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.cross_validation import train_test_split\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.ensemble import RandomForestClassifier as RF\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Column names:\n",
      "['State', 'Account Length', 'Area Code', 'Phone', \"Int'l Plan\", 'VMail Plan', 'VMail Message', 'Day Mins', 'Day Calls', 'Day Charge', 'Eve Mins', 'Eve Calls', 'Eve Charge', 'Night Mins', 'Night Calls', 'Night Charge', 'Intl Mins', 'Intl Calls', 'Intl Charge', 'CustServ Calls', 'Churn?']\n",
      "\n",
      "Sample data:\n",
      "\\Data Shape: there are 3333 rows and 21 columns\n"
     ]
    }
   ],
   "source": [
    "churn_df = pd.read_csv('churn_data.csv')\n",
    "col_names = churn_df.columns.tolist()\n",
    "\n",
    "# This just shows the names of the columsn you have to choose from\n",
    "print \"Column names:\"\n",
    "print col_names\n",
    "\n",
    "# Only taking some of the column names\n",
    "to_show = col_names[:6] + col_names[-6:]\n",
    "\n",
    "print \"\\nSample data:\"\n",
    "churn_df[to_show].head(6)\n",
    "\n",
    "print \"\\Data Shape: there are %d rows and %d columns\" % churn_df.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Rember ML code does not pick up on 'yes' and 'no' very well, so we'll need to change those values into something readable. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Isolate target data\n",
    "churn_result = churn_df['Churn?']\n",
    "\n",
    "# np.where() = Return elements, either from x or y, depending on condition.\n",
    "# if 'True' = 1, if not 'True' = 0\n",
    "y = np.where(churn_result == 'True.',1,0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Account Length Int'l Plan VMail Plan  VMail Message  Day Mins  Day Calls  \\\n",
      "0             128         no        yes             25     265.1        110   \n",
      "1             107         no        yes             26     161.6        123   \n",
      "2             137         no         no              0     243.4        114   \n",
      "3              84        yes         no              0     299.4         71   \n",
      "4              75        yes         no              0     166.7        113   \n",
      "\n",
      "   Day Charge  Eve Mins  Eve Calls  Eve Charge  Night Mins  Night Calls  \\\n",
      "0       45.07     197.4         99       16.78       244.7           91   \n",
      "1       27.47     195.5        103       16.62       254.4          103   \n",
      "2       41.38     121.2        110       10.30       162.6          104   \n",
      "3       50.90      61.9         88        5.26       196.9           89   \n",
      "4       28.34     148.3        122       12.61       186.9          121   \n",
      "\n",
      "   Night Charge  Intl Mins  Intl Calls  Intl Charge  CustServ Calls  \n",
      "0         11.01       10.0           3         2.70               1  \n",
      "1         11.45       13.7           3         3.70               1  \n",
      "2          7.32       12.2           5         3.29               0  \n",
      "3          8.86        6.6           7         1.78               2  \n",
      "4          8.41       10.1           3         2.73               3  \n"
     ]
    }
   ],
   "source": [
    "# We don't need all the columns so let's drop a lot of them\n",
    "to_drop = ['State', 'Area Code', 'Phone', 'Churn?']\n",
    "churn_feat_space = churn_df.drop(to_drop, axis = 1)\n",
    "\n",
    "print churn_feat_space.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Account Length Int'l Plan VMail Plan  VMail Message  Day Mins  Day Calls  \\\n",
      "0             128      False       True             25     265.1        110   \n",
      "1             107      False       True             26     161.6        123   \n",
      "2             137      False      False              0     243.4        114   \n",
      "3              84       True      False              0     299.4         71   \n",
