MachineLearning_Project_Notes.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Notes about the Intro to Machine Learning Project\n",
    "[Marcelo Tyszler](mailto:tyszler.jobs@gmail.com)\n",
    "\n",
    "26/Sep/2017\n",
    "\n",
    "In this notebook I summarize my steps and findings towards the Final Project in the Intro to Machine Learning course. This is in the Scope of the Udacity Data Analyst Nanodegree.\n",
    "\n",
    "# Choice of tools\n",
    "\n",
    "For this project I opted for:\n",
    "* Keep basic documentation and notes in the Jupyter Notebook\n",
    "* Save files in Github\n",
    "* Use PyCharm as Python environment\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Initial Data Exploration\n",
    "Initially I want to read all data and obtain initial summary statistics to get a feel of the full data and spot potential problems.\n",
    "\n",
    "I first load data for all available features. According to the documentation there should be 21 features:\n",
    "\n",
    "**financial features**: \\['salary', 'deferral_payments', 'total_payments', 'loan_advances', 'bonus', 'restricted_stock_deferred', 'deferred_income', 'total_stock_value', 'expenses', 'exercised_stock_options', 'other', 'long_term_incentive', 'restricted_stock', 'director_fees'] (all units are in US dollars)\n",
    "\n",
    "**email features**: \\['to_messages', 'email_address', 'from_poi_to_this_person', 'from_messages', 'from_this_person_to_poi', 'shared_receipt_with_poi'] (units are generally number of emails messages; notable exception is ‘email_address’, which is a text string)\n",
    "\n",
    "**POI label**: \\[‘poi’] (boolean, represented as integer)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pickle\n",
    "\n",
    "enron_data = pickle.load(open(\"final_project_dataset.pkl\", \"r\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of Persons: 146\n",
      "Features per Persons: 21\n"
     ]
    }
   ],
   "source": [
    "print \"Number of Persons: \" + str(len(enron_data))\n",
    "print \"Features per Persons: \" + str(len(enron_data[enron_data.keys()[0]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore I have 21 features about 146 persons. Let's double check the features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of Features:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['salary',\n",
       " 'to_messages',\n",
       " 'deferral_payments',\n",
       " 'total_payments',\n",
       " 'exercised_stock_options',\n",
       " 'bonus',\n",
       " 'restricted_stock',\n",
       " 'shared_receipt_with_poi',\n",
       " 'restricted_stock_deferred',\n",
       " 'total_stock_value',\n",
       " 'expenses',\n",
       " 'loan_advances',\n",
       " 'from_messages',\n",
       " 'other',\n",
       " 'from_this_person_to_poi',\n",
       " 'poi',\n",
       " 'director_fees',\n",
       " 'deferred_income',\n",
       " 'long_term_incentive',\n",
       " 'email_address',\n",
       " 'from_poi_to_this_person']"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print \"List of Features:\"\n",
    "enron_data[enron_data.keys()[0]].keys()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is what I expected according to the documentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's double check the list of persons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "List of Persons:\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "['ALLEN PHILLIP K',\n",
       " 'BADUM JAMES P',\n",
       " 'BANNANTINE JAMES M',\n",
       " 'BAXTER JOHN C',\n",
       " 'BAY FRANKLIN R',\n",
       " 'BAZELIDES PHILIP J',\n",
       " 'BECK SALLY W',\n",
       " 'BELDEN TIMOTHY N',\n",
       " 'BELFER ROBERT',\n",
       " 'BERBERIAN DAVID',\n",
       " 'BERGSIEKER RICHARD P',\n",
       " 'BHATNAGAR SANJAY',\n",
       " 'BIBI PHILIPPE A',\n",
       " 'BLACHMAN JEREMY M',\n",
       " 'BLAKE JR. NORMAN P',\n",
       " 'BOWEN JR RAYMOND M',\n",
       " 'BROWN MICHAEL',\n",
       " 'BUCHANAN HAROLD G',\n",
       " 'BUTTS ROBERT H',\n",
       " 'BUY RICHARD B',\n",
       " 'CALGER CHRISTOPHER F',\n",
       " 'CARTER REBECCA C',\n",
       " 'CAUSEY RICHARD A',\n",
       " 'CHAN RONNIE',\n",
       " 'CHRISTODOULOU DIOMEDES',\n",
       " 'CLINE KENNETH W',\n",
       " 'COLWELL WESLEY',\n",
       " 'CORDES WILLIAM R',\n",
       " 'COX DAVID',\n",
       " 'CUMBERLAND MICHAEL S',\n",
       " 'DEFFNER JOSEPH M',\n",
       " 'DELAINEY DAVID W',\n",
       " 'DERRICK JR. JAMES V',\n",
       " 'DETMERING TIMOTHY J',\n",
       " 'DIETRICH JANET R',\n",
       " 'DIMICHELE RICHARD G',\n",
       " 'DODSON KEITH',\n",
       " 'DONAHUE JR JEFFREY M',\n",
       " 'DUNCAN JOHN H',\n",
       " 'DURAN WILLIAM D',\n",
       " 'ECHOLS JOHN B',\n",
       " 'ELLIOTT STEVEN',\n",
       " 'FALLON JAMES B',\n",
       " 'FASTOW ANDREW S',\n",
       " 'FITZGERALD JAY L',\n",
       " 'FOWLER PEGGY',\n",
       " 'FOY JOE',\n",
       " 'FREVERT MARK A',\n",
       " 'FUGH JOHN L',\n",
       " 'GAHN ROBERT S',\n",
       " 'GARLAND C KEVIN',\n",
       " 'GATHMANN WILLIAM D',\n",
       " 'GIBBS DANA R',\n",
       " 'GILLIS JOHN',\n",
       " 'GLISAN JR BEN F',\n",
       " 'GOLD JOSEPH',\n",
       " 'GRAMM WENDY L',\n",
       " 'GRAY RODNEY',\n",
       " 'HAEDICKE MARK E',\n",
       " 'HANNON KEVIN P',\n",
       " 'HAUG DAVID L',\n",
       " 'HAYES ROBERT E',\n",
       " 'HAYSLETT RODERICK J',\n",
       " 'HERMANN ROBERT J',\n",
       " 'HICKERSON GARY J',\n",
       " 'HIRKO JOSEPH',\n",
       " 'HORTON STANLEY C',\n",
       " 'HUGHES JAMES A',\n",
       " 'HUMPHREY GENE E',\n",
       " 'IZZO LAWRENCE L',\n",
       " 'JACKSON CHARLENE R',\n",
       " 'JAEDICKE ROBERT',\n",
       " 'KAMINSKI WINCENTY J',\n",
       " 'KEAN STEVEN J',\n",
       " 'KISHKILL JOSEPH G',\n",
       " 'KITCHEN LOUISE',\n",
       " 'KOENIG MARK E',\n",
       " 'KOPPER MICHAEL J',\n",
       " 'LAVORATO JOHN J',\n",
       " 'LAY KENNETH L',\n",
       " 'LEFF DANIEL P',\n",
       " 'LEMAISTRE CHARLES',\n",
       " 'LEWIS RICHARD',\n",
       " 'LINDHOLM TOD A',\n",
       " 'LOCKHART EUGENE E',\n",
       " 'LOWRY CHARLES P',\n",
       " 'MARTIN AMANDA K',\n",
       " 'MCCARTY DANNY J',\n",
       " 'MCCLELLAN GEORGE',\n",
       " 'MCCONNELL MICHAEL S',\n",
       " 'MCDONALD REBECCA',\n",
       " 'MCMAHON JEFFREY',\n",
       " 'MENDELSOHN JOHN',\n",
       " 'METTS MARK',\n",
       " 'MEYER JEROME J',\n",
       " 'MEYER ROCKFORD G',\n",
       " 'MORAN MICHAEL P',\n",
       " 'MORDAUNT KRISTINA M',\n",
       " 'MULLER MARK S',\n",
       " 'MURRAY JULIA H',\n",
       " 'NOLES JAMES L',\n",
       " 'OLSON CINDY K',\n",
       " 'OVERDYKE JR JERE C',\n",
       " 'PAI LOU L',\n",
       " 'PEREIRA PAULO V. FERRAZ',\n",
       " 'PICKERING MARK R',\n",
       " 'PIPER GREGORY F',\n",
       " 'PIRO JIM',\n",
       " 'POWERS WILLIAM',\n",
       " 'PRENTICE JAMES',\n",
       " 'REDMOND BRIAN L',\n",
       " 'REYNOLDS LAWRENCE',\n",
       " 'RICE KENNETH D',\n",
       " 'RIEKER PAULA H',\n",
       " 'SAVAGE FRANK',\n",
       " 'SCRIMSHAW MATTHEW',\n",
       " 'SHANKMAN JEFFREY A',\n",
       " 'SHAPIRO RICHARD S',\n",
       " 'SHARP VICTORIA T',\n",
       " 'SHELBY REX',\n",
       " 'SHERRICK JEFFREY B',\n",
       " 'SHERRIFF JOHN R',\n",
       " 'SKILLING JEFFREY K',\n",
       " 'STABLER FRANK',\n",
       " 'SULLIVAN-SHAKLOVITZ COLLEEN',\n",
       " 'SUNDE MARTIN',\n",
       " 'TAYLOR MITCHELL S',\n",
       " 'THE TRAVEL AGENCY IN THE PARK',\n",
       " 'THORN TERENCE H',\n",
       " 'TILNEY ELIZABETH A',\n",
       " 'TOTAL',\n",
       " 'UMANOFF ADAM S',\n",
       " 'URQUHART JOHN A',\n",
       " 'WAKEHAM JOHN',\n",
       " 'WALLS JR ROBERT H',\n",
       " 'WALTERS GARETH W',\n",
       " 'WASAFF GEORGE',\n",
       " 'WESTFAHL RICHARD K',\n",
       " 'WHALEY DAVID A',\n",
       " 'WHALLEY LAWRENCE G',\n",
       " 'WHITE JR THOMAS E',\n",
       " 'WINOKUR JR. HERBERT S',\n",
       " 'WODRASKA JOHN',\n",
       " 'WROBEL BRUCE',\n",
       " 'YEAGER F SCOTT',\n",
       " 'YEAP SOON']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print \"List of Persons:\"\n",
    "sorted(enron_data.keys())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I spot 2 instances that need to be removed:  *TOTAL* and *THE TRAVEL AGENCY IN THE PARK*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'bonus': 'NaN',\n",
       " 'deferral_payments': 'NaN',\n",
       " 'deferred_income': 'NaN',\n",
       " 'director_fees': 'NaN',\n",
       " 'email_address': 'NaN',\n",
       " 'exercised_stock_options': 'NaN',\n",
       " 'expenses': 'NaN',\n",
       " 'from_messages': 'NaN',\n",
       " 'from_poi_to_this_person': 'NaN',\n",
       " 'from_this_person_to_poi': 'NaN',\n",
       " 'loan_advances': 'NaN',\n",
       " 'long_term_incentive': 'NaN',\n",
       " 'other': 362096,\n",
       " 'poi': False,\n",
       " 'restricted_stock': 'NaN',\n",
       " 'restricted_stock_deferred': 'NaN',\n",
       " 'salary': 'NaN',\n",
       " 'shared_receipt_with_poi': 'NaN',\n",
       " 'to_messages': 'NaN',\n",
       " 'total_payments': 362096,\n",
       " 'total_stock_value': 'NaN'}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data.pop('TOTAL',0)\n",
    "enron_data.pop('THE TRAVEL AGENCY IN THE PARK',0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how many POIs and non-POIs are in the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HANNON KEVIN P\n",
      "COLWELL WESLEY\n",
      "RIEKER PAULA H\n",
      "KOPPER MICHAEL J\n",
      "SHELBY REX\n",
      "DELAINEY DAVID W\n",
      "LAY KENNETH L\n",
      "BOWEN JR RAYMOND M\n",
      "BELDEN TIMOTHY N\n",
      "FASTOW ANDREW S\n",
      "CALGER CHRISTOPHER F\n",
      "RICE KENNETH D\n",
      "SKILLING JEFFREY K\n",
      "YEAGER F SCOTT\n",
      "HIRKO JOSEPH\n",
      "KOENIG MARK E\n",
      "CAUSEY RICHARD A\n",
      "GLISAN JR BEN F\n",
      "\n",
      "\n",
      "POIs:18\n",
      "non-POIs:126\n",
      "Total:144\n"
     ]
    }
   ],
   "source": [
    "POI = 0\n",
    "non_POI = 0\n",
    "for person in enron_data.keys():\n",
    "    if enron_data[person]['poi']:\n",
    "        print person\n",
    "        POI +=1\n",
    "    else:\n",
    "        non_POI +=1\n",
    "print \"\\n\"\n",
    "print \"POIs:\" + str(POI)\n",
    "print \"non-POIs:\" + str(non_POI)\n",
    "print \"Total:\" + str(POI+non_POI)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets get a feel for the data and print the data for some people"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "METTS MARK\n",
      "{'salary': 365788, 'to_messages': 807, 'deferral_payments': 'NaN', 'total_payments': 1061827, 'exercised_stock_options': 'NaN', 'bonus': 600000, 'restricted_stock': 585062, 'shared_receipt_with_poi': 702, 'restricted_stock_deferred': 'NaN', 'total_stock_value': 585062, 'expenses': 94299, 'loan_advances': 'NaN', 'from_messages': 29, 'other': 1740, 'from_this_person_to_poi': 1, 'poi': False, 'director_fees': 'NaN', 'deferred_income': 'NaN', 'long_term_incentive': 'NaN', 'email_address': 'mark.metts@enron.com', 'from_poi_to_this_person': 38}\n",
      "BAXTER JOHN C\n",
      "{'salary': 267102, 'to_messages': 'NaN', 'deferral_payments': 1295738, 'total_payments': 5634343, 'exercised_stock_options': 6680544, 'bonus': 1200000, 'restricted_stock': 3942714, 'shared_receipt_with_poi': 'NaN', 'restricted_stock_deferred': 'NaN', 'total_stock_value': 10623258, 'expenses': 11200, 'loan_advances': 'NaN', 'from_messages': 'NaN', 'other': 2660303, 'from_this_person_to_poi': 'NaN', 'poi': False, 'director_fees': 'NaN', 'deferred_income': -1386055, 'long_term_incentive': 1586055, 'email_address': 'NaN', 'from_poi_to_this_person': 'NaN'}\n",
      "ELLIOTT STEVEN\n",
      "{'salary': 170941, 'to_messages': 'NaN', 'deferral_payments': 'NaN', 'total_payments': 211725, 'exercised_stock_options': 4890344, 'bonus': 350000, 'restricted_stock': 1788391, 'shared_receipt_with_poi': 'NaN', 'restricted_stock_deferred': 'NaN', 'total_stock_value': 6678735, 'expenses': 78552, 'loan_advances': 'NaN', 'from_messages': 'NaN', 'other': 12961, 'from_this_person_to_poi': 'NaN', 'poi': False, 'director_fees': 'NaN', 'deferred_income': -400729, 'long_term_incentive': 'NaN', 'email_address': 'steven.elliott@enron.com', 'from_poi_to_this_person': 'NaN'}\n",
      "CORDES WILLIAM R\n",
      "{'salary': 'NaN', 'to_messages': 764, 'deferral_payments': 'NaN', 'total_payments': 'NaN', 'exercised_stock_options': 651850, 'bonus': 'NaN', 'restricted_stock': 386335, 'shared_receipt_with_poi': 58, 'restricted_stock_deferred': 'NaN', 'total_stock_value': 1038185, 'expenses': 'NaN', 'loan_advances': 'NaN', 'from_messages': 12, 'other': 'NaN', 'from_this_person_to_poi': 0, 'poi': False, 'director_fees': 'NaN', 'deferred_income': 'NaN', 'long_term_incentive': 'NaN', 'email_address': 'bill.cordes@enron.com', 'from_poi_to_this_person': 10}\n",
      "HANNON KEVIN P\n",
      "{'salary': 243293, 'to_messages': 1045, 'deferral_payments': 'NaN', 'total_payments': 288682, 'exercised_stock_options': 5538001, 'bonus': 1500000, 'restricted_stock': 853064, 'shared_receipt_with_poi': 1035, 'restricted_stock_deferred': 'NaN', 'total_stock_value': 6391065, 'expenses': 34039, 'loan_advances': 'NaN', 'from_messages': 32, 'other': 11350, 'from_this_person_to_poi': 21, 'poi': True, 'director_fees': 'NaN', 'deferred_income': -3117011, 'long_term_incentive': 1617011, 'email_address': 'kevin.hannon@enron.com', 'from_poi_to_this_person': 32}\n"
     ]
    }
   ],
   "source": [
    "test_keys = range(0,5)\n",
    "\n",
    "for key in test_keys:\n",
    "    print enron_data.keys()[key]\n",
    "    print(enron_data[enron_data.keys()[key]])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To get an even better look, I'll covert the data into a panda dataframe, and re-order the columns to match the pdf file."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "# Formatting for the output:\n",
    "pd.set_option('display.float_format', lambda x: '%.3f' % x)\n",
    "\n",
    "# Convert dictionary to DataFrame\n",
    "enron_data_df = pd.DataFrame.from_dict(enron_data, orient = 'index', dtype = float)\n",
    "\n",
    "# re-order columns\n",
    "enron_data_df = enron_data_df[\n",
    "['salary',\n",
    "'bonus',\n",
    "'long_term_incentive',\n",
    "'deferred_income',\n",
    "'deferral_payments',\n",
    "'loan_advances',\n",
    "'other',\n",
    "'expenses',\n",
    "'director_fees',\n",
    "'total_payments',\n",
    " 'exercised_stock_options',\n",
    "'restricted_stock',\n",
    " 'restricted_stock_deferred',\n",
    " 'total_stock_value',\n",
    " 'email_address',\n",
    " 'to_messages',\n",
    " 'shared_receipt_with_poi',\n",
    " 'from_messages',\n",
    " 'from_this_person_to_poi',\n",
    " 'poi',\n",
    " 'from_poi_to_this_person']]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print some rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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>salary</th>\n",
       "      <th>bonus</th>\n",
       "      <th>long_term_incentive</th>\n",
       "      <th>deferred_income</th>\n",
       "      <th>deferral_payments</th>\n",
       "      <th>loan_advances</th>\n",
       "      <th>other</th>\n",
       "      <th>expenses</th>\n",
       "      <th>director_fees</th>\n",
       "      <th>total_payments</th>\n",
       "      <th>...</th>\n",
       "      <th>restricted_stock</th>\n",
       "      <th>restricted_stock_deferred</th>\n",
       "      <th>total_stock_value</th>\n",
       "      <th>email_address</th>\n",
       "      <th>to_messages</th>\n",
       "      <th>shared_receipt_with_poi</th>\n",
       "      <th>from_messages</th>\n",
       "      <th>from_this_person_to_poi</th>\n",
       "      <th>poi</th>\n",
       "      <th>from_poi_to_this_person</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ALLEN PHILLIP K</th>\n",
       "      <td>201955.000</td>\n",
       "      <td>4175000.000</td>\n",
       "      <td>304805.000</td>\n",
       "      <td>-3081055.000</td>\n",
       "      <td>2869717.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>152.000</td>\n",
       "      <td>13868.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>4484442.000</td>\n",
       "      <td>...</td>\n",
       "      <td>126027.000</td>\n",
       "      <td>-126027.000</td>\n",
       "      <td>1729541.000</td>\n",
       "      <td>phillip.allen@enron.com</td>\n",
       "      <td>2902.000</td>\n",
       "      <td>1407.000</td>\n",
       "      <td>2195.000</td>\n",
       "      <td>65.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>47.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BADUM JAMES P</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>178980.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>3486.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>182466.000</td>\n",
       "      <td>...</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>257817.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BANNANTINE JAMES M</th>\n",
       "      <td>477.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>-5104.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>864523.000</td>\n",
       "      <td>56301.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>916197.000</td>\n",
       "      <td>...</td>\n",
       "      <td>1757552.000</td>\n",
       "      <td>-560222.000</td>\n",
       "      <td>5243487.000</td>\n",