      "4              75       True      False              0     166.7        113   \n",
      "\n",
      "   Day Charge  Eve Mins  Eve Calls  Eve Charge  Night Mins  Night Calls  \\\n",
      "0       45.07     197.4         99       16.78       244.7           91   \n",
      "1       27.47     195.5        103       16.62       254.4          103   \n",
      "2       41.38     121.2        110       10.30       162.6          104   \n",
      "3       50.90      61.9         88        5.26       196.9           89   \n",
      "4       28.34     148.3        122       12.61       186.9          121   \n",
      "\n",
      "   Night Charge  Intl Mins  Intl Calls  Intl Charge  CustServ Calls  \n",
      "0         11.01       10.0           3         2.70               1  \n",
      "1         11.45       13.7           3         3.70               1  \n",
      "2          7.32       12.2           5         3.29               0  \n",
      "3          8.86        6.6           7         1.78               2  \n",
      "4          8.41       10.1           3         2.73               3  \n"
     ]
    }
   ],
   "source": [
    "# Just as above 'yes' / 'no' has to be converted to boolean values\n",
    "# NumPy converts these from boolean to 1. and 0. ... later\n",
    "\n",
    "yes_no_cols = ['Int\\'l Plan','VMail Plan']\n",
    "churn_feat_space[yes_no_cols] = churn_feat_space[yes_no_cols] == 'yes'\n",
    "print churn_feat_space.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index([u'Account Length', u'Int'l Plan', u'VMail Plan', u'VMail Message',\n",
      "       u'Day Mins', u'Day Calls', u'Day Charge', u'Eve Mins', u'Eve Calls',\n",
      "       u'Eve Charge', u'Night Mins', u'Night Calls', u'Night Charge',\n",
      "       u'Intl Mins', u'Intl Calls', u'Intl Charge', u'CustServ Calls'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "# Pull out features for future use\n",
    "features = churn_feat_space.columns\n",
    "print features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature space holds 3333 observations and 17 features\n",
      "Unique target labels: [0 1]\n"
     ]
    }
   ],
   "source": [
    "X = churn_feat_space.as_matrix().astype(np.float)\n",
    "\n",
    "# This is important so pay attention\n",
    "\n",
    "# Standardization of a dataset is a common requirement for many \n",
    "# machine learning estimators: they might behave badly if the \n",
    "# individual feature do not more or less look like standard normally \n",
    "# distributed data (e.g. Gaussian with 0 mean and unit variance).\n",
    "\n",
    "# StandardScaler fixes this by normalizing each feature to a range \n",
    "# of around 1.0 to -1.0 thereby preventing models from misbehaving\n",
    "scaler = StandardScaler()\n",
    "\n",
    "# fit_transform() --> Learn a list of feature name, \n",
    "# indices mappings and transform X.\n",
    "# Like fit(X) followed by transform(X), but does not require \n",
    "# materializing X in memory.\n",
    "X = scaler.fit_transform(X)\n",
    "\n",
    "print \"Feature space holds %d observations and %d features\" % X.shape\n",
    "print \"Unique target labels:\", np.unique(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# K-Folds cross validation iterator.\n",
    "# Provides train/test indices to split data in \n",
    "# train test sets. Split dataset into k consecutive\n",
    "# folds (without shuffling by default).\n",
    "\n",
    "from sklearn.cross_validation import KFold\n",
    "\n",
    "def run_cv(X, y, clf_class, **kwargs):\n",
    "    # Construct a kfolds object\n",
    "    kf = KFold(len(y), n_folds=3, shuffle=True)\n",
    "    y_pred = y.copy()\n",
    "    \n",
    "    # Iterrate through the folds\n",
    "    for train_index, test_index in kf:\n",
    "        X_train, X_test = X[train_index], X[test_index]\n",
    "        y_train, y_test = y[train_index], y[test_index]\n",
    "        \n",
    "        # Initalize a classifier with key word arguments\n",
    "        clf = clf_class(**kwargs)\n",
    "        clf.fit(X_train, y_train)\n",
    "        \n",
    "        # Remember: first you train, then you fit, then you predict\n",
    "        y_pred[test_index] = clf.predict(X_test)\n",
    "        \n",
    "        return y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at these fairly unique algorithms support vector machines (SVM), random forests (RF), neighbors, linear modeling / regeress, and gradient boosting classification (GBC).\n",
    "\n",
    "Let's just take a look at when the classifier predicted the correct class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Logisitc Regression:\n",
      "0.957\n",
      "Gradient Boosting Classifier:\n",
      "0.984\n",
      "Support Vector Machines:\n",
      "0.976\n",
      "Random Forest:\n",
      "0.977\n",
      "k-nearest-neighbors:\n",
      "0.959\n"
     ]
    }
   ],
   "source": [
    "from sklearn.svm import SVC\n",
    "from sklearn.ensemble import RandomForestClassifier as RF\n",
    "from sklearn.neighbors import KNeighborsClassifier as KNN\n",
    "from sklearn.linear_model import LogisticRegression as LR\n",
    "from sklearn.ensemble import GradientBoostingClassifier as GBC\n",
    "from sklearn.metrics import average_precision_score\n",
    "\n",
    "def accuracy(y_true, y_pred):\n",
    "    #NumPy interpretes True and False as 1. and 0.\n",
    "    return np.mean(y_true == y_pred)\n",
    "\n",
    "print \"Logisitc Regression:\"\n",
    "print \"%.3f\" % accuracy(y, run_cv(X, y, LR))\n",
    "\n",
    "print \"Gradient Boosting Classifier:\"\n",
    "print \"%.3f\" % accuracy(y, run_cv(X, y, GBC))\n",
    "\n",
    "print \"Support Vector Machines:\"\n",
    "print \"%.3f\" % accuracy(y, run_cv(X, y, SVC))\n",
    "\n",
    "print \"Random Forest:\"\n",
    "print \"%.3f\" % accuracy(y, run_cv(X, y, RF))\n",
    "\n",
    "print \"k-nearest-neighbors:\"\n",
    "print \"%.3f\" % accuracy(y, run_cv(X, y, KNN))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Does the highest number mean the best? We'll see.\n",
    "\n",
    "Remember the output will change after every iteration of the models."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem with out comes aren;t necessarily equal. If my classifier predicted a customer would churn and they didn't, that's not the best but it's forgivable. However, if my classifier predicted a customer would return, I didn't act, and then they churned ... that's really bad."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|condition True|condition False|\n",
    "-|-|-\n",
    "prediction true|True Positive (TP)|False positive (FP)\n",
    "prediction False|False Negative (FN)|True Negative (TN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sensitivity, __Recall__ or True Positive Rate (TPR) quantify the models ability to predict our positive classes. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$TPR = TP / (TP + FN)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Specificity, __precision__ or True Negative Rate (TNR) quantify the models ability to predict our Negative classes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$TNR = TN / (TN + FP)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here is an example:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "|Apple|Orange|\n",
    "-|-|-\n",
    "prediction Apple|400|250\n",
    "prediction Orange|230|40"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$TPR = TP / (TP + FN) = 400 / (400+230) = 63.49Sensitive$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$TNR = TN / (TN + FP) = 40 / (40 + 250) = 13.79Specific$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we know what the confusion matrix does in theory, let's put this into application and get some stuff done!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [[2837   13]\n",
      " [  69  414]]"
     ]
    },
    {
     "data": {