       "      <td>james.bannantine@enron.com</td>\n",
       "      <td>566.000</td>\n",
       "      <td>465.000</td>\n",
       "      <td>29.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>39.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAXTER JOHN C</th>\n",
       "      <td>267102.000</td>\n",
       "      <td>1200000.000</td>\n",
       "      <td>1586055.000</td>\n",
       "      <td>-1386055.000</td>\n",
       "      <td>1295738.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>2660303.000</td>\n",
       "      <td>11200.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>5634343.000</td>\n",
       "      <td>...</td>\n",
       "      <td>3942714.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>10623258.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAY FRANKLIN R</th>\n",
       "      <td>239671.000</td>\n",
       "      <td>400000.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>-201641.000</td>\n",
       "      <td>260455.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>69.000</td>\n",
       "      <td>129142.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>827696.000</td>\n",
       "      <td>...</td>\n",
       "      <td>145796.000</td>\n",
       "      <td>-82782.000</td>\n",
       "      <td>63014.000</td>\n",
       "      <td>frank.bay@enron.com</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAZELIDES PHILIP J</th>\n",
       "      <td>80818.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>93750.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>684694.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>874.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>860136.000</td>\n",
       "      <td>...</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>1599641.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BECK SALLY W</th>\n",
       "      <td>231330.000</td>\n",
       "      <td>700000.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>566.000</td>\n",
       "      <td>37172.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>969068.000</td>\n",
       "      <td>...</td>\n",
       "      <td>126027.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>126027.000</td>\n",
       "      <td>sally.beck@enron.com</td>\n",
       "      <td>7315.000</td>\n",
       "      <td>2639.000</td>\n",
       "      <td>4343.000</td>\n",
       "      <td>386.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>144.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BELDEN TIMOTHY N</th>\n",
       "      <td>213999.000</td>\n",
       "      <td>5249999.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>-2334434.000</td>\n",
       "      <td>2144013.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>210698.000</td>\n",
       "      <td>17355.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>5501630.000</td>\n",
       "      <td>...</td>\n",
       "      <td>157569.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>1110705.000</td>\n",
       "      <td>tim.belden@enron.com</td>\n",
       "      <td>7991.000</td>\n",
       "      <td>5521.000</td>\n",
       "      <td>484.000</td>\n",
       "      <td>108.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>228.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BELFER ROBERT</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>-102500.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>3285.000</td>\n",
       "      <td>102500.000</td>\n",
       "      <td>...</td>\n",
       "      <td>nan</td>\n",
       "      <td>44093.000</td>\n",
       "      <td>-44093.000</td>\n",
       "      <td>NaN</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BERBERIAN DAVID</th>\n",
       "      <td>216582.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>11892.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>228474.000</td>\n",
       "      <td>...</td>\n",
       "      <td>869220.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>2493616.000</td>\n",
       "      <td>david.berberian@enron.com</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BERGSIEKER RICHARD P</th>\n",
       "      <td>187922.000</td>\n",
       "      <td>250000.000</td>\n",
       "      <td>180250.000</td>\n",
       "      <td>-485813.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>427316.000</td>\n",
       "      <td>59175.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>618850.000</td>\n",
       "      <td>...</td>\n",
       "      <td>659249.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>659249.000</td>\n",
       "      <td>rick.bergsieker@enron.com</td>\n",
       "      <td>383.000</td>\n",
       "      <td>233.000</td>\n",
       "      <td>59.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>4.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BHATNAGAR SANJAY</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>137864.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>137864.000</td>\n",
       "      <td>15456290.000</td>\n",
       "      <td>...</td>\n",
       "      <td>-2604490.000</td>\n",
       "      <td>15456290.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>sanjay.bhatnagar@enron.com</td>\n",
       "      <td>523.000</td>\n",
       "      <td>463.000</td>\n",
       "      <td>29.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BIBI PHILIPPE A</th>\n",
       "      <td>213625.000</td>\n",
       "      <td>1000000.000</td>\n",
       "      <td>369721.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>425688.000</td>\n",
       "      <td>38559.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>2047593.000</td>\n",
       "      <td>...</td>\n",
       "      <td>378082.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>1843816.000</td>\n",
       "      <td>philippe.bibi@enron.com</td>\n",
       "      <td>1607.000</td>\n",
       "      <td>1336.000</td>\n",
       "      <td>40.000</td>\n",
       "      <td>8.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>23.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BLACHMAN JEREMY M</th>\n",
       "      <td>248546.000</td>\n",
       "      <td>850000.000</td>\n",
       "      <td>831809.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>272.000</td>\n",
       "      <td>84208.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>2014835.000</td>\n",
       "      <td>...</td>\n",
       "      <td>189041.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>954354.000</td>\n",
       "      <td>jeremy.blachman@enron.com</td>\n",
       "      <td>2475.000</td>\n",
       "      <td>2326.000</td>\n",
       "      <td>14.000</td>\n",
       "      <td>2.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>25.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BLAKE JR. NORMAN P</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>-113784.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>1279.000</td>\n",
       "      <td>113784.000</td>\n",
       "      <td>1279.000</td>\n",
       "      <td>...</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>NaN</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BOWEN JR RAYMOND M</th>\n",
       "      <td>278601.000</td>\n",
       "      <td>1350000.000</td>\n",
       "      <td>974293.000</td>\n",
       "      <td>-833.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>1621.000</td>\n",
       "      <td>65907.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>2669589.000</td>\n",
       "      <td>...</td>\n",
       "      <td>252055.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>252055.000</td>\n",
       "      <td>raymond.bowen@enron.com</td>\n",
       "      <td>1858.000</td>\n",
       "      <td>1593.000</td>\n",
       "      <td>27.000</td>\n",
       "      <td>15.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>140.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BROWN MICHAEL</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>49288.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>49288.000</td>\n",
       "      <td>...</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>michael.brown@enron.com</td>\n",
       "      <td>1486.000</td>\n",
       "      <td>761.000</td>\n",
       "      <td>41.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>13.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BUCHANAN HAROLD G</th>\n",
       "      <td>248017.000</td>\n",
       "      <td>500000.000</td>\n",
       "      <td>304805.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>1215.000</td>\n",
       "      <td>600.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>1054637.000</td>\n",
       "      <td>...</td>\n",
       "      <td>189041.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>1014505.000</td>\n",
       "      <td>john.buchanan@enron.com</td>\n",
       "      <td>1088.000</td>\n",
       "      <td>23.000</td>\n",
       "      <td>125.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BUTTS ROBERT H</th>\n",
       "      <td>261516.000</td>\n",
       "      <td>750000.000</td>\n",
       "      <td>175000.000</td>\n",
       "      <td>-75000.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>150656.000</td>\n",
       "      <td>9410.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>1271582.000</td>\n",
       "      <td>...</td>\n",
       "      <td>417619.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>417619.000</td>\n",
       "      <td>bob.butts@enron.com</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BUY RICHARD B</th>\n",
       "      <td>330546.000</td>\n",
       "      <td>900000.000</td>\n",
       "      <td>769862.000</td>\n",
       "      <td>-694862.000</td>\n",
       "      <td>649584.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>400572.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>2355702.000</td>\n",
       "      <td>...</td>\n",
       "      <td>901657.000</td>\n",
       "      <td>nan</td>\n",
       "      <td>3444470.000</td>\n",
       "      <td>rick.buy@enron.com</td>\n",
       "      <td>3523.000</td>\n",
       "      <td>2333.000</td>\n",
       "      <td>1053.000</td>\n",
       "      <td>71.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>156.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>20 rows × 21 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                         salary       bonus  long_term_incentive  \\\n",
       "ALLEN PHILLIP K      201955.000 4175000.000           304805.000   \n",
       "BADUM JAMES P               nan         nan                  nan   \n",
       "BANNANTINE JAMES M      477.000         nan                  nan   \n",
       "BAXTER JOHN C        267102.000 1200000.000          1586055.000   \n",
       "BAY FRANKLIN R       239671.000  400000.000                  nan   \n",
       "BAZELIDES PHILIP J    80818.000         nan            93750.000   \n",
       "BECK SALLY W         231330.000  700000.000                  nan   \n",
       "BELDEN TIMOTHY N     213999.000 5249999.000                  nan   \n",
       "BELFER ROBERT               nan         nan                  nan   \n",
       "BERBERIAN DAVID      216582.000         nan                  nan   \n",
       "BERGSIEKER RICHARD P 187922.000  250000.000           180250.000   \n",
       "BHATNAGAR SANJAY            nan         nan                  nan   \n",
       "BIBI PHILIPPE A      213625.000 1000000.000           369721.000   \n",
       "BLACHMAN JEREMY M    248546.000  850000.000           831809.000   \n",
       "BLAKE JR. NORMAN P          nan         nan                  nan   \n",
       "BOWEN JR RAYMOND M   278601.000 1350000.000           974293.000   \n",
       "BROWN MICHAEL               nan         nan                  nan   \n",
       "BUCHANAN HAROLD G    248017.000  500000.000           304805.000   \n",
       "BUTTS ROBERT H       261516.000  750000.000           175000.000   \n",
       "BUY RICHARD B        330546.000  900000.000           769862.000   \n",
       "\n",
       "                      deferred_income  deferral_payments  loan_advances  \\\n",
       "ALLEN PHILLIP K          -3081055.000        2869717.000            nan   \n",
       "BADUM JAMES P                     nan         178980.000            nan   \n",
       "BANNANTINE JAMES M          -5104.000                nan            nan   \n",
       "BAXTER JOHN C            -1386055.000        1295738.000            nan   \n",
       "BAY FRANKLIN R            -201641.000         260455.000            nan   \n",
       "BAZELIDES PHILIP J                nan         684694.000            nan   \n",
       "BECK SALLY W                      nan                nan            nan   \n",
       "BELDEN TIMOTHY N         -2334434.000        2144013.000            nan   \n",
       "BELFER ROBERT                     nan        -102500.000            nan   \n",
       "BERBERIAN DAVID                   nan                nan            nan   \n",
       "BERGSIEKER RICHARD P      -485813.000                nan            nan   \n",
       "BHATNAGAR SANJAY                  nan                nan            nan   \n",
       "BIBI PHILIPPE A                   nan                nan            nan   \n",
       "BLACHMAN JEREMY M                 nan                nan            nan   \n",
       "BLAKE JR. NORMAN P        -113784.000                nan            nan   \n",
       "BOWEN JR RAYMOND M           -833.000                nan            nan   \n",
       "BROWN MICHAEL                     nan                nan            nan   \n",
       "BUCHANAN HAROLD G                 nan                nan            nan   \n",
       "BUTTS ROBERT H             -75000.000                nan            nan   \n",
       "BUY RICHARD B             -694862.000         649584.000            nan   \n",
       "\n",
       "                           other   expenses  director_fees  total_payments  \\\n",
       "ALLEN PHILLIP K          152.000  13868.000            nan     4484442.000   \n",
       "BADUM JAMES P                nan   3486.000            nan      182466.000   \n",
       "BANNANTINE JAMES M    864523.000  56301.000            nan      916197.000   \n",
       "BAXTER JOHN C        2660303.000  11200.000            nan     5634343.000   \n",
       "BAY FRANKLIN R            69.000 129142.000            nan      827696.000   \n",
       "BAZELIDES PHILIP J       874.000        nan            nan      860136.000   \n",
       "BECK SALLY W             566.000  37172.000            nan      969068.000   \n",
       "BELDEN TIMOTHY N      210698.000  17355.000            nan     5501630.000   \n",
       "BELFER ROBERT                nan        nan       3285.000      102500.000   \n",
       "BERBERIAN DAVID              nan  11892.000            nan      228474.000   \n",
       "BERGSIEKER RICHARD P  427316.000  59175.000            nan      618850.000   \n",
       "BHATNAGAR SANJAY      137864.000        nan     137864.000    15456290.000   \n",
       "BIBI PHILIPPE A       425688.000  38559.000            nan     2047593.000   \n",
       "BLACHMAN JEREMY M        272.000  84208.000            nan     2014835.000   \n",
       "BLAKE JR. NORMAN P           nan   1279.000     113784.000        1279.000   \n",
       "BOWEN JR RAYMOND M      1621.000  65907.000            nan     2669589.000   \n",
       "BROWN MICHAEL                nan  49288.000            nan       49288.000   \n",
       "BUCHANAN HAROLD G       1215.000    600.000            nan     1054637.000   \n",
       "BUTTS ROBERT H        150656.000   9410.000            nan     1271582.000   \n",
       "BUY RICHARD B         400572.000        nan            nan     2355702.000   \n",
       "\n",
       "                               ...             restricted_stock  \\\n",
       "ALLEN PHILLIP K                ...                   126027.000   \n",
       "BADUM JAMES P                  ...                          nan   \n",
       "BANNANTINE JAMES M             ...                  1757552.000   \n",
       "BAXTER JOHN C                  ...                  3942714.000   \n",
       "BAY FRANKLIN R                 ...                   145796.000   \n",
       "BAZELIDES PHILIP J             ...                          nan   \n",
       "BECK SALLY W                   ...                   126027.000   \n",
       "BELDEN TIMOTHY N               ...                   157569.000   \n",
       "BELFER ROBERT                  ...                          nan   \n",
       "BERBERIAN DAVID                ...                   869220.000   \n",
       "BERGSIEKER RICHARD P           ...                   659249.000   \n",
       "BHATNAGAR SANJAY               ...                 -2604490.000   \n",
       "BIBI PHILIPPE A                ...                   378082.000   \n",
       "BLACHMAN JEREMY M              ...                   189041.000   \n",
       "BLAKE JR. NORMAN P             ...                          nan   \n",
       "BOWEN JR RAYMOND M             ...                   252055.000   \n",
       "BROWN MICHAEL                  ...                          nan   \n",
       "BUCHANAN HAROLD G              ...                   189041.000   \n",
       "BUTTS ROBERT H                 ...                   417619.000   \n",
       "BUY RICHARD B                  ...                   901657.000   \n",
       "\n",
       "                      restricted_stock_deferred  total_stock_value  \\\n",