      "image/png": 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QgdDMrB98ssTMas+B0Mxqz4HQzGrPgdDMas+BsGYkrZR0raSFkr4raZ0u1rWH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\new6EZlZ7DoRmVnv/H9dNEVc+01myAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10be06a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [[2845    5]\n",
      " [  68  415]]"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bf6df10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [[2835   15]\n",
      " [ 102  381]]"
     ]
    },
    {
     "data": {
      "image/png": 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S/J2Av4+I2ZI2A04G9o+IP6eh7TRJ/wZ8C5gaEQ9L+l5d3bULSc8GZkXEkak3\nORY4CXhNRExO2z8A2CkipqQyV0l6K/Ai8C7g9cBo4C7gzi68DmarcQCshvUk3ZUe/xy4ABgHPBIR\ns9P8vwJeDfwiBad1gNuAXYGHI+LhVO4/gQ832MbbgL8HiOzq+uclbVpX5kDggNQWAa8gC8IbAv8d\nEUuBpZKuKrrDZq1wAKyGF2u9sJp0yO+F/Czg2oh4X125N6Rlg2nlJ0UCTo+I8+q28fEW1jXrOB8D\nrIZmASw//3ZgL0k7AEhaX9JOZPfzmiBpu1TuPU3quoF0wkPSCEkbAs8DG+TKXAN8SNIrUrmtJb0S\nuBk4QtIYSRsAh671Hpq1wQGwGpr1zlbOj4jfAx8ELpN0N3ArsEsalv4jMDOdBFnSpK5PAPtJuofs\n+N2kiHgauFXSPZK+HBHXAZcBt6VyPwDGRsQc4PvAPcCPgTuK7a5Za3wzBDOrLPcAzayyHADNrLIc\nAM2sshwAzayyHADNrLIcAM2sshwAzayy/hddGW2498IKUwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bd430d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [[2837   13]\n",
      " [  49  434]]"
     ]
    },
    {
     "data": {
      "image/png": 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VC5UKlmZmg+ILPGZmJThYmpmV4GBpZlaCg6WZWQkOlrYWSaslXStpsaTzJa3T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\nwcHSzKwEB0szsxIcLM3MSvj/47tTgO2fJw8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c71ad50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [[2823   27]\n",
      " [ 127  356]]"
     ]
    },
    {
     "data": {
      "image/png": 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A1dCsd/bG/Ih4FvgEcLGk3wC3AtukYenfA1enkyDPNKnrfwB7SLqb7PjddhGx\nELhV0t2STo+I64GLgdtSuR8Ba0bEHOBS4G7gv4A7ir1cs/b4ZghmVlnuAZpZZTkAmlllOQCaWWU5\nAJpZZTkAmlllOQCaWWU5AJpZZf1/G/tb3SQLkucAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c6a6b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "from sklearn.metrics import precision_score\n",
    "from sklearn.metrics import recall_score\n",
    "\n",
    "def draw_confusion_matrices(confusion_matricies, class_names):\n",
    "    # tolist() takes an array and puts the elements into a list\n",
    "    class_names = class_names.tolist()\n",
    "    \n",
    "    for cm in confusion_matrices:\n",
    "        classifier, cm = cm[0], cm[1]\n",
    "        print (cm)\n",
    "        # print recall_score(cm[0], cm[1])\n",
    "        # print precision_score((cm[0], cm[1]))\n",
    "        \n",
    "        fig = plt.figure()\n",
    "        ax = fig.add_subplot(111)\n",
    "\n",
    "        # matshow() is essentailly a heatmap\n",
    "        cax = ax.matshow(cm)\n",
    "        plt.title('Confusion matrix for %s' % classifier)\n",
    "        fig.colorbar(cax)\n",
    "        ax.set_xticklabels([''] + class_names)\n",
    "        ax.set_yticklabels([''] + class_names)\n",
    "        plt.xlabel('Predicted')\n",
    "        plt.ylabel('True')\n",
    "        plt.show()\n",
    "        \n",
    "y = np.array(y)\n",
    "class_names = np.unique(y)\n",
    "\n",
    "confusion_matrices = [\n",
    "    ( \"Support Vector Machines\", confusion_matrix(y, run_cv(X, y, SVC)) ),\n",
    "    ( \"Random Forest\", confusion_matrix(y, run_cv(X, y, RF)) ),\n",
    "    ( \"K-Nearest-Neighbors\", confusion_matrix(y, run_cv(X, y, KNN)) ),\n",
    "    ( \"Gradient Boosting Classifier\", confusion_matrix(y, run_cv(X, y, GBC)) ),\n",
    "    ( \"Logisitic Regression\", confusion_matrix(y, run_cv(X, y, LR)) )\n",
    "]\n",
    "\n",
    "# Pyplot code not included to reduce clutter\n",
    "# from chrun_display import draw_confusion_matrices\n",
    "%matplotlib inline\n",
    "\n",
    "draw_confusion_matrices(confusion_matrices,class_names)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Figure out how to cut code that returns the precision_score and recall_score"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "An important question might be: when someone 'churns' how often is my classifier correct?\n",
    "\n",
    "Another one is how \"precise\" is my classifier? Or how often does that person acutally churn?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is an ROC plot? It is a receiver operating characteristic. It is a graphical plot that illustrates the performance of a binary classifier system as its discrimination threshold is caried.\n",
    "\n",
    "It is mapped by plotting the true positive rate against the false positive rate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Support vector machines:\n"
     ]
    },
    {
     "data": {
      "image/png": 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YvvjiC1JSUiranBqFcbeFycqC5GTr8+nTAPz6669888034Af/+Mc/+F9cHOl5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\nweCnGAdgMBgMfopxAAaDweCn/D8dHPg4wOUvogAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c34ca10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Random forests:\n"
     ]
    },
    {
     "data": {
      "image/png": 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xeXCUOYL63zuUvYpQPsXeodDjjovzpUVlRB3Swb01/YPb7Sa8n8aEDnW0Cwi4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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c90bd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "K-nearest-neighbors:\n"
     ]
    },
    {
     "data": {
      "image/png": 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+w9i+PaCaok9Lo9oa9ZMmweDB0L37b+YbsLhcxp6OJebwb2vhxGbG4u/ub1P0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\nCHebWpa3NgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10b679fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Gradient Boosting Classifier:\n"
     ]
    },
    {
     "data": {
      "image/png": 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fgENc/Zgx8Ntv8MQTxS7SYDBcJqrK3r177RE+wcHB/jap3BIfH098fLxXaX06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\njAEwGAwGL8UYAIPBYPBS/j9D6E6mwzsVOQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c57b350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve, auc\n",
    "from scipy import interp\n",
    "\n",
    "def plot_roc(X, y, clf_class, ** kwargs):\n",
    "    # K Fold Cross-validation is used to generalize to an independent\n",
    "    # dataset. It is mainly used in settings where the goal is prediction,\n",
    "    # and one wants to estimate how accurately a predictive model\n",
    "    # will perform in practice\n",
    "    kf = KFold(len(y), n_folds = 5, shuffle = True)\n",
    "    y_prob = np.zeros((len(y),2))\n",
    "    mean_tpr = 0.0\n",
    "    mean_fpr = np.linspace(0, 1, 100)\n",
    "    all_tpr = []\n",
    "    \n",
    "    for i, (train_index, test_index) in enumerate(kf):\n",
    "        X_train, X_test = X[train_index], X[test_index]\n",
    "        y_train = y[train_index]\n",
    "        clf = clf_class(**kwargs)\n",
    "        clf.fit(X_train, y_train)\n",
    "        \n",
    "        # Predict probabilities, not classes\n",
    "        y_prob[test_index] = clf.predict_proba(X_test)\n",
    "        fpr, tpr, thresholds = roc_curve(y[test_index], y_prob[test_index, 1])\n",
    "        mean_tpr += interp(mean_fpr, fpr, tpr)\n",
    "        mean_tpr[0] = 0.0\n",
    "        roc_auc = auc(fpr, tpr)\n",
    "        plt.plot(fpr, tpr, lw=1, label='ROC fold %d (area = %0.2f)' % (i, roc_auc))\n",
    "    mean_tpr /= len(kf)\n",
    "    mean_tpr[-1] = 1.0\n",
    "    mean_auc = auc(mean_fpr, mean_tpr)\n",
    "    plt.plot(mean_fpr, mean_tpr, 'k--',label='Mean ROC (area = %0.2f)' % mean_auc, lw=2)\n",
    "    \n",
    "    # This is the diag line down the center of the grid\n",
    "    plt.plot([0, 1], [0, 1],'--', color=(0.6, 0.6, 0.6), label = 'Random')\n",
    "    \n",