       "ALLEN PHILLIP K                     -126027.000        1729541.000   \n",
       "BADUM JAMES P                               nan         257817.000   \n",
       "BANNANTINE JAMES M                  -560222.000        5243487.000   \n",
       "BAXTER JOHN C                               nan       10623258.000   \n",
       "BAY FRANKLIN R                       -82782.000          63014.000   \n",
       "BAZELIDES PHILIP J                          nan        1599641.000   \n",
       "BECK SALLY W                                nan         126027.000   \n",
       "BELDEN TIMOTHY N                            nan        1110705.000   \n",
       "BELFER ROBERT                         44093.000         -44093.000   \n",
       "BERBERIAN DAVID                             nan        2493616.000   \n",
       "BERGSIEKER RICHARD P                        nan         659249.000   \n",
       "BHATNAGAR SANJAY                   15456290.000                nan   \n",
       "BIBI PHILIPPE A                             nan        1843816.000   \n",
       "BLACHMAN JEREMY M                           nan         954354.000   \n",
       "BLAKE JR. NORMAN P                          nan                nan   \n",
       "BOWEN JR RAYMOND M                          nan         252055.000   \n",
       "BROWN MICHAEL                               nan                nan   \n",
       "BUCHANAN HAROLD G                           nan        1014505.000   \n",
       "BUTTS ROBERT H                              nan         417619.000   \n",
       "BUY RICHARD B                               nan        3444470.000   \n",
       "\n",
       "                                   email_address to_messages  \\\n",
       "ALLEN PHILLIP K          phillip.allen@enron.com    2902.000   \n",
       "BADUM JAMES P                                NaN         nan   \n",
       "BANNANTINE JAMES M    james.bannantine@enron.com     566.000   \n",
       "BAXTER JOHN C                                NaN         nan   \n",
       "BAY FRANKLIN R               frank.bay@enron.com         nan   \n",
       "BAZELIDES PHILIP J                           NaN         nan   \n",
       "BECK SALLY W                sally.beck@enron.com    7315.000   \n",
       "BELDEN TIMOTHY N            tim.belden@enron.com    7991.000   \n",
       "BELFER ROBERT                                NaN         nan   \n",
       "BERBERIAN DAVID        david.berberian@enron.com         nan   \n",
       "BERGSIEKER RICHARD P   rick.bergsieker@enron.com     383.000   \n",
       "BHATNAGAR SANJAY      sanjay.bhatnagar@enron.com     523.000   \n",
       "BIBI PHILIPPE A          philippe.bibi@enron.com    1607.000   \n",
       "BLACHMAN JEREMY M      jeremy.blachman@enron.com    2475.000   \n",
       "BLAKE JR. NORMAN P                           NaN         nan   \n",
       "BOWEN JR RAYMOND M       raymond.bowen@enron.com    1858.000   \n",
       "BROWN MICHAEL            michael.brown@enron.com    1486.000   \n",
       "BUCHANAN HAROLD G        john.buchanan@enron.com    1088.000   \n",
       "BUTTS ROBERT H               bob.butts@enron.com         nan   \n",
       "BUY RICHARD B                 rick.buy@enron.com    3523.000   \n",
       "\n",
       "                      shared_receipt_with_poi  from_messages  \\\n",
       "ALLEN PHILLIP K                      1407.000       2195.000   \n",
       "BADUM JAMES P                             nan            nan   \n",
       "BANNANTINE JAMES M                    465.000         29.000   \n",
       "BAXTER JOHN C                             nan            nan   \n",
       "BAY FRANKLIN R                            nan            nan   \n",
       "BAZELIDES PHILIP J                        nan            nan   \n",
       "BECK SALLY W                         2639.000       4343.000   \n",
       "BELDEN TIMOTHY N                     5521.000        484.000   \n",
       "BELFER ROBERT                             nan            nan   \n",
       "BERBERIAN DAVID                           nan            nan   \n",
       "BERGSIEKER RICHARD P                  233.000         59.000   \n",
       "BHATNAGAR SANJAY                      463.000         29.000   \n",
       "BIBI PHILIPPE A                      1336.000         40.000   \n",
       "BLACHMAN JEREMY M                    2326.000         14.000   \n",
       "BLAKE JR. NORMAN P                        nan            nan   \n",
       "BOWEN JR RAYMOND M                   1593.000         27.000   \n",
       "BROWN MICHAEL                         761.000         41.000   \n",
       "BUCHANAN HAROLD G                      23.000        125.000   \n",
       "BUTTS ROBERT H                            nan            nan   \n",
       "BUY RICHARD B                        2333.000       1053.000   \n",
       "\n",
       "                      from_this_person_to_poi   poi  from_poi_to_this_person  \n",
       "ALLEN PHILLIP K                        65.000 0.000                   47.000  \n",
       "BADUM JAMES P                             nan 0.000                      nan  \n",
       "BANNANTINE JAMES M                      0.000 0.000                   39.000  \n",
       "BAXTER JOHN C                             nan 0.000                      nan  \n",
       "BAY FRANKLIN R                            nan 0.000                      nan  \n",
       "BAZELIDES PHILIP J                        nan 0.000                      nan  \n",
       "BECK SALLY W                          386.000 0.000                  144.000  \n",
       "BELDEN TIMOTHY N                      108.000 1.000                  228.000  \n",
       "BELFER ROBERT                             nan 0.000                      nan  \n",
       "BERBERIAN DAVID                           nan 0.000                      nan  \n",
       "BERGSIEKER RICHARD P                    0.000 0.000                    4.000  \n",
       "BHATNAGAR SANJAY                        1.000 0.000                    0.000  \n",
       "BIBI PHILIPPE A                         8.000 0.000                   23.000  \n",
       "BLACHMAN JEREMY M                       2.000 0.000                   25.000  \n",
       "BLAKE JR. NORMAN P                        nan 0.000                      nan  \n",
       "BOWEN JR RAYMOND M                     15.000 1.000                  140.000  \n",
       "BROWN MICHAEL                           1.000 0.000                   13.000  \n",
       "BUCHANAN HAROLD G                       0.000 0.000                    0.000  \n",
       "BUTTS ROBERT H                            nan 0.000                      nan  \n",
       "BUY RICHARD B                          71.000 0.000                  156.000  \n",
       "\n",
       "[20 rows x 21 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df.head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and summary statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\marcelot\\AppData\\Local\\Continuum\\Anaconda2\\lib\\site-packages\\numpy\\lib\\function_base.py:3834: RuntimeWarning: Invalid value encountered in percentile\n",
      "  RuntimeWarning)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>salary</th>\n",
       "      <th>bonus</th>\n",
       "      <th>long_term_incentive</th>\n",
       "      <th>deferred_income</th>\n",
       "      <th>deferral_payments</th>\n",
       "      <th>loan_advances</th>\n",
       "      <th>other</th>\n",
       "      <th>expenses</th>\n",
       "      <th>director_fees</th>\n",
       "      <th>total_payments</th>\n",
       "      <th>exercised_stock_options</th>\n",
       "      <th>restricted_stock</th>\n",
       "      <th>restricted_stock_deferred</th>\n",
       "      <th>total_stock_value</th>\n",
       "      <th>to_messages</th>\n",
       "      <th>shared_receipt_with_poi</th>\n",
       "      <th>from_messages</th>\n",
       "      <th>from_this_person_to_poi</th>\n",
       "      <th>poi</th>\n",
       "      <th>from_poi_to_this_person</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>94.000</td>\n",
       "      <td>81.000</td>\n",
       "      <td>65.000</td>\n",
       "      <td>48.000</td>\n",
       "      <td>38.000</td>\n",
       "      <td>3.000</td>\n",
       "      <td>91.000</td>\n",
       "      <td>94.000</td>\n",
       "      <td>16.000</td>\n",
       "      <td>123.000</td>\n",
       "      <td>101.000</td>\n",
       "      <td>109.000</td>\n",
       "      <td>17.000</td>\n",
       "      <td>125.000</td>\n",
       "      <td>86.000</td>\n",
       "      <td>86.000</td>\n",
       "      <td>86.000</td>\n",
       "      <td>86.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>86.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>284087.543</td>\n",
       "      <td>1201773.074</td>\n",
       "      <td>746491.200</td>\n",
       "      <td>-581049.812</td>\n",
       "      <td>841602.526</td>\n",
       "      <td>27975000.000</td>\n",
       "      <td>466410.516</td>\n",
       "      <td>54192.011</td>\n",
       "      <td>89822.875</td>\n",
       "      <td>2641805.935</td>\n",
       "      <td>2959559.257</td>\n",
       "      <td>1147424.092</td>\n",
       "      <td>621892.824</td>\n",
       "      <td>3352073.024</td>\n",
       "      <td>2073.860</td>\n",
       "      <td>1176.465</td>\n",
       "      <td>608.791</td>\n",
       "      <td>41.233</td>\n",
       "      <td>0.125</td>\n",
       "      <td>64.895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>177131.115</td>\n",
       "      <td>1441679.438</td>\n",
       "      <td>862917.422</td>\n",
       "      <td>942076.403</td>\n",
       "      <td>1289322.626</td>\n",
       "      <td>46382560.031</td>\n",
       "      <td>1397375.608</td>\n",
       "      <td>46108.377</td>\n",
       "      <td>41112.701</td>\n",
       "      <td>9524693.906</td>\n",
       "      <td>5499449.599</td>\n",
       "      <td>2249770.357</td>\n",
       "      <td>3845528.350</td>\n",
       "      <td>6532883.097</td>\n",
       "      <td>2582.701</td>\n",
       "      <td>1178.318</td>\n",
       "      <td>1841.034</td>\n",
       "      <td>100.073</td>\n",
       "      <td>0.332</td>\n",
       "      <td>86.979</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>477.000</td>\n",
       "      <td>70000.000</td>\n",
       "      <td>69223.000</td>\n",
       "      <td>-3504386.000</td>\n",
       "      <td>-102500.000</td>\n",
       "      <td>400000.000</td>\n",
       "      <td>2.000</td>\n",
       "      <td>148.000</td>\n",
       "      <td>3285.000</td>\n",
       "      <td>148.000</td>\n",
       "      <td>3285.000</td>\n",
       "      <td>-2604490.000</td>\n",
       "      <td>-1787380.000</td>\n",
       "      <td>-44093.000</td>\n",
       "      <td>57.000</td>\n",
       "      <td>2.000</td>\n",
       "      <td>12.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>nan</td>\n",
       "      <td>0.000</td>\n",
       "      <td>nan</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1111258.000</td>\n",
       "      <td>8000000.000</td>\n",
       "      <td>5145434.000</td>\n",
       "      <td>-833.000</td>\n",
       "      <td>6426990.000</td>\n",
       "      <td>81525000.000</td>\n",
       "      <td>10359729.000</td>\n",
       "      <td>228763.000</td>\n",
       "      <td>137864.000</td>\n",
       "      <td>103559793.000</td>\n",
       "      <td>34348384.000</td>\n",
       "      <td>14761694.000</td>\n",
       "      <td>15456290.000</td>\n",
       "      <td>49110078.000</td>\n",
       "      <td>15149.000</td>\n",
       "      <td>5521.000</td>\n",
       "      <td>14368.000</td>\n",
       "      <td>609.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>528.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           salary       bonus  long_term_incentive  deferred_income  \\\n",
       "count      94.000      81.000               65.000           48.000   \n",
       "mean   284087.543 1201773.074           746491.200      -581049.812   \n",
       "std    177131.115 1441679.438           862917.422       942076.403   \n",
       "min       477.000   70000.000            69223.000     -3504386.000   \n",
       "25%           nan         nan                  nan              nan   \n",
       "50%           nan         nan                  nan              nan   \n",
       "75%           nan         nan                  nan              nan   \n",
       "max   1111258.000 8000000.000          5145434.000         -833.000   \n",
       "\n",
       "       deferral_payments  loan_advances        other   expenses  \\\n",
       "count             38.000          3.000       91.000     94.000   \n",
       "mean          841602.526   27975000.000   466410.516  54192.011   \n",
       "std          1289322.626   46382560.031  1397375.608  46108.377   \n",
       "min          -102500.000     400000.000        2.000    148.000   \n",
       "25%                  nan            nan          nan        nan   \n",
       "50%                  nan            nan          nan        nan   \n",
       "75%                  nan            nan          nan        nan   \n",
       "max          6426990.000   81525000.000 10359729.000 228763.000   \n",
       "\n",
       "       director_fees  total_payments  exercised_stock_options  \\\n",
       "count         16.000         123.000                  101.000   \n",
       "mean       89822.875     2641805.935              2959559.257   \n",
       "std        41112.701     9524693.906              5499449.599   \n",
       "min         3285.000         148.000                 3285.000   \n",
       "25%              nan             nan                      nan   \n",
       "50%              nan             nan                      nan   \n",
       "75%              nan             nan                      nan   \n",
       "max       137864.000   103559793.000             34348384.000   \n",
       "\n",
       "       restricted_stock  restricted_stock_deferred  total_stock_value  \\\n",
       "count           109.000                     17.000            125.000   \n",
       "mean        1147424.092                 621892.824        3352073.024   \n",
       "std         2249770.357                3845528.350        6532883.097   \n",
       "min        -2604490.000               -1787380.000         -44093.000   \n",
       "25%                 nan                        nan                nan   \n",
       "50%                 nan                        nan                nan   \n",
       "75%                 nan                        nan                nan   \n",
       "max        14761694.000               15456290.000       49110078.000   \n",
       "\n",
       "       to_messages  shared_receipt_with_poi  from_messages  \\\n",
       "count       86.000                   86.000         86.000   \n",
       "mean      2073.860                 1176.465        608.791   \n",
       "std       2582.701                 1178.318       1841.034   \n",
       "min         57.000                    2.000         12.000   \n",
       "25%            nan                      nan            nan   \n",
       "50%            nan                      nan            nan   \n",
       "75%            nan                      nan            nan   \n",
       "max      15149.000                 5521.000      14368.000   \n",
       "\n",
       "       from_this_person_to_poi     poi  from_poi_to_this_person  \n",
       "count                   86.000 144.000                   86.000  \n",
       "mean                    41.233   0.125                   64.895  \n",
       "std                    100.073   0.332                   86.979  \n",
       "min                      0.000   0.000                    0.000  \n",
       "25%                        nan   0.000                      nan  \n",
       "50%                        nan   0.000                      nan  \n",
       "75%                        nan   0.000                      nan  \n",
       "max                    609.000   1.000                  528.000  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's convert all NaN to 0 to see the data better"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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>salary</th>\n",
       "      <th>bonus</th>\n",
       "      <th>long_term_incentive</th>\n",
       "      <th>deferred_income</th>\n",
       "      <th>deferral_payments</th>\n",
       "      <th>loan_advances</th>\n",
       "      <th>other</th>\n",
       "      <th>expenses</th>\n",
       "      <th>director_fees</th>\n",
       "      <th>total_payments</th>\n",
       "      <th>exercised_stock_options</th>\n",
       "      <th>restricted_stock</th>\n",
       "      <th>restricted_stock_deferred</th>\n",
       "      <th>total_stock_value</th>\n",
       "      <th>to_messages</th>\n",
       "      <th>shared_receipt_with_poi</th>\n",
       "      <th>from_messages</th>\n",
       "      <th>from_this_person_to_poi</th>\n",
       "      <th>poi</th>\n",
       "      <th>from_poi_to_this_person</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>185446.035</td>\n",
       "      <td>675997.354</td>\n",
       "      <td>336957.833</td>\n",
       "      <td>-193683.271</td>\n",
       "      <td>222089.556</td>\n",
       "      <td>582812.500</td>\n",
       "      <td>294745.535</td>\n",
       "      <td>35375.340</td>\n",
       "      <td>9980.319</td>\n",
       "      <td>2256542.569</td>\n",
       "      <td>2075801.979</td>\n",
       "      <td>868536.292</td>\n",
       "      <td>73417.903</td>\n",
       "      <td>2909785.611</td>\n",
       "      <td>1238.556</td>\n",
       "      <td>702.611</td>\n",
       "      <td>363.583</td>\n",
       "      <td>24.625</td>\n",
       "      <td>0.125</td>\n",
       "      <td>38.757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>197042.124</td>\n",
       "      <td>1233155.256</td>\n",
       "      <td>687182.568</td>\n",
       "      <td>606011.135</td>\n",
       "      <td>754101.303</td>\n",
       "      <td>6794471.779</td>\n",
       "      <td>1131325.453</td>\n",
       "      <td>45309.303</td>\n",
       "      <td>31300.575</td>\n",
       "      <td>8847188.787</td>\n",
       "      <td>4795513.145</td>\n",
       "      <td>2016572.389</td>\n",
       "      <td>1301983.390</td>\n",
       "      <td>6189018.075</td>\n",
       "      <td>2237.565</td>\n",
       "      <td>1077.291</td>\n",
       "      <td>1450.675</td>\n",
       "      <td>79.778</td>\n",
       "      <td>0.332</td>\n",
       "      <td>74.277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-3504386.000</td>\n",
       "      <td>-102500.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-2604490.000</td>\n",
       "      <td>-1787380.000</td>\n",
       "      <td>-44093.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-37086.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>90192.750</td>\n",
       "      <td>0.000</td>\n",
       "      <td>24345.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>244326.500</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>210596.000</td>\n",
       "      <td>300000.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>919.000</td>\n",
       "      <td>20182.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>941359.500</td>\n",
       "      <td>608293.500</td>\n",
       "      <td>360528.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>965955.000</td>\n",
       "      <td>347.500</td>\n",
       "      <td>114.000</td>\n",
       "      <td>17.500</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>4.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>269667.500</td>\n",
       "      <td>800000.000</td>\n",
       "      <td>374586.250</td>\n",
       "      <td>0.000</td>\n",
       "      <td>8535.500</td>\n",
       "      <td>0.000</td>\n",
       "      <td>148577.000</td>\n",
       "      <td>53328.250</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1945668.250</td>\n",
       "      <td>1683580.250</td>\n",
       "      <td>737456.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2295175.750</td>\n",
       "      <td>1623.000</td>\n",
       "      <td>933.750</td>\n",
       "      <td>53.000</td>\n",
       "      <td>14.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>41.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1111258.000</td>\n",
       "      <td>8000000.000</td>\n",
       "      <td>5145434.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>6426990.000</td>\n",
       "      <td>81525000.000</td>\n",
       "      <td>10359729.000</td>\n",
       "      <td>228763.000</td>\n",
       "      <td>137864.000</td>\n",
       "      <td>103559793.000</td>\n",
       "      <td>34348384.000</td>\n",
       "      <td>14761694.000</td>\n",
       "      <td>15456290.000</td>\n",
       "      <td>49110078.000</td>\n",
       "      <td>15149.000</td>\n",
       "      <td>5521.000</td>\n",
       "      <td>14368.000</td>\n",
       "      <td>609.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>528.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           salary       bonus  long_term_incentive  deferred_income  \\\n",
       "count     144.000     144.000              144.000          144.000   \n",
       "mean   185446.035  675997.354           336957.833      -193683.271   \n",
       "std    197042.124 1233155.256           687182.568       606011.135   \n",
       "min         0.000       0.000                0.000     -3504386.000   \n",
       "25%         0.000       0.000                0.000       -37086.000   \n",
       "50%    210596.000  300000.000                0.000            0.000   \n",
       "75%    269667.500  800000.000           374586.250            0.000   \n",
       "max   1111258.000 8000000.000          5145434.000            0.000   \n",
       "\n",
       "       deferral_payments  loan_advances        other   expenses  \\\n",
       "count            144.000        144.000      144.000    144.000   \n",
       "mean          222089.556     582812.500   294745.535  35375.340   \n",
       "std           754101.303    6794471.779  1131325.453  45309.303   \n",
       "min          -102500.000          0.000        0.000      0.000   \n",
       "25%                0.000          0.000        0.000      0.000   \n",
       "50%                0.000          0.000      919.000  20182.000   \n",
       "75%             8535.500          0.000   148577.000  53328.250   \n",
       "max          6426990.000   81525000.000 10359729.000 228763.000   \n",
       "\n",
       "       director_fees  total_payments  exercised_stock_options  \\\n",
       "count        144.000         144.000                  144.000   \n",
       "mean        9980.319     2256542.569              2075801.979   \n",
       "std        31300.575     8847188.787              4795513.145   \n",
       "min            0.000           0.000                    0.000   \n",
       "25%            0.000       90192.750                    0.000   \n",
       "50%            0.000      941359.500               608293.500   \n",
       "75%            0.000     1945668.250              1683580.250   \n",
       "max       137864.000   103559793.000             34348384.000   \n",
       "\n",
       "       restricted_stock  restricted_stock_deferred  total_stock_value  \\\n",
       "count           144.000                    144.000            144.000   \n",
       "mean         868536.292                  73417.903        2909785.611   \n",
       "std         2016572.389                1301983.390        6189018.075   \n",
       "min        -2604490.000               -1787380.000         -44093.000   \n",
       "25%           24345.000                      0.000         244326.500   \n",
       "50%          360528.000                      0.000         965955.000   \n",
       "75%          737456.000                      0.000        2295175.750   \n",
       "max        14761694.000               15456290.000       49110078.000   \n",
       "\n",
       "       to_messages  shared_receipt_with_poi  from_messages  \\\n",
       "count      144.000                  144.000        144.000   \n",
       "mean      1238.556                  702.611        363.583   \n",
       "std       2237.565                 1077.291       1450.675   \n",
       "min          0.000                    0.000          0.000   \n",
       "25%          0.000                    0.000          0.000   \n",
       "50%        347.500                  114.000         17.500   \n",
       "75%       1623.000                  933.750         53.000   \n",
       "max      15149.000                 5521.000      14368.000   \n",
       "\n",
       "       from_this_person_to_poi     poi  from_poi_to_this_person  \n",
       "count                  144.000 144.000                  144.000  \n",
       "mean                    24.625   0.125                   38.757  \n",
       "std                     79.778   0.332                   74.277  \n",
       "min                      0.000   0.000                    0.000  \n",
       "25%                      0.000   0.000                    0.000  \n",
       "50%                      0.000   0.000                    4.000  \n",
       "75%                     14.000   0.000                   41.250  \n",
       "max                    609.000   1.000                  528.000  "
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df = enron_data_df.fillna(0)\n",
    "enron_data_df.describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One thing that gets my attention is that *deferral_payments* has negative values, which should not be the case.\n",
    "\n",
    "Let's see who has this problem:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BELFER ROBERT\n"
     ]
    }
   ],
   "source": [
    "for person in enron_data.keys():\n",
    "    if enron_data[person]['deferral_payments']<0:\n",
    "        print person"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see the full data from this person:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "salary                            0.000\n",
       "bonus                             0.000\n",
       "long_term_incentive               0.000\n",
       "deferred_income                   0.000\n",
       "deferral_payments           -102500.000\n",
       "loan_advances                     0.000\n",
       "other                             0.000\n",
       "expenses                          0.000\n",
       "director_fees                  3285.000\n",
       "total_payments               102500.000\n",
       "exercised_stock_options        3285.000\n",
       "restricted_stock                  0.000\n",
       "restricted_stock_deferred     44093.000\n",
       "total_stock_value            -44093.000\n",
       "email_address                       NaN\n",
       "to_messages                       0.000\n",
       "shared_receipt_with_poi           0.000\n",
       "from_messages                     0.000\n",
       "from_this_person_to_poi           0.000\n",
       "poi                               0.000\n",
       "from_poi_to_this_person           0.000\n",
       "Name: BELFER ROBERT, dtype: object"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df.loc['BELFER ROBERT']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By comparing with the PDF, I notice that the financial data is imported wrongly, with a shift in financial columns. You can see that *total_payments* should be 3285, but is listed as 102500, which is the value of the expenses..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before fixing it, I'll check if this happens more often. A way to check is re-create the *total_payments* by adding the other columns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "enron_data_df['compute_total_payment'] = \\\n",
    "enron_data_df['salary'] + \\\n",
    "enron_data_df['bonus'] + \\\n",
    "enron_data_df['long_term_incentive'] + \\\n",
    "enron_data_df['deferred_income'] + \\\n",
    "enron_data_df['deferral_payments'] + \\\n",
    "enron_data_df['loan_advances'] + \\\n",
    "enron_data_df['other'] +  \\\n",
    "enron_data_df['expenses'] + \\\n",
    "enron_data_df['director_fees'] \n",
    "\n",
    "enron_data_df['compute_total_stock'] = \\\n",
    "enron_data_df['exercised_stock_options'] + \\\n",
    "enron_data_df['restricted_stock'] + \\\n",
    "enron_data_df['restricted_stock_deferred'] \n",
    "\n",
    "\n",
    "enron_data_df['check_total_payment'] = enron_data_df['compute_total_payment'] == enron_data_df['total_payments']\n",
    "enron_data_df['check_total_stock'] = enron_data_df['compute_total_stock'] == enron_data_df['total_stock_value']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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>salary</th>\n",
       "      <th>bonus</th>\n",
       "      <th>long_term_incentive</th>\n",
       "      <th>deferred_income</th>\n",
       "      <th>deferral_payments</th>\n",
       "      <th>loan_advances</th>\n",
       "      <th>other</th>\n",
       "      <th>expenses</th>\n",
       "      <th>director_fees</th>\n",
       "      <th>total_payments</th>\n",
       "      <th>...</th>\n",
       "      <th>to_messages</th>\n",
       "      <th>shared_receipt_with_poi</th>\n",
       "      <th>from_messages</th>\n",
       "      <th>from_this_person_to_poi</th>\n",
       "      <th>poi</th>\n",
       "      <th>from_poi_to_this_person</th>\n",
       "      <th>compute_total_payment</th>\n",
       "      <th>compute_total_stock</th>\n",
       "      <th>check_total_payment</th>\n",
       "      <th>check_total_stock</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>BELFER ROBERT</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-102500.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>3285.000</td>\n",
       "      <td>102500.000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-99215.000</td>\n",
       "      <td>47378.000</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BHATNAGAR SANJAY</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>137864.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>137864.000</td>\n",
       "      <td>15456290.000</td>\n",
       "      <td>...</td>\n",
       "      <td>523.000</td>\n",
       "      <td>463.000</td>\n",
       "      <td>29.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>275728.000</td>\n",
       "      <td>15456290.000</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 25 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  salary  bonus  long_term_incentive  deferred_income  \\\n",
       "BELFER ROBERT      0.000  0.000                0.000            0.000   \n",
       "BHATNAGAR SANJAY   0.000  0.000                0.000            0.000   \n",
       "\n",
       "                  deferral_payments  loan_advances      other  expenses  \\\n",
       "BELFER ROBERT           -102500.000          0.000      0.000     0.000   \n",
       "BHATNAGAR SANJAY              0.000          0.000 137864.000     0.000   \n",
       "\n",
       "                  director_fees  total_payments        ...          \\\n",
       "BELFER ROBERT          3285.000      102500.000        ...           \n",
       "BHATNAGAR SANJAY     137864.000    15456290.000        ...           \n",
       "\n",
       "                  to_messages  shared_receipt_with_poi  from_messages  \\\n",
       "BELFER ROBERT           0.000                    0.000          0.000   \n",
       "BHATNAGAR SANJAY      523.000                  463.000         29.000   \n",
       "\n",
       "                  from_this_person_to_poi   poi  from_poi_to_this_person  \\\n",
       "BELFER ROBERT                       0.000 0.000                    0.000   \n",
       "BHATNAGAR SANJAY                    1.000 0.000                    0.000   \n",
       "\n",
       "                  compute_total_payment  compute_total_stock  \\\n",
       "BELFER ROBERT                -99215.000            47378.000   \n",
       "BHATNAGAR SANJAY             275728.000         15456290.000   \n",
       "\n",
       "                  check_total_payment  check_total_stock  \n",
       "BELFER ROBERT                   False              False  \n",
       "BHATNAGAR SANJAY                False              False  \n",
       "\n",
       "[2 rows x 25 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df[enron_data_df['check_total_payment']==0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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>salary</th>\n",
       "      <th>bonus</th>\n",
       "      <th>long_term_incentive</th>\n",
       "      <th>deferred_income</th>\n",
       "      <th>deferral_payments</th>\n",
       "      <th>loan_advances</th>\n",
       "      <th>other</th>\n",
       "      <th>expenses</th>\n",
       "      <th>director_fees</th>\n",
       "      <th>total_payments</th>\n",
       "      <th>...</th>\n",
       "      <th>to_messages</th>\n",
       "      <th>shared_receipt_with_poi</th>\n",
       "      <th>from_messages</th>\n",
       "      <th>from_this_person_to_poi</th>\n",
       "      <th>poi</th>\n",
       "      <th>from_poi_to_this_person</th>\n",
       "      <th>compute_total_payment</th>\n",
       "      <th>compute_total_stock</th>\n",
       "      <th>check_total_payment</th>\n",
       "      <th>check_total_stock</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>BELFER ROBERT</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-102500.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>3285.000</td>\n",
       "      <td>102500.000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-99215.000</td>\n",
       "      <td>47378.000</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BHATNAGAR SANJAY</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>137864.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>137864.000</td>\n",
       "      <td>15456290.000</td>\n",
       "      <td>...</td>\n",
       "      <td>523.000</td>\n",
       "      <td>463.000</td>\n",
       "      <td>29.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>275728.000</td>\n",
       "      <td>15456290.000</td>\n",
       "      <td>False</td>\n",
       "      <td>False</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>2 rows × 25 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                  salary  bonus  long_term_incentive  deferred_income  \\\n",
       "BELFER ROBERT      0.000  0.000                0.000            0.000   \n",
       "BHATNAGAR SANJAY   0.000  0.000                0.000            0.000   \n",
       "\n",
       "                  deferral_payments  loan_advances      other  expenses  \\\n",