    "    # Remember there are n_folds = 5, there there will be 0 - 4 ROC folds\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.show()\n",
    "\n",
    "print \"Support vector machines:\"\n",
    "plot_roc(X,y,SVC,probability=True)\n",
    "\n",
    "print \"Random forests:\"\n",
    "plot_roc(X,y,RF,n_estimators=18)\n",
    "\n",
    "print \"K-nearest-neighbors:\"\n",
    "plot_roc(X,y,KNN)\n",
    "\n",
    "print \"Gradient Boosting Classifier:\"\n",
    "plot_roc(X,y,GBC)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that we understand the accuracy of each individual model lets dice a little deeper to get a better understanding of what features or behaviors are causing our customers to churn."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going to use RandomForestClassifier to build decision trees to predict churn.\n",
    "\n",
    "First step is to build the decision tree to calculate the information gain.\n",
    "\n",
    "Let's look at the Top 1- features in our dataset that contribute to customer churn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature ranking:\n",
      "1. Account Length (0.163057)\n",
      "2. Int'l Plan (0.143775)\n",
      "3. VMail Plan (0.074115)\n",
      "4. VMail Message (0.071675)\n",
      "5. Day Mins (0.064395)\n",
      "6. Day Calls (0.039133)\n",
      "7. Day Charge (0.029995)\n",
      "8. Eve Mins (0.026002)\n",
      "9. Eve Calls (0.024487)\n",
      "10. Eve Charge (0.016137)\n"
     ]
    },
    {
     "data": {
      "image/png": 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EgRL+BThh2TIkzfgBzKr9CcuWDXgPI2K2MtWzD+bbVM9huacQZKpnRK9lqmcMRL51RMxP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\nRESBEv4REQVK+EdEFCjhHxFRoP8P8RYUN+McbEEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10c898f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "train_index, test_index = train_test_split(churn_df.index)\n",
    "\n",
    "forest = RF()\n",
    "forest_fit = forest.fit(X[train_index], y[train_index])\n",
    "forest_predictions = forest_fit.predict(X[test_index])\n",
    "\n",
    "importances = forest_fit.feature_importances_[:10]\n",
    "std = np.std([tree.feature_importances_ for tree in forest.estimators_], axis = 0)\n",
    "indices = np.argsort(importances)[::-1]\n",
    "\n",
    "# Print the feature ranking\n",
    "print(\"Feature ranking:\")\n",
    "\n",
    "for f in range(10):\n",
    "    print(\"%d. %s (%f)\" % (f + 1, features[f], importances[indices[f]]))\n",
    "    \n",
    "# Plot the feature importances of the forest\n",
    "# import pylab as pl\n",
    "\n",
    "plt.figure()\n",
    "plt.title(\"Feature importances\")\n",
    "# yerr --> the y error of the graph\n",
    "plt.bar(range(10), importances[indices], yerr=std[indices], color=\"r\", align=\"center\")\n",
    "plt.xticks(range(10), indices)\n",
    "plt.xlim([-1, 10])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we need to think is probabilities.\n",
    "\n",
    "To think of a customer as expected value of churn, we can gague their value and expected loss.\n",
    "\n",
    "E.g. Do you want edo reach out to a customer with an 80% churn risk who pays $20,000 annually or the client who is worth $100K with a 40% churn risk? How much should you spend on each client?\n",
    "\n",
    "This is different from ML ...you need to produce a prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def run_prob_cv(X, y, clf_class, roc=False, **kwargs):\n",
    "    kf = KFold(len(y), n_folds=5, shuffle=True)\n",
    "    y_prob = np.zeros((len(y),2))\n",
    "    for train_index, test_index in kf:\n",
    "        X_train, X_test = X[train_index], X[test_index]\n",
    "        y_train = y[train_index]\n",
    "        \n",
    "        # The CLF is the estimator that is then fitted to the model.\n",
    "        clf = clf_class(**kwargs)\n",
    "        clf.fit(X_train,y_train)\n",
    "        \n",
    "        # Predict probabilities, not classes\n",
    "        # predict_proba() --> svm_model stores all parameters needed to predict a given value.\n",