       "BELFER ROBERT           -102500.000          0.000      0.000     0.000   \n",
       "BHATNAGAR SANJAY              0.000          0.000 137864.000     0.000   \n",
       "\n",
       "                  director_fees  total_payments        ...          \\\n",
       "BELFER ROBERT          3285.000      102500.000        ...           \n",
       "BHATNAGAR SANJAY     137864.000    15456290.000        ...           \n",
       "\n",
       "                  to_messages  shared_receipt_with_poi  from_messages  \\\n",
       "BELFER ROBERT           0.000                    0.000          0.000   \n",
       "BHATNAGAR SANJAY      523.000                  463.000         29.000   \n",
       "\n",
       "                  from_this_person_to_poi   poi  from_poi_to_this_person  \\\n",
       "BELFER ROBERT                       0.000 0.000                    0.000   \n",
       "BHATNAGAR SANJAY                    1.000 0.000                    0.000   \n",
       "\n",
       "                  compute_total_payment  compute_total_stock  \\\n",
       "BELFER ROBERT                -99215.000            47378.000   \n",
       "BHATNAGAR SANJAY             275728.000         15456290.000   \n",
       "\n",
       "                  check_total_payment  check_total_stock  \n",
       "BELFER ROBERT                   False              False  \n",
       "BHATNAGAR SANJAY                False              False  \n",
       "\n",
       "[2 rows x 25 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df[enron_data_df['check_total_stock']==0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Therefore, besides *BELFER ROBERT* I see the problem also with *BHATNAGAR SANJAY*.\n",
    "\n",
    "Let's print the full data for this person also."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "salary                                            0.000\n",
       "bonus                                             0.000\n",
       "long_term_incentive                               0.000\n",
       "deferred_income                                   0.000\n",
       "deferral_payments                                 0.000\n",
       "loan_advances                                     0.000\n",
       "other                                        137864.000\n",
       "expenses                                          0.000\n",
       "director_fees                                137864.000\n",
       "total_payments                             15456290.000\n",
       "exercised_stock_options                     2604490.000\n",
       "restricted_stock                           -2604490.000\n",
       "restricted_stock_deferred                  15456290.000\n",
       "total_stock_value                                 0.000\n",
       "email_address                sanjay.bhatnagar@enron.com\n",
       "to_messages                                     523.000\n",
       "shared_receipt_with_poi                         463.000\n",
       "from_messages                                    29.000\n",
       "from_this_person_to_poi                           1.000\n",
       "poi                                               0.000\n",
       "from_poi_to_this_person                           0.000\n",
       "compute_total_payment                        275728.000\n",
       "compute_total_stock                        15456290.000\n",
       "check_total_payment                               False\n",
       "check_total_stock                                 False\n",
       "Name: BHATNAGAR SANJAY, dtype: object"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df.loc['BHATNAGAR SANJAY']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Both cases have a shift in the financial columns. Let's fix this manually in the data dictionary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "enron_data['BHATNAGAR SANJAY'] = {'bonus': 'NaN',\n",
    " 'deferral_payments': 'NaN',\n",
    " 'deferred_income': 'NaN',\n",
    " 'director_fees': 'NaN',\n",
    " 'email_address': 'sanjay.bhatnagar@enron.com',\n",
    " 'exercised_stock_options': 15456290,\n",
    " 'expenses': 137864,\n",
    " 'from_messages': 29,\n",
    " 'from_poi_to_this_person': 0,\n",
    " 'from_this_person_to_poi': 1,\n",
    " 'loan_advances': 'NaN',\n",
    " 'long_term_incentive': 'NaN',\n",
    " 'other': 'NaN',\n",
    " 'poi': False,\n",
    " 'restricted_stock': 2604490,\n",
    " 'restricted_stock_deferred': -2604490,\n",
    " 'salary': 'NaN',\n",
    " 'shared_receipt_with_poi': 463,\n",
    " 'to_messages': 523,\n",
    " 'total_payments': 137864,\n",
    " 'total_stock_value': 15456290}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "enron_data['BELFER ROBERT'] ={'bonus': 'NaN',\n",
    " 'deferral_payments': 'NaN',\n",
    " 'deferred_income': -102500,\n",
    " 'director_fees': 102500 ,\n",
    " 'email_address': 'NaN',\n",
    " 'exercised_stock_options': 'NaN' ,\n",
    " 'expenses': 3285,\n",
    " 'from_messages': 'NaN',\n",
    " 'from_poi_to_this_person': 'NaN',\n",
    " 'from_this_person_to_poi': 'NaN',\n",
    " 'loan_advances': 'NaN',\n",
    " 'long_term_incentive': 'NaN',\n",
    " 'other': 'NaN',\n",
    " 'poi': False,\n",
    " 'restricted_stock': 44093,\n",
    " 'restricted_stock_deferred': -44093,\n",
    " 'salary': 'NaN',\n",
    " 'shared_receipt_with_poi': 'NaN',\n",
    " 'to_messages': 'NaN',\n",
    " 'total_payments': 3285,\n",
    " 'total_stock_value': 'NaN'}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's re-import and double check."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Convert dictionary to DataFrame\n",
    "enron_data_df = pd.DataFrame.from_dict(enron_data, orient = 'index', dtype = float)\n",
    "\n",
    "# re-order columns\n",
    "enron_data_df = enron_data_df[\n",
    "['salary',\n",
    "'bonus',\n",
    "'long_term_incentive',\n",
    "'deferred_income',\n",
    "'deferral_payments',\n",
    "'loan_advances',\n",
    "'other',\n",
    "'expenses',\n",
    "'director_fees',\n",
    "'total_payments',\n",
    " 'exercised_stock_options',\n",
    "'restricted_stock',\n",
    " 'restricted_stock_deferred',\n",
    " 'total_stock_value',\n",
    " 'email_address',\n",
    " 'to_messages',\n",
    " 'shared_receipt_with_poi',\n",
    " 'from_messages',\n",
    " 'from_this_person_to_poi',\n",
    " 'poi',\n",
    " 'from_poi_to_this_person']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "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>salary</th>\n",
       "      <th>bonus</th>\n",
       "      <th>long_term_incentive</th>\n",
       "      <th>deferred_income</th>\n",
       "      <th>deferral_payments</th>\n",
       "      <th>loan_advances</th>\n",
       "      <th>other</th>\n",
       "      <th>expenses</th>\n",
       "      <th>director_fees</th>\n",
       "      <th>total_payments</th>\n",
       "      <th>exercised_stock_options</th>\n",
       "      <th>restricted_stock</th>\n",
       "      <th>restricted_stock_deferred</th>\n",
       "      <th>total_stock_value</th>\n",
       "      <th>to_messages</th>\n",
       "      <th>shared_receipt_with_poi</th>\n",
       "      <th>from_messages</th>\n",
       "      <th>from_this_person_to_poi</th>\n",
       "      <th>poi</th>\n",
       "      <th>from_poi_to_this_person</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "      <td>144.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>185446.035</td>\n",
       "      <td>675997.354</td>\n",
       "      <td>336957.833</td>\n",
       "      <td>-194395.076</td>\n",
       "      <td>222801.361</td>\n",
       "      <td>582812.500</td>\n",
       "      <td>293788.146</td>\n",
       "      <td>36355.542</td>\n",
       "      <td>9711.924</td>\n",
       "      <td>2149475.618</td>\n",
       "      <td>2165027.778</td>\n",
       "      <td>905015.965</td>\n",
       "      <td>-52616.583</td>\n",
       "      <td>3017427.160</td>\n",
       "      <td>1238.556</td>\n",
       "      <td>702.611</td>\n",
       "      <td>363.583</td>\n",
       "      <td>24.625</td>\n",
       "      <td>0.125</td>\n",
       "      <td>38.757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>197042.124</td>\n",
       "      <td>1233155.256</td>\n",
       "      <td>687182.568</td>\n",
       "      <td>605842.222</td>\n",
       "      <td>753841.107</td>\n",
       "      <td>6794471.779</td>\n",
       "      <td>1131517.461</td>\n",
       "      <td>45990.417</td>\n",
       "      <td>30422.535</td>\n",
       "      <td>8779364.388</td>\n",
       "      <td>4923320.048</td>\n",
       "      <td>2000356.656</td>\n",
       "      <td>273183.474</td>\n",
       "      <td>6271527.950</td>\n",
       "      <td>2237.565</td>\n",
       "      <td>1077.291</td>\n",
       "      <td>1450.675</td>\n",
       "      <td>79.778</td>\n",
       "      <td>0.332</td>\n",
       "      <td>74.277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-3504386.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-2604490.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>-39072.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>87471.500</td>\n",
       "      <td>0.000</td>\n",
       "      <td>44093.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>256376.500</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>210596.000</td>\n",
       "      <td>300000.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>882.500</td>\n",
       "      <td>21937.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>913825.000</td>\n",
       "      <td>608293.500</td>\n",
       "      <td>361978.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>980534.500</td>\n",
       "      <td>347.500</td>\n",
       "      <td>114.000</td>\n",
       "      <td>17.500</td>\n",
       "      <td>0.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>4.000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>269667.500</td>\n",
       "      <td>800000.000</td>\n",
       "      <td>374586.250</td>\n",
       "      <td>0.000</td>\n",
       "      <td>8535.500</td>\n",
       "      <td>0.000</td>\n",
       "      <td>148577.000</td>\n",
       "      <td>54234.500</td>\n",
       "      <td>0.000</td>\n",
       "      <td>1885158.250</td>\n",
       "      <td>1683580.250</td>\n",
       "      <td>857103.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>2372703.250</td>\n",
       "      <td>1623.000</td>\n",
       "      <td>933.750</td>\n",
       "      <td>53.000</td>\n",
       "      <td>14.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>41.250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1111258.000</td>\n",
       "      <td>8000000.000</td>\n",
       "      <td>5145434.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>6426990.000</td>\n",
       "      <td>81525000.000</td>\n",
       "      <td>10359729.000</td>\n",
       "      <td>228763.000</td>\n",
       "      <td>125034.000</td>\n",
       "      <td>103559793.000</td>\n",
       "      <td>34348384.000</td>\n",
       "      <td>14761694.000</td>\n",
       "      <td>0.000</td>\n",
       "      <td>49110078.000</td>\n",
       "      <td>15149.000</td>\n",
       "      <td>5521.000</td>\n",
       "      <td>14368.000</td>\n",
       "      <td>609.000</td>\n",
       "      <td>1.000</td>\n",
       "      <td>528.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           salary       bonus  long_term_incentive  deferred_income  \\\n",
       "count     144.000     144.000              144.000          144.000   \n",
       "mean   185446.035  675997.354           336957.833      -194395.076   \n",
       "std    197042.124 1233155.256           687182.568       605842.222   \n",
       "min         0.000       0.000                0.000     -3504386.000   \n",
       "25%         0.000       0.000                0.000       -39072.000   \n",
       "50%    210596.000  300000.000                0.000            0.000   \n",
       "75%    269667.500  800000.000           374586.250            0.000   \n",
       "max   1111258.000 8000000.000          5145434.000            0.000   \n",
       "\n",
       "       deferral_payments  loan_advances        other   expenses  \\\n",
       "count            144.000        144.000      144.000    144.000   \n",
       "mean          222801.361     582812.500   293788.146  36355.542   \n",
       "std           753841.107    6794471.779  1131517.461  45990.417   \n",
       "min                0.000          0.000        0.000      0.000   \n",
       "25%                0.000          0.000        0.000      0.000   \n",
       "50%                0.000          0.000      882.500  21937.000   \n",
       "75%             8535.500          0.000   148577.000  54234.500   \n",
       "max          6426990.000   81525000.000 10359729.000 228763.000   \n",
       "\n",
       "       director_fees  total_payments  exercised_stock_options  \\\n",
       "count        144.000         144.000                  144.000   \n",
       "mean        9711.924     2149475.618              2165027.778   \n",
       "std        30422.535     8779364.388              4923320.048   \n",
       "min            0.000           0.000                    0.000   \n",
       "25%            0.000       87471.500                    0.000   \n",
       "50%            0.000      913825.000               608293.500   \n",
       "75%            0.000     1885158.250              1683580.250   \n",
       "max       125034.000   103559793.000             34348384.000   \n",
       "\n",
       "       restricted_stock  restricted_stock_deferred  total_stock_value  \\\n",
       "count           144.000                    144.000            144.000   \n",
       "mean         905015.965                 -52616.583        3017427.160   \n",
       "std         2000356.656                 273183.474        6271527.950   \n",
       "min               0.000               -2604490.000              0.000   \n",
       "25%           44093.000                      0.000         256376.500   \n",
       "50%          361978.000                      0.000         980534.500   \n",
       "75%          857103.000                      0.000        2372703.250   \n",
       "max        14761694.000                      0.000       49110078.000   \n",
       "\n",
       "       to_messages  shared_receipt_with_poi  from_messages  \\\n",
       "count      144.000                  144.000        144.000   \n",
       "mean      1238.556                  702.611        363.583   \n",
       "std       2237.565                 1077.291       1450.675   \n",
       "min          0.000                    0.000          0.000   \n",
       "25%          0.000                    0.000          0.000   \n",
       "50%        347.500                  114.000         17.500   \n",
       "75%       1623.000                  933.750         53.000   \n",
       "max      15149.000                 5521.000      14368.000   \n",
       "\n",
       "       from_this_person_to_poi     poi  from_poi_to_this_person  \n",
       "count                  144.000 144.000                  144.000  \n",
       "mean                    24.625   0.125                   38.757  \n",
       "std                     79.778   0.332                   74.277  \n",
       "min                      0.000   0.000                    0.000  \n",
       "25%                      0.000   0.000                    0.000  \n",
       "50%                      0.000   0.000                    4.000  \n",
       "75%                     14.000   0.000                   41.250  \n",
       "max                    609.000   1.000                  528.000  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df = enron_data_df.fillna(0)\n",
    "enron_data_df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "enron_data_df['compute_total_payment'] = \\\n",
    "enron_data_df['salary'] + \\\n",
    "enron_data_df['bonus'] + \\\n",
    "enron_data_df['long_term_incentive'] + \\\n",
    "enron_data_df['deferred_income'] + \\\n",
    "enron_data_df['deferral_payments'] + \\\n",
    "enron_data_df['loan_advances'] + \\\n",
    "enron_data_df['other'] +  \\\n",
    "enron_data_df['expenses'] + \\\n",
    "enron_data_df['director_fees'] \n",
    "\n",
    "enron_data_df['compute_total_stock'] = \\\n",
    "enron_data_df['exercised_stock_options'] + \\\n",
    "enron_data_df['restricted_stock'] + \\\n",
    "enron_data_df['restricted_stock_deferred'] \n",
    "\n",
    "\n",
    "enron_data_df['check_total_payment'] = enron_data_df['compute_total_payment'] == enron_data_df['total_payments']\n",
    "enron_data_df['check_total_stock'] = enron_data_df['compute_total_stock'] == enron_data_df['total_stock_value']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "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>salary</th>\n",
       "      <th>bonus</th>\n",
       "      <th>long_term_incentive</th>\n",
       "      <th>deferred_income</th>\n",
       "      <th>deferral_payments</th>\n",
       "      <th>loan_advances</th>\n",
       "      <th>other</th>\n",
       "      <th>expenses</th>\n",
       "      <th>director_fees</th>\n",
       "      <th>total_payments</th>\n",
       "      <th>...</th>\n",
       "      <th>to_messages</th>\n",
       "      <th>shared_receipt_with_poi</th>\n",
       "      <th>from_messages</th>\n",
       "      <th>from_this_person_to_poi</th>\n",
       "      <th>poi</th>\n",
       "      <th>from_poi_to_this_person</th>\n",
       "      <th>compute_total_payment</th>\n",
       "      <th>compute_total_stock</th>\n",
       "      <th>check_total_payment</th>\n",
       "      <th>check_total_stock</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>0 rows × 25 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [salary, bonus, long_term_incentive, deferred_income, deferral_payments, loan_advances, other, expenses, director_fees, total_payments, exercised_stock_options, restricted_stock, restricted_stock_deferred, total_stock_value, email_address, to_messages, shared_receipt_with_poi, from_messages, from_this_person_to_poi, poi, from_poi_to_this_person, compute_total_payment, compute_total_stock, check_total_payment, check_total_stock]\n",
       "Index: []\n",
       "\n",
       "[0 rows x 25 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df[enron_data_df['check_total_payment']==0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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>salary</th>\n",
       "      <th>bonus</th>\n",
       "      <th>long_term_incentive</th>\n",
       "      <th>deferred_income</th>\n",
       "      <th>deferral_payments</th>\n",
       "      <th>loan_advances</th>\n",
       "      <th>other</th>\n",
       "      <th>expenses</th>\n",
       "      <th>director_fees</th>\n",
       "      <th>total_payments</th>\n",
       "      <th>...</th>\n",
       "      <th>to_messages</th>\n",
       "      <th>shared_receipt_with_poi</th>\n",
       "      <th>from_messages</th>\n",
       "      <th>from_this_person_to_poi</th>\n",
       "      <th>poi</th>\n",
       "      <th>from_poi_to_this_person</th>\n",
       "      <th>compute_total_payment</th>\n",
       "      <th>compute_total_stock</th>\n",
       "      <th>check_total_payment</th>\n",
       "      <th>check_total_stock</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>0 rows × 25 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "Empty DataFrame\n",
       "Columns: [salary, bonus, long_term_incentive, deferred_income, deferral_payments, loan_advances, other, expenses, director_fees, total_payments, exercised_stock_options, restricted_stock, restricted_stock_deferred, total_stock_value, email_address, to_messages, shared_receipt_with_poi, from_messages, from_this_person_to_poi, poi, from_poi_to_this_person, compute_total_payment, compute_total_stock, check_total_payment, check_total_stock]\n",
       "Index: []\n",
       "\n",
       "[0 rows x 25 columns]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data_df[enron_data_df['check_total_stock']==0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The problem with shift is solved and all data points are at least internally consistent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Value outliers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I'll check variable by variable which values fall too far from the median. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll ignore the 0s, in order to spot outliers more easily\n",
    "\n",
    "In this code I go through each colum and find the persons with values outside the extended IQR, as per John Tukey's method. I used a very conservative factor of 2 to spot the extreme outliers.\n",
    "\n",
    "I count how often a person shows up as an outlier, and print this list below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "salary: 7\n",
      "BANNANTINE JAMES M       477.000\n",
      "GRAY RODNEY             6615.000\n",
      "WHALLEY LAWRENCE G    510364.000\n",
      "PICKERING MARK R      655037.000\n",
      "FREVERT MARK A       1060932.000\n",
      "LAY KENNETH L        1072321.000\n",
      "SKILLING JEFFREY K   1111258.000\n",
      "Name: salary, dtype: float64\n",
      "\n",
      "bonus: 8\n",
      "DELAINEY DAVID W     3000000.000\n",
      "WHALLEY LAWRENCE G   3000000.000\n",
      "KITCHEN LOUISE       3100000.000\n",
      "ALLEN PHILLIP K      4175000.000\n",
      "BELDEN TIMOTHY N     5249999.000\n",
      "SKILLING JEFFREY K   5600000.000\n",
      "LAY KENNETH L        7000000.000\n",
      "LAVORATO JOHN J      8000000.000\n",
      "Name: bonus, dtype: float64\n",
      "\n",
      "long_term_incentive: 4\n",
      "LAVORATO JOHN J   2035380.000\n",
      "ECHOLS JOHN B     2234774.000\n",
      "LAY KENNETH L     3600000.000\n",
      "MARTIN AMANDA K   5145434.000\n",
      "Name: long_term_incentive, dtype: float64\n",
      "\n",
      "deferred_income: 5\n",
      "RICE KENNETH D     -3504386.000\n",
      "FREVERT MARK A     -3367011.000\n",
      "HANNON KEVIN P     -3117011.000\n",
      "ALLEN PHILLIP K    -3081055.000\n",
      "BELDEN TIMOTHY N   -2334434.000\n",
      "Name: deferred_income, dtype: float64\n",
      "\n",
      "deferral_payments: 4\n",
      "ALLEN PHILLIP K    2869717.000\n",
      "HUMPHREY GENE E    2964506.000\n",
      "HORTON STANLEY C   3131860.000\n",
      "FREVERT MARK A     6426990.000\n",
      "Name: deferral_payments, dtype: float64\n",
      "\n",
      "loan_advances: 0\n",
      "Series([], Name: loan_advances, dtype: float64)\n",
      "\n",
      "other: 9\n",
      "WHITE JR THOMAS E    1085463.000\n",
      "IZZO LAWRENCE L      1553729.000\n",
      "SHELBY REX           1573324.000\n",
      "PAI LOU L            1829457.000\n",
      "SHERRIFF JOHN R      1852186.000\n",
      "BAXTER JOHN C        2660303.000\n",
      "MARTIN AMANDA K      2818454.000\n",
      "FREVERT MARK A       7427621.000\n",
      "LAY KENNETH L       10359729.000\n",
      "Name: other, dtype: float64\n",
      "\n",
      "expenses: 2\n",
      "URQUHART JOHN A    228656.000\n",
      "MCCLELLAN GEORGE   228763.000\n",
      "Name: expenses, dtype: float64\n",
      "\n",
      "director_fees: 3\n",
      "POWERS WILLIAM    17500.000\n",
      "URQUHART JOHN A   36666.000\n",
      "MEYER JEROME J    38346.000\n",
      "Name: director_fees, dtype: float64\n",
      "\n",
      "total_payments: 7\n",
      "BELDEN TIMOTHY N       5501630.000\n",
      "BAXTER JOHN C          5634343.000\n",
      "MARTIN AMANDA K        8407016.000\n",
      "SKILLING JEFFREY K     8682716.000\n",
      "LAVORATO JOHN J       10425757.000\n",
      "FREVERT MARK A        17252530.000\n",
      "LAY KENNETH L        103559793.000\n",
      "Name: total_payments, dtype: float64\n",
      "\n",
      "exercised_stock_options: 12\n",
      "BAXTER JOHN C          6680544.000\n",
      "REDMOND BRIAN L        7509039.000\n",
      "DIMICHELE RICHARD G    8191755.000\n",
      "YEAGER F SCOTT         8308552.000\n",
      "DERRICK JR. JAMES V    8831913.000\n",
      "FREVERT MARK A        10433518.000\n",
      "PAI LOU L             15364167.000\n",
      "BHATNAGAR SANJAY      15456290.000\n",
      "SKILLING JEFFREY K    19250000.000\n",
      "RICE KENNETH D        19794175.000\n",
      "Name: exercised_stock_options, dtype: float64\n",
      "\n",
      "restricted_stock: 13\n",
      "CAUSEY RICHARD A     2502063.000\n",
      "BHATNAGAR SANJAY     2604490.000\n",
      "RICE KENNETH D       2748364.000\n",
      "WHALLEY LAWRENCE G   2796177.000\n",
      "YEAGER F SCOTT       3576206.000\n",
      "IZZO LAWRENCE L      3654808.000\n",
      "BAXTER JOHN C        3942714.000\n",
      "KEAN STEVEN J        4131594.000\n",
      "FREVERT MARK A       4188667.000\n",
      "SKILLING JEFFREY K   6843672.000\n",
      "Name: restricted_stock, dtype: float64\n",
      "\n",
      "restricted_stock_deferred: 2\n",
      "BHATNAGAR SANJAY      -2604490.000\n",
      "DERRICK JR. JAMES V   -1787380.000\n",
      "Name: restricted_stock_deferred, dtype: float64\n",
      "\n",
      "total_stock_value: 12\n",
      "DIMICHELE RICHARD G    8317782.000\n",
      "DERRICK JR. JAMES V    8831913.000\n",
      "BAXTER JOHN C         10623258.000\n",
      "YEAGER F SCOTT        11884758.000\n",
      "FREVERT MARK A        14622185.000\n",
      "WHITE JR THOMAS E     15144123.000\n",
      "BHATNAGAR SANJAY      15456290.000\n",
      "RICE KENNETH D        22542539.000\n",
      "PAI LOU L             23817930.000\n",
      "SKILLING JEFFREY K    26093672.000\n",
      "Name: total_stock_value, dtype: float64\n",
      "\n",
      "to_messages: 6\n",
      "LAVORATO JOHN J      7259.000\n",
      "BECK SALLY W         7315.000\n",
      "BELDEN TIMOTHY N     7991.000\n",
      "KITCHEN LOUISE       8305.000\n",
      "KEAN STEVEN J       12754.000\n",
      "SHAPIRO RICHARD S   15149.000\n",
      "Name: to_messages, dtype: float64\n",
      "\n",
      "shared_receipt_with_poi: 1\n",
      "BELDEN TIMOTHY N   5521.000\n",
      "Name: shared_receipt_with_poi, dtype: float64\n",
      "\n",
      "from_messages: 17\n",
      "BELDEN TIMOTHY N       484.000\n",
      "WHALLEY LAWRENCE G     556.000\n",
      "DERRICK JR. JAMES V    909.000\n",
      "BUY RICHARD B         1053.000\n",
      "HAYSLETT RODERICK J   1061.000\n",
      "HORTON STANLEY C      1073.000\n",
      "SHAPIRO RICHARD S     1215.000\n",
      "KITCHEN LOUISE        1728.000\n",
      "HAEDICKE MARK E       1941.000\n",
      "ALLEN PHILLIP K       2195.000\n",
      "Name: from_messages, dtype: float64\n",
      "\n",
      "from_this_person_to_poi: 8\n",
      "BELDEN TIMOTHY N      108.000\n",
      "KAMINSKI WINCENTY J   171.000\n",
      "KITCHEN LOUISE        194.000\n",
      "MCCONNELL MICHAEL S   194.000\n",
      "BECK SALLY W          386.000\n",
      "KEAN STEVEN J         387.000\n",
      "LAVORATO JOHN J       411.000\n",
      "DELAINEY DAVID W      609.000\n",
      "Name: from_this_person_to_poi, dtype: float64\n",
      "\n",
      "from_poi_to_this_person: 5\n",
      "COLWELL WESLEY     240.000\n",
      "FREVERT MARK A     242.000\n",
      "KITCHEN LOUISE     251.000\n",
      "DIETRICH JANET R   305.000\n",
      "LAVORATO JOHN J    528.000\n",
      "Name: from_poi_to_this_person, dtype: float64\n",
      "\n",
      "compute_total_payment: 7\n",
      "BELDEN TIMOTHY N       5501630.000\n",
      "BAXTER JOHN C          5634343.000\n",
      "MARTIN AMANDA K        8407016.000\n",
      "SKILLING JEFFREY K     8682716.000\n",
      "LAVORATO JOHN J       10425757.000\n",
      "FREVERT MARK A        17252530.000\n",
      "LAY KENNETH L        103559793.000\n",
      "Name: compute_total_payment, dtype: float64\n",
      "\n",
      "compute_total_stock: 12\n",
      "DIMICHELE RICHARD G    8317782.000\n",
      "DERRICK JR. JAMES V    8831913.000\n",
      "BAXTER JOHN C         10623258.000\n",
      "YEAGER F SCOTT        11884758.000\n",
      "FREVERT MARK A        14622185.000\n",
      "WHITE JR THOMAS E     15144123.000\n",
      "BHATNAGAR SANJAY      15456290.000\n",
      "RICE KENNETH D        22542539.000\n",
      "PAI LOU L             23817930.000\n",
      "SKILLING JEFFREY K    26093672.000\n",
      "Name: compute_total_stock, dtype: float64\n",
      "\n",
      "Total Cases:21\n"
     ]
    }
   ],
   "source": [
    "problem_persons = dict()\n",
    "\n",
    "cases = 0\n",
    "for column_name in list(enron_data_df):\n",
    "    if enron_data_df[column_name].dtype == 'float' and column_name != 'poi':\n",
    "        cases +=1\n",
    "        test_data = enron_data_df[enron_data_df[column_name]!=0]\n",
    "        Q1 = test_data[column_name].quantile(0.25)\n",
    "        Q3 = test_data[column_name].quantile(0.75)\n",
    "        IQR = Q3 - Q1\n",
    "\n",
    "        # Filtering Values between Q1-1.5IQR and Q3+1.5IQR\n",
    "        query_str = '(@Q1 - 2 * @IQR) >= ' + column_name + ' or  (@Q3 + 2 * @IQR) <=' + column_name\n",
    "        filtered = test_data.query(query_str)\n",
    "\n",
    "        print column_name + \": \" + str(len(filtered))\n",
    "        filtered = filtered.sort_values(column_name)\n",
    "        print filtered[column_name].head(10)\n",
    "        print \"\"\n",
    "        \n",
    "        for person in filtered.index.tolist():\n",
    "            try:\n",
    "               problem_persons[person] = 1 + problem_persons[person]\n",
    "            except:\n",
    "               problem_persons[person] = 1 \n",
    "\n",
    "print \"Total Cases:\" + str(cases)\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "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>Count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>FREVERT MARK A</th>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LAY KENNETH L</th>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BELDEN TIMOTHY N</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>SKILLING JEFFREY K</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>LAVORATO JOHN J</th>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BAXTER JOHN C</th>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DERRICK JR. JAMES V</th>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KITCHEN LOUISE</th>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>PAI LOU L</th>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BHATNAGAR SANJAY</th>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>RICE KENNETH D</th>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MARTIN AMANDA K</th>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>KEAN STEVEN J</th>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YEAGER F SCOTT</th>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WHITE JR THOMAS E</th>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>WHALLEY LAWRENCE G</th>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ALLEN PHILLIP K</th>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DIMICHELE RICHARD G</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>HIRKO JOSEPH</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DELAINEY DAVID W</th>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                     Count\n",
       "FREVERT MARK A          11\n",
       "LAY KENNETH L           10\n",
       "BELDEN TIMOTHY N         8\n",
       "SKILLING JEFFREY K       8\n",
       "LAVORATO JOHN J          8\n",
       "BAXTER JOHN C            7\n",
       "DERRICK JR. JAMES V      5\n",
       "KITCHEN LOUISE           5\n",
       "PAI LOU L                5\n",
       "BHATNAGAR SANJAY         5\n",
       "RICE KENNETH D           5\n",
       "MARTIN AMANDA K          4\n",
       "KEAN STEVEN J            4\n",
       "YEAGER F SCOTT           4\n",
       "WHITE JR THOMAS E        4\n",
       "WHALLEY LAWRENCE G       4\n",
       "ALLEN PHILLIP K          4\n",
       "DIMICHELE RICHARD G      3\n",
       "HIRKO JOSEPH             3\n",
       "DELAINEY DAVID W         3"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "problem_persons_df = pd.DataFrame.from_dict(problem_persons, orient = 'index', dtype = int)\n",
    "problem_persons_df.columns = ['Count']\n",
    "problem_persons_df = problem_persons_df.sort_values('Count', ascending = False)\n",
    "problem_persons_df.head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As expected *LAY KENNETH L* and *SKILLING JEFFREY K* show up at the top of the list. However, a few new names are also there: *FREVERT MARK A*, *BELDEN TIMOTHY N*, *LAVORATO JOHN J*.\n",
    "\n",
    "In particular, *FREVERT MARK A* seems to be a strong outlier since it shows up in 11 cases. However, it seems like real outliers, so I will keep them \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Iniitial Feature Selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the small sample above I notice that certain features contain many *NaN* values. In order to access the usability of certain features, I should check how many *NaN* exist, and in particular, what is the breakdown between POI and non-POI to have a sense of the bias that certain features might bring.\n",
    "\n",
    "I'll also use the opportunity to create lists of features to be used later."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "salary\n",
      "NaN in POIs: 1 (5.56%)\n",
      "NaN in non-POIs: 49 (38.89%)\n",
      "Valid: 94 (65.28%)\n",
      "\n",
      "to_messages\n",
      "NaN in POIs: 4 (22.22%)\n",
      "NaN in non-POIs: 54 (42.86%)\n",
      "Valid: 86 (59.72%)\n",
      "\n",
      "deferral_payments\n",
      "NaN in POIs: 13 (72.22%)\n",
      "NaN in non-POIs: 94 (74.6%)\n",
      "Valid: 37 (25.69%)\n",
      "\n",
      "total_payments\n",
      "NaN in POIs: 0 (0.0%)\n",
      "NaN in non-POIs: 21 (16.67%)\n",
      "Valid: 123 (85.42%)\n",
      "\n",
      "exercised_stock_options\n",
      "NaN in POIs: 6 (33.33%)\n",
      "NaN in non-POIs: 38 (30.16%)\n",
      "Valid: 100 (69.44%)\n",
      "\n",
      "bonus\n",
      "NaN in POIs: 2 (11.11%)\n",
      "NaN in non-POIs: 61 (48.41%)\n",
      "Valid: 81 (56.25%)\n",
      "\n",
      "restricted_stock\n",
      "NaN in POIs: 1 (5.56%)\n",
      "NaN in non-POIs: 33 (26.19%)\n",
      "Valid: 110 (76.39%)\n",
      "\n",
      "shared_receipt_with_poi\n",
      "NaN in POIs: 4 (22.22%)\n",
      "NaN in non-POIs: 54 (42.86%)\n",
      "Valid: 86 (59.72%)\n",
      "\n",
      "restricted_stock_deferred\n",
      "NaN in POIs: 18 (100.0%)\n",
      "NaN in non-POIs: 109 (86.51%)\n",
      "Valid: 17 (11.81%)\n",
      "\n",
      "total_stock_value\n",
      "NaN in POIs: 0 (0.0%)\n",
      "NaN in non-POIs: 19 (15.08%)\n",
      "Valid: 125 (86.81%)\n",
      "\n",
      "expenses\n",
      "NaN in POIs: 0 (0.0%)\n",
      "NaN in non-POIs: 48 (38.1%)\n",
      "Valid: 96 (66.67%)\n",