    "        y_prob[test_index] = clf.predict_proba(X_test)\n",
    "    return y_prob"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If I predict there's a 20% likelihood of x occuring tomorrow I don't get to live out all the possible outcomes of the universe. It either happens or it doesn't.\n",
    "\n",
    "So new we need to use pandas to compare the predictions made by the random forest against the actual outcomes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0    1755\n",
       "0.1     720\n",
       "0.2     251\n",
       "0.3     121\n",
       "0.5      81\n",
       "0.4      80\n",
       "0.8      71\n",
       "0.7      69\n",
       "0.9      65\n",
       "0.6      64\n",
       "1.0      56\n",
       "dtype: int64"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import warnings\n",
    "# Adding a warning\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "# Use 10 estimators so predictions are all multiples of 0.1\n",
    "pred_prob = run_prob_cv(X, y, RF, n_estimators=10)\n",
    "pred_churn = pred_prob[:,1]\n",
    "is_churn = y == 1\n",
    "\n",
    "# Number of times a predicted probability is assigned to an observation\n",
    "counts = pd.value_counts(pred_churn)\n",
    "counts[:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pred_prob</th>\n",
       "      <th>count</th>\n",
       "      <th>true_prob</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>1755</td>\n",
       "      <td>0.027350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.1</td>\n",
       "      <td>720</td>\n",
       "      <td>0.031944</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.2</td>\n",
       "      <td>251</td>\n",
       "      <td>0.051793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.3</td>\n",
       "      <td>121</td>\n",
       "      <td>0.132231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.4</td>\n",
       "      <td>80</td>\n",
       "      <td>0.412500</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.5</td>\n",
       "      <td>81</td>\n",
       "      <td>0.629630</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.6</td>\n",
       "      <td>64</td>\n",
       "      <td>0.750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.7</td>\n",
       "      <td>69</td>\n",
       "      <td>0.869565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.8</td>\n",
       "      <td>71</td>\n",
       "      <td>0.985915</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.9</td>\n",
       "      <td>65</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.0</td>\n",
       "      <td>56</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    pred_prob  count  true_prob\n",
       "0         0.0   1755   0.027350\n",
       "1         0.1    720   0.031944\n",
       "2         0.2    251   0.051793\n",
       "3         0.3    121   0.132231\n",
       "4         0.4     80   0.412500\n",
       "5         0.5     81   0.629630\n",
       "6         0.6     64   0.750000\n",
       "7         0.7     69   0.869565\n",
       "8         0.8     71   0.985915\n",
       "9         0.9     65   1.000000\n",
       "10        1.0     56   1.000000"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from collections import defaultdict\n",
    "# Returns a new dictionary-like object\n",
    "\n",
    "true_prob = defaultdict(float)\n",
    "\n",
    "# calculate true probabilities\n",
    "for prob in counts.index:\n",
    "    true_prob[prob] = np.mean(is_churn[pred_churn == prob])\n",
    "true_prob = pd.Series(true_prob)\n",
    "\n",
    "# pandas-fu\n",
    "counts = pd.concat([counts,true_prob], axis=1).reset_index()\n",
    "counts.columns = ['pred_prob', 'count', 'true_prob']\n",
    "counts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From this we can see we predicted a churn probability of 90% but the actual churn was 100%.\n",
    "While for 80% the actual churn was 98%"
   ]
  }
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