      "\n",
      "loan_advances\n",
      "NaN in POIs: 17 (94.44%)\n",
      "NaN in non-POIs: 124 (98.41%)\n",
      "Valid: 3 (2.08%)\n",
      "\n",
      "from_messages\n",
      "NaN in POIs: 4 (22.22%)\n",
      "NaN in non-POIs: 54 (42.86%)\n",
      "Valid: 86 (59.72%)\n",
      "\n",
      "other\n",
      "NaN in POIs: 0 (0.0%)\n",
      "NaN in non-POIs: 54 (42.86%)\n",
      "Valid: 90 (62.5%)\n",
      "\n",
      "from_this_person_to_poi\n",
      "NaN in POIs: 4 (22.22%)\n",
      "NaN in non-POIs: 54 (42.86%)\n",
      "Valid: 86 (59.72%)\n",
      "\n",
      "poi\n",
      "NaN in POIs: 0 (0.0%)\n",
      "NaN in non-POIs: 0 (0.0%)\n",
      "Valid: 144 (100.0%)\n",
      "\n",
      "director_fees\n",
      "NaN in POIs: 18 (100.0%)\n",
      "NaN in non-POIs: 111 (88.1%)\n",
      "Valid: 15 (10.42%)\n",
      "\n",
      "deferred_income\n",
      "NaN in POIs: 7 (38.89%)\n",
      "NaN in non-POIs: 88 (69.84%)\n",
      "Valid: 49 (34.03%)\n",
      "\n",
      "long_term_incentive\n",
      "NaN in POIs: 6 (33.33%)\n",
      "NaN in non-POIs: 73 (57.94%)\n",
      "Valid: 65 (45.14%)\n",
      "\n",
      "email_address\n",
      "NaN in POIs: 0 (0.0%)\n",
      "NaN in non-POIs: 33 (26.19%)\n",
      "Valid: 111 (77.08%)\n",
      "\n",
      "from_poi_to_this_person\n",
      "NaN in POIs: 4 (22.22%)\n",
      "NaN in non-POIs: 54 (42.86%)\n",
      "Valid: 86 (59.72%)\n"
     ]
    }
   ],
   "source": [
    "initial_selection_features = ['poi']\n",
    "all_features = ['poi']\n",
    "\n",
    "for feature in enron_data[enron_data.keys()[0]].keys():\n",
    "    nan_poi = 0\n",
    "    nan_non_poi = 0\n",
    "    valid_data = 0 \n",
    "    print \"\\n\"+feature\n",
    "    for person in enron_data.keys():\n",
    "        if enron_data[person][feature] =='NaN':\n",
    "            if enron_data[person]['poi']:\n",
    "                nan_poi +=1\n",
    "            else:\n",
    "                nan_non_poi +=1\n",
    "        else:\n",
    "            valid_data +=1\n",
    "    print \"NaN in POIs: \" + str(nan_poi) + \" (\" + str(round(float(nan_poi)/float(POI)*100,2))+\"%)\"\n",
    "    print \"NaN in non-POIs: \" + str(nan_non_poi) + \" (\" + str(round(float(nan_non_poi)/float(non_POI)*100,2))+\"%)\"\n",
    "    print \"Valid: \" + str(valid_data)  +\" (\" + str(round(float(valid_data)/float(POI+non_POI)*100,2))+\"%)\"\n",
    "    #print \"Total:\" + str(valid_data+nan_poi+nan_non_poi)\n",
    "    \n",
    "    # Keep feature only if at least 50% is valid:\n",
    "    if round(float(valid_data)/float(POI+non_POI)*100,2)>50:\n",
    "        # ignore email_address, since it is just text, and poi, which must be first\n",
    "        if feature !=\"email_address\" and feature !=\"poi\":\n",
    "            initial_selection_features.append(feature)\n",
    "            \n",
    "    # save all features to allow for comparison:\n",
    "    # ignore email_address, since it is just text, and poi, which must be first\n",
    "    if feature !=\"email_address\" and feature !=\"poi\":\n",
    "        all_features.append(feature)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the test above, I notice that certain features are not good\n",
    "candidates for the classifer.\n",
    "\n",
    "In particular, *deferral_payments*, *restricted_stock_deferred*,*loan_advances*,\n",
    "*director_fees* have very low valid points to be seriously considered.\n",
    "\n",
    "As a general cut-off, I decide to drop any feature with less than 50% valid points\n",
    "will not be considered. I kept 14 features, listed below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'salary', 'to_messages', 'total_payments', 'exercised_stock_options', 'bonus', 'restricted_stock', 'shared_receipt_with_poi', 'total_stock_value', 'expenses', 'from_messages', 'other', 'from_this_person_to_poi', 'from_poi_to_this_person']\n",
      "\n",
      " Numbers of features: 14\n"
     ]
    }
   ],
   "source": [
    "print  initial_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(initial_selection_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Feature Creation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I do not expect *to_messages* to be any informative to identify a POI. Likewise the absolute number of messages to/from poi or shared are less likely to be explanatory than their respective share version. I make therefore the transformation and update the list of features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "share_shared_receipt_with_poi\n",
      "NaN in POIs: 4 (22.22%)\n",
      "NaN in non-POIs: 54 (42.86%)\n",
      "Valid: 86 (59.72%)\n",
      "\n",
      "share_from_this_person_to_poi\n",
      "NaN in POIs: 4 (22.22%)\n",
      "NaN in non-POIs: 54 (42.86%)\n",
      "Valid: 86 (59.72%)\n",
      "\n",
      "share_from_poi_to_this_person\n",
      "NaN in POIs: 4 (22.22%)\n",
      "NaN in non-POIs: 54 (42.86%)\n",
      "Valid: 86 (59.72%)\n"
     ]
    }
   ],
   "source": [
    "initial_selection_features.remove('to_messages')\n",
    "initial_selection_features.remove('from_messages')\n",
    "initial_selection_features.remove('shared_receipt_with_poi')\n",
    "initial_selection_features.remove('from_this_person_to_poi')\n",
    "initial_selection_features.remove('from_poi_to_this_person')\n",
    "\n",
    "\n",
    "# supporting function  \n",
    "def convert_to_share(data, abs_var_name, base_var_name,new_var_name):\n",
    "    for person in data.keys():\n",
    "        if  data[person][abs_var_name] == \"NaN\" or  data[person][base_var_name] == \"NaN\":\n",
    "            data[person][new_var_name] = \"NaN\"\n",
    "        else:\n",
    "            data[person][new_var_name] = float(data[person][abs_var_name])/float(data[person][base_var_name])\n",
    "\n",
    "    return data\n",
    "   \n",
    "enron_data = convert_to_share(enron_data, 'shared_receipt_with_poi', 'to_messages','share_shared_receipt_with_poi') \n",
    "enron_data = convert_to_share(enron_data, 'from_this_person_to_poi', 'from_messages','share_from_this_person_to_poi') \n",
    "enron_data = convert_to_share(enron_data, 'from_poi_to_this_person', 'to_messages','share_from_poi_to_this_person') \n",
    "\n",
    "for feature in ['share_shared_receipt_with_poi','share_from_this_person_to_poi','share_from_poi_to_this_person']:\n",
    "    all_features.append(feature)\n",
    "    initial_selection_features.append(feature)\n",
    "    nan_poi = 0\n",
    "    nan_non_poi = 0\n",
    "    valid_data = 0 \n",
    "    print \"\\n\"+feature\n",
    "    for person in enron_data.keys():\n",
    "        if enron_data[person][feature] =='NaN':\n",
    "            if enron_data[person]['poi']:\n",
    "                nan_poi +=1\n",
    "            else:\n",
    "                nan_non_poi +=1\n",
    "        else:\n",
    "            valid_data +=1\n",
    "    print \"NaN in POIs: \" + str(nan_poi) + \" (\" + str(round(float(nan_poi)/float(POI)*100,2))+\"%)\"\n",
    "    print \"NaN in non-POIs: \" + str(nan_non_poi) + \" (\" + str(round(float(nan_non_poi)/float(non_POI)*100,2))+\"%)\"\n",
    "    print \"Valid: \" + str(valid_data)  +\" (\" + str(round(float(valid_data)/float(POI+non_POI)*100,2))+\"%)\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And this is how the list of features looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'salary', 'total_payments', 'exercised_stock_options', 'bonus', 'restricted_stock', 'total_stock_value', 'expenses', 'other', 'share_shared_receipt_with_poi', 'share_from_this_person_to_poi', 'share_from_poi_to_this_person']\n",
      "\n",
      " Numbers of features: 12\n"
     ]
    }
   ],
   "source": [
    "print  initial_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(initial_selection_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I transform this according to feature format and check the initial listing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append(\"./tools/\") \n",
    "\n",
    "from feature_format import featureFormat, targetFeatureSplit\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "data = featureFormat(enron_data, initial_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "143\n"
     ]
    }
   ],
   "source": [
    "# some checks\n",
    "print len(data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I noticed that one data point was dropped. Let's find out who, since this needs to be added to the initial list of outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LOCKHART EUGENE E\n"
     ]
    }
   ],
   "source": [
    "for person in enron_data.keys():\n",
    "    suspect = person\n",
    "    for key in enron_data[enron_data.keys()[0]].keys():\n",
    "        suspect_found = True\n",
    "        if (enron_data[person][key] !=\"NaN\" and  enron_data[person][key] !=0):\n",
    "            suspect_found = False\n",
    "            break\n",
    "    if suspect_found:\n",
    "        print suspect\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'bonus': 'NaN',\n",
       " 'deferral_payments': 'NaN',\n",
       " 'deferred_income': 'NaN',\n",
       " 'director_fees': 'NaN',\n",
       " 'email_address': 'NaN',\n",
       " 'exercised_stock_options': 'NaN',\n",
       " 'expenses': 'NaN',\n",
       " 'from_messages': 'NaN',\n",
       " 'from_poi_to_this_person': 'NaN',\n",
       " 'from_this_person_to_poi': 'NaN',\n",
       " 'loan_advances': 'NaN',\n",
       " 'long_term_incentive': 'NaN',\n",
       " 'other': 'NaN',\n",
       " 'poi': False,\n",
       " 'restricted_stock': 'NaN',\n",
       " 'restricted_stock_deferred': 'NaN',\n",
       " 'salary': 'NaN',\n",
       " 'share_from_poi_to_this_person': 'NaN',\n",
       " 'share_from_this_person_to_poi': 'NaN',\n",
       " 'share_shared_receipt_with_poi': 'NaN',\n",
       " 'shared_receipt_with_poi': 'NaN',\n",
       " 'to_messages': 'NaN',\n",
       " 'total_payments': 'NaN',\n",
       " 'total_stock_value': 'NaN'}"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "enron_data.pop('LOCKHART EUGENE E',0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I visualy inspect all initially selected variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AAIAJCN4AAACACQjeAAAAgAkI3gAAAIAJCN4AAACACQjeAAAAgAkI3gAAAIAJCN4AAACA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\nCbDwJiIiIiKSAAtvIiIiIiIJ/B/EQOW2kpoq5wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc81b0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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syjAAAAAsizIMAAAAy6IMAwAAwLIowwAAALAsyjAAAAAsizIMAAAAy6IMAwAAwLIowwAA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\nWZRhAAAAWNb/A7c8HH7CXYYzAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcd86c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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nrwwDAAAAZiEMAwAAIGARhgEAABCwCMMAAAAIWIRhAAAABCzCMAAAAAIWYRgAAAABizAM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xded4fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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+wKWK0FucoAYAAHAcsWChDoSqlVl1nwKRD9SSnaPDc7/HyWkpgLALAADQC7FgoZpX1SiQ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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe491dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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co4cfflh///vfVVVVpaqqKn388cd6+OGHNXz48IAWWFNTo9dee00PPPCA+vbt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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe98ed68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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DMFRVVaWNGzdq+vTpIQ1oGIZGjhyprl27atmyZfr66681btw4nXXWWbrhhhtC+rUAAABq\nxeZk+8ttrejiXYrNydaRBfk2pUIgTBfcvLw8zZo1S5LkcrlkGIb/7927dw9tOkmlpaW6+OKLNWXK\nFMXGxuqcc85Rz549tWHDBgouAACwTFRJwxewamwd4cP0WRRefvll3Xnnnfrkk0+UkJCgVatWadmy\nZerYsaP69OkT8oDt2rXTk08+qdjYWEnShg0btG7dOl166aUh/1oAAAC1atolmVpH+DBdcPfs2aNf\n/epX8ng86tSpkzZu3KgLL7xQEyZM0GuvvWZFRr/evXvrN7/5jdLS0nTttdda+rUAAMDprSJrrKqT\nU+qsVSenqCJrrE2JECjTBTc2NlY+n0+SdM4552jbtm2SpI4dO6q4uDi06b5j7ty5eu6557R582Y9\n9thjln4tAABwevOlputwXr68/QdKGRny9h/IG8wihOk9uOnp6frDH/6ghx9+WBdffLFee+01jRw5\nUhs2bFBcXJwVGf1+/OMfS5ImTpyo++67TxMmTFB0dGDfgtvNNS2sUDtX5msdZmwt5ms9Zmwt5mux\n7t3lzf+TPPEx8h6ulMtXE9w79HFSoX7+mv7/aNy4cbr99tv18ssv6+abb9Zzzz2nHj16qLKy0pJT\nd+3fv18ff/yxrr76av/aD37wAx0/flzl5eVq3bp1QI8THx8T8mz4H+ZrPWZsLeZrPWZsLeZrPWYc\nOUwX3B/96Ed6//33VVFRobi4OC1ZskRvvvmmzjrrLF1//fUhD1hUVKR7771Xq1atUlLSiU3dGzdu\nVGJiYsDlVpIOH66Uz1cT8nynO7c7SvHxMczXQszYWszXeszYWszXeszYerUzDhXTBff+++/Xz3/+\nc1122WWSpLZt22r48OEhC/Rdl1xyiTp37qxJkyZp4sSJKioq0pw5c3TPPfeYehyfr0bV1TwprcJ8\nrceMrcV8rceMrcV8rceMI0dQZ1G4/fbb1bt3b+Xk5GjXrl3f/0mnICoqSvPmzVNsbKyGDBmiyZMn\na9iwYfrNb35j6dcFAABAZHIZtVdqMGHv3r1avny5li9fri+++ELdunXToEGD1LdvX8vfaBassrKj\n/NZlgejoKCUkxDFfCzFjazFf6zFjazFf6zFj69XOOFSCesvamWeeqREjRmjZsmVavny5unfvrpkz\nZyojIyNkwQAAAIBgnNKZLj755BMtX75c7777rgzDUL9+/UKVCwAAAAiK6YL71Vdfafny5XrzzTe1\na9cu9ejRQ7/73e903XXXqUWLFlZkBAAAAAJmuuD27dtXZ599tgYOHKhBgwYpOTnZilwAAABAUEwX\n3IULF6pHjx4nvU9FRYWee+45jRs3LuhgAAAAQDBMv8ns+8qtdKLg/vGPfwwqEAAAAHAquHA1AAAA\nHIWCCwAAAEeh4AIAAMBRKLgAAABwFAouAAAAHIWCCwAAAEexrOAahmHVQwMAAACNMl1wd+3a1eB6\ndXW1cnJyJEnx8fF64oknTi0ZAAAAEATTBffWW2/V7t2766xt2rRJgwYN0vz58yVJzZs3V//+/UOT\nEAAAADDBdMHt3LmzMjMztWfPHh0/flzZ2dkaPHiwWrVqpddff92KjAAAAEDAos1+QnZ2tu677z5l\nZmaqRYsW+uabb/TQQw9pyJAhVuQDAACwjbuwQLG52dKB/YpNbKOjo8fKl5pudyx8D9MF1+12a86c\nOZowYYLefPNNvfrqq+rSpYsV2QAAAGzjLixQ/G2Zii4+8f4jjyT3hgIdzsun5Ia5gAruxIkT6625\nXC5FR0dr/Pjx6t69u399xowZoUsHAABgk9icbH+5rRVdvEuxOdk6siDfplQIREAFt6ioqMH1rl27\nnvR2AACASBVVss/UOsJHQAU3P//kv6VUVVWpefPmIQkEAAAQDmraJZlaR/gwfRYFr9eriRMn6vnn\nn/evXX/99Zo8ebKqqqpCGg4AAMAuFVljVZ2cUmetOjlFFVljbUqEQJkuuDNmzND69euVlpbmX5s4\ncaLWrFmj7OzskIYDAACwiy81XYfz8uXtP1DKyJC3/0DeYBYhTJ9F4f3339fcuXPrFNxrrrlGrVu3\n1vjx4/XAAw+ENCAAAIBdfKnpqnhxkTwJcaooOypfdY3dkRAA00dwjx49qvj4+HrriYmJOnToUEhC\nAQAAAMEyXXBTU1M1f/581dT87zcYwzD00ksv6ZJLLglpOAAAAMAs01sUxo4dq1tvvVVr1qxR586d\nJUmff/65Dh48qAULFoQ8IAAAAGCG6SO4Xbp00fLly3XDDTeoqqpKNTU1uvHGG/W3v/3Nf15cAAAA\nwC6mj+BK0tlnn63x48eHOgsAAABwykwfwZWkDz74QIMHD1Zqaqq6d++uIUOGaMWKFaHOhjBXWBil\n4cM9ysiQhg/3qLAwqKcTAABASJk+gvvee+9pzJgx6tOnj2644QYZhqF169ZpzJgxmjt3rvr06WNF\nToSZwsIo3XZbjIqLa0tttDZsiFJeXqVSUzmFCgAAsI/pgjtv3jyNGjVKo0eP9q8NHz5cubm5eu65\n5yi4p4mcnObfKrcnFBdHKSenuRYsOGZTKgAAgCC2KHz55Ze66aab6q3feOON2rp1a0hCIfyVlLhM\nrQMAADQV0wU3KSlJO3bsqLe+Y8cOtWrVKiShEP7atTNMrQMAADQV0wX3xhtv1NSpU7Vq1SqVl5er\nvLxcq1at0rRp09SvXz8rMiIMZWVVKTm57l7b5OQaZWVV2ZQIAADgBNN7cO+55x5t3bpVd911l1yu\nE/8cbRiGrrzySo0dOzbkARGeUlNrlJdXqdxcj8rKopWQUK3Ro728wQwAANjOdMH1eDyaN2+etm/f\nrq1bt8owDF144YXq2LGjDIN/nj6dpKbW6MUXvUpIiFZZmVfV1ZRbAABgP9NbFPr06aODBw+qY8eO\n6tu3r/r166eOHTtq7969uuyyy6zICAAAYAt3YYFihw+VMjIUO3yo3IUFdkdCAAI6gvv2229r9erV\nkqTi4mI98sgj8ng8de5TXFzs37IAAAAQ6dyFBYq/LVPRxbskSR5J7g0FOpyXL19qur3hcFIBFdy0\ntDS9+uqr/i0Iu3fvVrNmzfy3u1wuxcbGatasWdakBAAAaGKxOdn+clsruniXYnOydWRBvk2pEIiA\nCm779u21cOFCSVJmZqZyc3N1xhlnWBoMAADATlEl+0ytI3yY3oObn59fp9weOHBA77zzjoqKikIa\nDAAAwE417ZJMrSN8mC64W7du1XXXXad169bp8OHD6t+/v37729+qX79++ve//21FRgAAgCZXkTVW\n1ckpddaqk1NUkcVpUcOd6YI7a9YsnXvuubrgggv05ptvqrq6WqtWrdIdd9yhp556yoqMAAAATc6X\nmq7Defny9h8oZWTI238gbzCLEKbPg/vxxx9r6dKlatOmjVavXq0rrrhCZ555pn7+858rLy/PiowA\nAAC28KWmq+LFRfIkxKmi7Kh8nPM9Ipg+ghsVFaXmzZururpaa9euVc+ePSVJR48eVYsWLUIeEAAA\nADDD9BHc1NRUPf/880pMTJTX61WvXr20d+9ePfnkk0pNTbUiIwAAABAw00dwJ0+erE2bNumVV17R\npEmTlJiYqD/84Q/avn277r//fisyAgAAAAFzGbVXbzgFBw4c0BlnnCG32y1J8nq9euONN/TrX//6\nlAOGSlnZUVWzbybkoqOjlJAQx3wtxIytxXytx4ytxXytx4ytVzvjUDF9BLchiYmJ/nIrSUeOHNHU\nqVND8dCSpL179yorK0uXXnqprrjiCs2cOVNVVVUhe3wAAAA4h+k9uHbIyspS69at9ac//UkHDx7U\npEmT5Ha7dd9999kdDQAAAGEmJEdwrfTll1/q008/1YwZM9SxY0d169ZNWVlZevPNN+2OBgAAgDAU\n9gW3Xbt2mj9/vhITE/1rhmHoyJEjNqYCAABAuAr7gtuqVStdfvnl/o8Nw9CiRYv005/+1MZUAAAA\nCFcRsQf325544glt2bJFf/7zn+2OAgAAgDAUUQV39uzZys/P11NPPaWOHTua+ly3O+wPVkek2rky\nX+swY2sxX+sxY2sxX+sxY+uFeraWFdwQnF63jkcffVSLFy/W7NmzdfXVV5v+/Pj4mJDmQV3M13rM\n2FrM13rM2FrM13rMOHJYUnDj4uI0ZsyYkD1ebm6uFi9erOzsbF1zzTVBPcbhw5Xy+Tg5c6i53VGK\nj49hvhZixtZivtZjxtZivtZjxtarnXGoBFRwJ06cGPADzpgxQzExMbrnnnuCDvVt27dv17PPPqu7\n7rpLaWlpKi0t9d/Wtm3bgB/H56vh6iMWYr7WY8bWYr7WY8bWYr7WY8aRI6CCW1RUZHWORn3wwQeq\nqanRs88+q2effVbSie0PLpdLmzdvti0XAAAAwpPLCPVm2TDF9aOtwfW5rceMrcV8rceMrcV8rceM\nrVc745A9XjCfVF1drf3798vn80k6cUS1qqpKGzduVP/+/UMWDgAAADDLdMH95z//qQceeEAHDhyo\nd1uLFi0ouAAAALCV6ZOOPfnkk7r44ov1/PPPq0WLFsrNzdWkSZPUsmVLzZ4924qMAAAAQMBMH8Hd\ntm2bHn/8cXXq1EkXXXSRYmNjlZmZqdjYWL3wwgtBnaMWAAAACBXTR3DdbrdatWolSTr33HO1detW\nSdJll12m7du3hzYdAAAAYJLpgvvDH/5QK1eulCRdcMEF2rBhgyRpz549oU0GAAAABMH0FoWRI0cq\nKytLzZo104033qi5c+dq5MiR+uKLL3TZZZdZkREAAAAImOkjuFdffbWWLl2q1NRUtW/fXvPnz5fb\n7VafPn306KOPWpERAAAACJjpgpubm6sLLrhAnTp1kiT16NFDzz77rMaNG6fc3NyQBwQAAADMCGiL\nwvbt2/3nvX3mmWfUqVMnnXHGGXXus3XrVi1ZskQPPvhg6FMCAAAAAQqo4O7atUt33323XC6XJGn0\n6NEN3u8Xv/hF6JIBAAAAQQio4F555ZVauXKlampq/HtwExMT/be7XC7FxsaqdevWlgUFAAAAAhHw\nWRQ6dOggSfrggw/UoUMH/9FcAAAAIJyYfpNZcnKyVq5cqcGDBys1NVXdu3fXkCFDtGLFCivyAQAA\nAKaYLrjvvfeeRo8eraSkJI0dO1ajR49WmzZtNGbMGH3wwQdWZAQAAAACZvpCD/PmzdOoUaPqvNFs\n+PDhys3N1XPPPac+ffqENCAAAABghukjuF9++aVuuummeus33nijtm7dGpJQAAAAQLBMF9ykpCTt\n2LGj3vqOHTvUqlWrkIQCAAAAgmW64N54442aOnWqVq1apfLycpWXl2vVqlWaNm2a+vbta0VGAAAA\nIGCm9+Dec8892rp1q+666y7/qcIMw9CVV16p8ePHhzwgwldhYZRycz06cEBKTPRo9GivUlNr7I4F\nAABOc6YLbr9+/fTaa6/pwIED2rp1qwzD0IUXXqiWLVvqiiuu0Jo1a6zIiTBTWBil226LUXFx7T8C\nRGvDhijl5VVScgEAgK0CKrhvv/22Vq9eLUkqLi7Wo48+Ko/H47999erVKi4u5uIPp5GcnObfKrcn\nFBdHKSenuRYsOGZTKgAAgAALblpaml599VUZhiFJ2r17t5o1a+a/vfZSvbNmzbImJcLOV181/MtM\nY+sAAABNJaCC2759ey1cuFCSlJmZqWeeeUbx8fGWBkN427+/4fcn7t9PwQUAAPYyfRaF/Px8yi3U\ntq3RyHoTBwEAAPgO0wUXkKTWrRsuuAkJDa8DAAA0FQougtRwka3dpw0AAGAXCi6Ccvx4w3ttG1sH\nAABoKhRcBKVdu4aP1Da2DgAA0FQouAhKVlaVkpPrXtAhOblGWVlVNiUCAAA4wfSVzABJSk2tUV5e\npXJzPSori1ZCQjWX6gUAAGGBgougpabW6MUXvUpIiFZZmVfV1ZRbAABgP7YoAAAAwFEouAAAAHAU\nCi4AAAAchYILAAAAR6HgAgAAwFEouAAAAHAUCi4AAAAchYILAAAAR6HgAgAAwFEouAAAAI1wFxYo\ndvhQKSNDscOHyl1YYHckBIBL9QIAADTAXVig+NsyFV28S5LkkeTeUKDDefnypabbGw4nxRFcAACA\nBsTmZPtpvKZiAAAX/ElEQVTLba3o4l2Kzcm2KRECRcEFAABoQFTJPlPrCB8UXAAAgAbUtEsytY7w\nQcEFAABoQEXWWFUnp9RZq05OUUXWWJsSIVC8yQwAAKABvtR0Hc7LV1zuU/KU7Zc3oY2Ojv4tbzCL\nABRcAACARvhS01Xx4iJ5EuJUUXZUvuoauyMhABG1RaGqqko33XST1q1bZ3cUSCosjNLw4R5lZEjD\nh3tUWBhRTycAAOBQEXMEt6qqSuPGjdO2bdvsjgKdKLe33Raj4uLaUhutDRuilJdXqdRUfrsFAAD2\niYhDbtu3b9fgwYNVVFRkdxT8V05O82+V2xOKi6OUk9PcpkQAAAAnRETBXbt2rXr27KnFixfLMAy7\n40BSSYnL1DoAAEBTiYgtCjfffLPdEfAd7do1/ItGY+sAAABNJSKO4CL8ZGVVKTm57l7b5OQaZWVV\n2ZQIAADghIg4ghsKbjddPpS6d5cWLjymnJzmOnAgWomJ1crKqlJamsTvTaFV+9zlOWwN5ms9Zmwt\n5ms9Zmy9UM/2tCm48fExdkdwnN69T/w5IVqn0dPJFjyHrcV8rceMrcV8rceMI8dp00gOH66Uz8fp\nq0LN7Y5SfHwM87UQM7YW87UeM7YW87UeM7Ze7YxD5bQpuD5fjaq5+ohlmK/1mLG1mK/1mLG1mK/1\nmHHkiLjNJC4Xp6ECAABA4yLuCO7mzZvtjoD/KiyMUm6uRwcOSImJHo0e7eUqZgAAwHYRV3ARHrhU\nLwAACFcRt0UB4YFL9QIAgHBFwUVQuFQvAAAIVxRcBKVZs4YvydvYOgAAQFOh4CJIDR+p5SwXAADA\nbhRcBKWsrOH1AweaNgcAAMB3UXARlP37G37q7N/PEVwAAGAvCi6C0rZtw3tt27Zt4iAAAADfQcFF\nUM47r+Fz3Ta2DgAA0FQouAjKxRdXS/ruUVzjv+sAAAD2oeAiKAsXelT/TAouLVzIhR4AAIC9KLgI\nSnl5Y+u8yQwAANiLgougtGzZ2DoXegAAAPai4CIow4Z51dAe3GHDquyIAwAA4EfBRVA2bYpWQ3tw\nT6wDAOAM7sICxQ4fKmVkKHb4ULkLC+yOhADQRhCUkpKG99o2tg4AQKRxFxYo/rZMRRfvkiR5JLk3\nFOhwXr58qen2hsNJcQQXQWnskryNXcIXAIBIE5uT7S+3taKLdyk2J9umRAgUBRdB2bGj4afO11/z\nlAIAOENUyT5T6wgftBEE5fjxhrciNLYOAECkqWmXZGod4YOCi6AYRsOnA2tsHQCASFORNVbVySl1\n1qqTU1SRNdamRAgUbzJDUKKjpeoGrsrbrFnTZwEAwAq+1HQdzstXXO5T8pTtlzehjY6O/i1vMIsA\nFFwEpW1bac+e+utt2nAEFwDgHL7UdFW8uEiehDhVlB2Vr7rG7kgIAFsUEJRrrqlSQxd6uOaa43bE\nAQAA8KPgIigrVjRXQxd6WLGCPQoAAMBeFFwE5dChxtY5iwIAALAXBRdBqWlkC1Jj6wAAAE2Fgoug\nJCc3/Gays8/mTWYAAMBeFFwE5eKLGz5Ue9FFHMIFAAD2ouAiKNdff1xud92jtW63oeuv5ywKAADA\nXhRcBOWdd5rJ56v7hjKfz6V33uEsCgAAwF4UXASlpKThsyU0tg4AQCRyFxYodvhQKSNDscOHyl1Y\nYHckBIArmSEozZo1/GayxtYBAIg07sICxd+WqejiXZIkjyT3hgIdzsvncr1hjiO4CEp5ecNHahtb\nBwAg0sTmZPvLba3o4l2Kzcm2KRECRcFFUHbubPip09g6AACRJqpkn6l1hA/aCIJyvJGTJTS2DgBA\npKlpl2RqHeGDgougNH4lM/bgAgCcoSJrrKqTU+qsVSenqCJrrE2JECjeZIageL0N77X1evmdCQDg\nDL7UdB3Oy1dc7lPylO2XN6GNjo7+LW8wiwAUXATFMAxJ9UvuiXUAAJzBvXWLotetkcrLFd2ypdxb\nt1BwIwAFF0HxeKSKiobXAQBwguZL/qT4MaPk8vkkSe4jRxQ/ZpQOS6oafIu94XBS/HsyghLVyDMn\nKoojuAAAZ2g5fZq/3NZy+XxqOX2aTYkQKAougnL0aMN7cI8e5SkFAHAGV3m5qXWED9oIgtLYXlv2\n4AIAnMJo2dLUOsIHBRdBauyKZVzJDADgDMeuuU7fPWxj/Hcd4Y2CCwAA0IAWby+vd9jGJanF22/a\nEQcmUHABAAAa4Dp0qJH1g02cBGZRcAEAABriamTbXWPrCBsUXAAAgAZUX9zZ1DrCBwUXAACgAd7r\nrm/wTWbe6663Iw5MoOACAAA0IHbhiw2+ySx24Ys2pIEZEVFwq6qqNGnSJP3kJz9RRkaG8vLy7I4E\nAAAczlV2oOH1g2VNnARmRdsdIBCzZs3Spk2blJ+fr6KiIj3wwANKTk7Wtddea3c0AADgVMePN7xe\nVdW0OWBa2B/Brays1GuvvaaHHnpInTp10tVXX60RI0Zo0aJFdkcDAABO1qyZuXWEjbAvuFu2bJHP\n51Nqaqp/rVu3bvr0009tTAUAAJyu8Uv1tmriJDAr7AtuSUmJWrdurejo/+2maNOmjbxer8rK2AMD\nAACsUZPYtpH1Nk2cBGaF/R7cyspKNW/evM5a7cdVJvbAuN1h3+UdIzqaWYdS7XOX57A1mK/1mLG1\nmK913PtLGlyP2l/Ca12Ihfr5G/YF1+Px1CuytR/HxMQE/Djx8YHfF6fCpYSEOLtDOBLPYWsxX+sx\nY2sxXws0csUyt4vXunAX9gX3zDPP1MGDB1VTU6OoqBPtvrS0VC1atFB8fHzAj3P4cKV8vhqrYp6G\nYtTwDpcalZVVNnUYR3O7oxQfH8Nz2CLM13rM2FrM1zotL+6sZqtX1Vuv+nFnHS07akMi56p9HodK\n2Bfciy66SNHR0SosLFR6erokaf369erc2dxl8ny+GlVX84MfOj6dON31t3+7NST5mLNFeA5bi/la\njxlbi/mG3pHJ03TG0MFyl+zzr/naJan8oWnyMeuwFvYbSFq0aKEBAwZoypQp2rhxo95//33l5eXp\n1ltvtTvaaW3fvmOSqiXV/oDXSKr+7zoAAJHPl5quQy8vkbf/QCkjQ97+A3Xo5SXypabbHQ3fw2UY\nxncvsxx2jh07pmnTpundd99Vq1atNGLECGVmZpp6jLKyo/xma4Ho6CglJMQxXwsxY2sxX+sxY2sx\nX+sxY+vVzjhkjxeyR7JQixYtNGPGDM2YMcPuKAAAAAhzYb9FAQAAADCDggsAAABHoeACAADAUSi4\nAAAAcBQKLgAAAByFggsAAABHoeACAADAUSi4AAAAcBQKLgAAAByFggsAAABHoeACAADAUSi4AAAA\ncBQKLgAAAByFggsAAABHoeACAADAUSi4AAAAcBQKLgAAAByFggsAAABHoeACAADAUSi4AAAAcBQK\nLgAAAByFggsAAABHoeACAADAUSi4AAAAcBQKLgAAAByFggsAAABHoeACAADAUSi4AAAAcBQKLgAA\nAByFggsAAABHoeACAADAUSi4AAAAcBQKLgAAAByFggsAAABHoeACAADAUSi4AAAAcBQKLgAAAByF\nggsAAABHoeACAADAUSi4AAAAcBQKLgAAAByFggsAAABHoeACAADAUSi4AAAAcBQKLgAAAByFggsA\nAABHoeACAADAUSi4AAAAcJSIKrh33HGH3njjDbtjAAAAIIxFRME1DEOPPvqo/vWvf9kdBQAAAGEu\n2u4A32fv3r267777VFRUpPj4eLvjAAAAIMyF/RHcTZs2qUOHDvrLX/6iuLg4u+MAAAAgzIX9Edyr\nrrpKV111ld0xAAAAECFsL7her1d79+5t8LZ27dopJiamiRMBAAAgktlecD/55BMNGzZMLper3m25\nubnq06dPSL6O2x32uzEiUu1cma91mLG1mK/1mLG1mK/1mLH1Qj1b2wtujx49tGXLFsu/Tnw8R4Kt\nxHytx4ytxXytx4ytxXytx4wjB7+KAAAAwFEouAAAAHCUiCq4De3TBQAAAL7NZRiGYXcIAAAAIFQi\n6gguAAAA8H0ouAAAAHAUCi4AAAAchYILAAAAR6HgAgAAwFEcWXDnzJmjnj176tJLL9Xs2bNPet/C\nwkINGTJEaWlp6tu3r5YuXdpEKSNHVVWVJk2apJ/85CfKyMhQXl5eo/fdtGmTBg8erNTUVP3qV7/S\n559/3oRJI5eZGf/973/XwIEDlZaWpgEDBmjlypVNmDQymZlvraKiIqWlpWndunVNkDDymZnxF198\noVtuuUVdu3ZV//79tWbNmiZMGpnMzHfFihXq16+f0tLSNHToUG3atKkJk0a+qqoq3XTTTSf92ee1\nLniBzDckr3OGw7zwwgvGVVddZRQUFBhr1qwxMjIyjAULFjR435KSEuMnP/mJkZ2dbezYscN46623\njC5duhh///vfmzh1eHvkkUeMAQMGGJs3bzZWrFhhpKenG++++269+1VUVBiXX3658cQTTxjbt283\npk+fblx++eVGZWWlDakjS6Az3rx5s9G5c2dj0aJFxs6dO41FixYZP/7xj40tW7bYkDpyBDrfb7vj\njjuMTp06GWvXrm2ilJEt0BkfOXLEuPzyy42HH37Y2Llzp5GTk2N0797d2L9/vw2pI0eg8/3Pf/5j\ndOnSxVi2bJmxc+dO45FHHjEuv/xy49ixYzakjjxer9cYNWrUSX/2ea0LXiDzDdXrnOMK7pVXXmm8\n/vrr/o+XLVtm9O7du8H7vvLKK0a/fv3qrE2ePNn43e9+Z2nGSFJRUWF06dLFWLdunX9t3rx5RmZm\nZr37Ll261Lj66qvrrF177bV1/v9AfWZmPGfOHOPOO++ss3b77bcb2dnZlueMVGbmW2vZsmXGzTff\nTMENkJkZv/TSS8a1115bZ+2Xv/ylsWrVKstzRioz883LyzN+8Ytf+D8uLy83LrzwQuOzzz5rkqyR\nbNu2bcaAAQOMAQMGnPRnn9e64AQ631C9zjlqi8K+ffv0zTffqHv37v61bt26affu3SotLa13/169\nemnGjBn11o8cOWJpzkiyZcsW+Xw+paam+te6deumTz/9tN59P/30U3Xr1q3OWnp6uj7++GPLc0Yy\nMzMeNGiQxo8fX2+9vLzc0oyRzMx8JamsrEy///3v9eijj8rgOjgBMTPjdevWqXfv3nXWli5dql69\nelmeM1KZmW/r1q21bds2FRQUyDAM/fnPf1arVq10zjnnNGXkiLR27Vr17NlTixcvPunPPq91wQl0\nvqF6nYs2nTCMlZSUyOVyKSkpyb/Wtm1bGYahPXv2qG3btnXu36FDB3Xo0MH/8f79+/X2228rKyur\nyTKHu5KSErVu3VrR0f97qrRp00Zer1dlZWVKSEjwr+/bt08/+tGP6nx+mzZttG3btibLG4nMzPiC\nCy6o87n/+c9/9O9//1u33HJLk+WNNGbmK0kzZ87UoEGD1LFjx6aOGrHMzHjXrl265JJL9PDDD2vl\nypU6++yzdf/99ys9Pd2O6BHBzHz79eunlStX6pZbbpHb7VZUVJT+8Ic/qFWrVnZEjyg333xzQPfj\ntS44gc43VK9zEXcE1+v1aufOnQ3+qaiokCQ1b97cf//av1dVVX3v4957771KSkrSr3/9a+u+gQhT\nWVlZZ55S4zM9duxYg/f9vtmf7szM+NsOHDige++9V926dVOfPn0szRjJzMz3X//6lz7++GP9v//3\n/5osnxOYmXFFRYXmz5+vpKQkzZ8/X927d9cdd9yhvXv3NlneSGNmvgcPHlRpaammTJmipUuXauDA\ngZowYYIOHDjQZHmdjte6pnMqr3MRdwT3k08+0bBhw+Ryuerd9rvf/U7SiR/47/7wx8TENPqYFRUV\nuueee7Rz50698sor8ng8FiSPTB6Pp94PbWMzbey+LVq0sDZkhDMz41qlpaW67bbb5HK59PTTT1ue\nMZIFOl+v16spU6Zo6tSp9V68cHJmnsNut1sXXXSRRo8eLUnq1KmTPvzwQy1btkwjR45smsARxsx8\n58yZowsvvNB/tOyRRx5R37599Ze//EUjRoxomsAOx2td0zjV17mIK7g9evTQli1bGrxt3759mjNn\njkpLS/1bD2q3LbRr167BzykvL9eIESNUVFSkl156SSkpKZZlj0RnnnmmDh48qJqaGkVFnTjgX1pa\nqhYtWig+Pr7efUtKSuqslZaWNjp7nGBmxpK0d+9eDRs2TG63W/n5+fX+iR11BTrfTz/9VEVFRbr3\n3nvr7A+78847NXDgQE2dOrWpo0cMM8/hdu3a1fsnyPPOO0/ffPNNk+WNNGbm+/nnn2vYsGH+j10u\nlzp16qTdu3c3aWYn47XOeqF4nYu4LQonk5SUpPbt22vDhg3+tfXr16t9+/b19t9KkmEYGj16tIqL\ni7Vo0SL23DXgoosuUnR0tAoLC/1r69evV+fOnevdt2vXrvU22RcUFNR5YwTqMzPjyspKjRgxQs2a\nNdOiRYsafF6jrkDn27VrV7333ntatmyZ/vrXv+qvf/2rJOmxxx5jX/73MPMcTk1NrXeQ4ssvv1Ry\ncrLlOSOVmfkmJSXV2wv61Vdf6eyzz7Y85+mC1zprhep1zlEFV5KGDBmiOXPmaO3atVqzZo2efPJJ\n3Xrrrf7bDxw44N+ru3TpUq1du1bTp09Xy5YtVVpaqtLSUh06dMiu+GGnRYsWGjBggKZMmaKNGzfq\n/fffV15enn+mpaWl8nq9kqTrrrtOR44c0eOPP67t27dr+vTpqqysVN++fe38FsKemRk/99xzKioq\n0owZM1RTU+N/znIWhcYFOt/mzZsrJSWlzh/pRGFITEy081sIe2aew0OGDNEXX3yh3Nxc7dy5U08/\n/bSKiorUv39/O7+FsGZmvr/61a+0dOlSLVu2TDt37tScOXP0zTffaODAgXZ+CxGP1zprWfI6Z/5M\nZuHN5/MZM2fONHr06GH07NnTePLJJ+vcftVVVxlz5841DON/J3L/7p+TnR/zdFRZWWlMmDDBSEtL\nM3r16mUsXLjQf9uFF15Y59x/n376qTFo0CCja9euxuDBg43NmzfbETniBDrj66+/vsHn7IQJE+yK\nHhHMPIe/jfPgBs7MjAsKCoxBgwYZXbp0MQYNGmSsX7/ejsgRxcx8X3vtNaNv375Genq6MXToUP47\nHITv/uzzWhdaJ5tvqF7nXIbBiR4BAADgHI7bogAAAIDTGwUXAAAAjkLBBQAAgKNQcAEAAOAoFFwA\nAAA4CgUXAAAAjkLBBQAAgKNQcAEAAOAoFFwAAAA4SrTdAQAAUu/evbV7927/xy6XS7Gxsbr44os1\nZswYde/e3X/bW2+9pVdffVWbN2+Wz+fTeeedpwEDBmjo0KFq1qyZ/34TJ05UcXGxFi5c2KTfCwDY\njSO4ABAm7rjjDn344Yf68MMPtXr1ai1evFgtW7bUiBEjtGfPHknS5MmT9dBDDykjI0OLFy/WsmXL\nNHToUC1YsECZmZmqrKy0+bsAAPtxBBcAwkRMTIzatGnj/7ht27aaNm2aevXqpRUrVqhly5Z6/fXX\ntXDhQqWnp/vvd8455+hnP/uZBgwYoFmzZmnq1Kk2pAeA8MERXAAIY263W5LUvHlz5efnq1evXnXK\nba2zzjpLw4cP1+uvv67y8vKmjgkAYYWCCwBhau/evXrkkUcUGxurXr16afPmzerWrVuj9+/Zs6e8\nXq82btzYhCkBIPywRQEAwsTzzz+vF154QZLk8/l0/PhxdezYUTk5OXK73TIMQ61bt2708xMSEiRJ\nZWVlTZIXAMIVBRcAwsSQIUM0bNgwSVJUVJTOOOMMtWzZUpJUVVUll8ulI0eONPr5hw4dkvS/ogsA\npyu2KABAmDjjjDOUkpKilJQUJScn+8utdGIP7iWXXKL169c3+vlr1qyRx+PRJZdc0hRxASBsUXAB\nIELcfvvt+r//+z+tXbu23m379u3TSy+9pIEDB9YpxgBwOmKLAgBEiOuvv16ffPKJ7rrrLt1zzz3q\n06ePPB6P1q9fr5ycHJ199tmaMGGC3TEBwHYUXAAIAy6XK6D7PfDAA7r00kuVn5+vvLw8eb1enXfe\neRo2bJh+85vfKDqa/6wDgMswDMPuEAAAAECosAcXAAAAjkLBBQAAgKNQcAEAAOAoFFwAAAA4CgUX\nAAAAjkLBBQAAgKNQcAEAAOAoFFwAAAA4CgUXAAAAjkLBBQAAgKNQcAEAAOAoFFwAAAA4yv8Hb3Qe\n7nvBNbIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdfebfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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yRAsXLgwf29jYqJUrV/b73pervf0cv22awOm0y+0eSn9NRI/NRX/NR4/NRX/NR4/N19tj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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe98ae48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SAAAAsC3KMAAAAGyLMgwAAADbogwDAADAtijDAAAAsC3KMAAAAGyLMgwAAADbogwDAADA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xceea2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3XA2H4REjRujxxx/XrFmzmkKp3+/XSy+9pMsuuyyszUmSw+FoFnobPycnJwfU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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xe12eba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IilmzouuCcC2v16ZZs1whqggAAIDdJBAk33/f1DgftAQAAKFjShiOjo7WDTfc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\n/gU72QJKWoJOfwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcc2e908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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S0tStWzf98Ic/VF5enhU1opVzu/3Ky/Np2bIYlZY65XJVa9KkSi7uAwAAYWc6LNvtdkVH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xc9b64a8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sb\n",
    "\n",
    "for i in range(1,len(initial_selection_features)):\n",
    "\n",
    "    for point in data:\n",
    "        if point[0]==1:\n",
    "            plt.scatter(point[0], point[i], color = \"r\")\n",
    "        else:\n",
    "            plt.scatter(point[0], point[i], color = \"b\")\n",
    "\n",
    "    plt.xlabel('POI')\n",
    "    plt.ylabel(initial_selection_features[i])\n",
    "    plt\n",
    "    plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I notice that *total_payments* has clear outlier. I investigate who it is"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "LAY KENNETH L\n",
      "103559793\n"
     ]
    }
   ],
   "source": [
    "start = 0\n",
    "suspect = \"\"\n",
    "for person in enron_data.keys():\n",
    "    if  enron_data[person]['total_payments']!= \"NaN\" and enron_data[person]['total_payments'] > start:\n",
    "        suspect =  person\n",
    "        start = enron_data[person]['total_payments']\n",
    "\n",
    "print suspect\n",
    "print start\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Classifier\n",
    "Prepare data for classification and testing. I will test performance using the *tester.py* file provided by Udacity."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\marcelot\\AppData\\Local\\Continuum\\Anaconda2\\lib\\site-packages\\sklearn\\cross_validation.py:44: DeprecationWarning: This module was deprecated in version 0.18 in favor of the model_selection module into which all the refactored classes and functions are moved. Also note that the interface of the new CV iterators are different from that of this module. This module will be removed in 0.20.\n",
      "  \"This module will be removed in 0.20.\", DeprecationWarning)\n"
     ]
    }
   ],
   "source": [
    "from tester import test_classifier"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Create 4 initial classifiers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.naive_bayes import GaussianNB\n",
    "from sklearn.svm import SVC\n",
    "from sklearn.tree import DecisionTreeClassifier\n",
    "from sklearn.ensemble import AdaBoostClassifier\n",
    "\n",
    "\n",
    "# Naive Bayes\n",
    "clf_NB = GaussianNB()\n",
    "\n",
    "# SVM\n",
    "clf_SVM = SVC()\n",
    "\n",
    "# Decision Tree\n",
    "clf_TREE = DecisionTreeClassifier()\n",
    "\n",
    "# AdaBoost:\n",
    "clf_ADA = AdaBoostClassifier()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Compare initial performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "GaussianNB(priors=None)\n",
      "\tAccuracy: 0.84627\tPrecision: 0.37271\tRecall: 0.22400\tF1: 0.27983\tF2: 0.24343\n",
      "\tTotal predictions: 15000\tTrue positives:  448\tFalse positives:  754\tFalse negatives: 1552\tTrue negatives: 12246\n",
      "\n",
      "Got a divide by zero when trying out: SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,\n",
      "  decision_function_shape=None, degree=3, gamma='auto', kernel='rbf',\n",
      "  max_iter=-1, probability=False, random_state=None, shrinking=True,\n",
      "  tol=0.001, verbose=False)\n",
      "Precision or recall may be undefined due to a lack of true positive predicitons.\n",
      "DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=None,\n",
      "            max_features=None, max_leaf_nodes=None,\n",
      "            min_impurity_split=1e-07, min_samples_leaf=1,\n",
      "            min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
      "            presort=False, random_state=None, splitter='best')\n",
      "\tAccuracy: 0.80593\tPrecision: 0.29019\tRecall: 0.31500\tF1: 0.30209\tF2: 0.30970\n",
      "\tTotal predictions: 15000\tTrue positives:  630\tFalse positives: 1541\tFalse negatives: 1370\tTrue negatives: 11459\n",
      "\n",
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
      "          learning_rate=1.0, n_estimators=50, random_state=None)\n",
      "\tAccuracy: 0.85593\tPrecision: 0.45034\tRecall: 0.36500\tF1: 0.40320\tF2: 0.37938\n",
      "\tTotal predictions: 15000\tTrue positives:  730\tFalse positives:  891\tFalse negatives: 1270\tTrue negatives: 12109\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_classifier(clf_NB, enron_data, initial_selection_features)\n",
    "test_classifier(clf_SVM, enron_data, initial_selection_features)\n",
    "test_classifier(clf_TREE, enron_data, initial_selection_features)\n",
    "test_classifier(clf_ADA, enron_data, initial_selection_features)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "AdaBoost has the best performance, so we go further only with it."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the feature importances importances on the training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "salary: 0.2\n",
      "total_payments: 0.18\n",
      "exercised_stock_options: 0.12\n",
      "bonus: 0.16\n",
      "restricted_stock: 0.1\n",
      "total_stock_value: 0.04\n",
      "expenses: 0.08\n",
      "other: 0.02\n",
      "share_shared_receipt_with_poi: 0.04\n",
      "share_from_this_person_to_poi: 0.02\n",
      "share_from_poi_to_this_person: 0.04\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(initial_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(round(imp,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tune this model, optimizing F1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\marcelot\\AppData\\Local\\Continuum\\Anaconda2\\lib\\site-packages\\sklearn\\metrics\\classification.py:1113: UndefinedMetricWarning: F-score is ill-defined and being set to 0.0 due to no predicted samples.\n",
      "  'precision', 'predicted', average, warn_for)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=10, error_score='raise',\n",
       "       estimator=AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
       "          learning_rate=1.0, n_estimators=50, random_state=None),\n",
       "       fit_params={}, iid=True, n_jobs=1,\n",
       "       param_grid={'n_estimators': [1, 5, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 50, 100, 1000, 2000], 'learning_rate': [0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9, 1, 2, 3, 5, 10]},\n",
       "       pre_dispatch='2*n_jobs', refit=True, return_train_score=True,\n",
       "       scoring='f1', verbose=0)"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import GridSearchCV\n",
    "parameters = {'learning_rate':[0.1, 0.2, 0.3, 0.5, 0.7,0.8, 0.9, 1, 2,3, 5, 10],'n_estimators':[1,5,8,10,11, 12, 13, 14, 15, 16, 17, 18,50,100,1000, 2000] }\n",
    "clf_ADA = AdaBoostClassifier()\n",
    "clf = GridSearchCV(clf_ADA, parameters, scoring = 'f1', cv = 10 )\n",
    "clf.fit(features, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'n_estimators': 16, 'learning_rate': 0.9}\n",
      "0.551282051282\n"
     ]
    }
   ],
   "source": [
    "print clf.best_params_\n",
    "print clf.best_score_ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double check performance of the best model, and obtain the other metrics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
      "          learning_rate=0.9, n_estimators=16, random_state=None)\n",
      "\tAccuracy: 0.87300\tPrecision: 0.53251\tRecall: 0.38900\tF1: 0.44958\tF2: 0.41116\n",
      "\tTotal predictions: 15000\tTrue positives:  778\tFalse positives:  683\tFalse negatives: 1222\tTrue negatives: 12317\n",
      "\n"
     ]
    }
   ],
   "source": [
    "lr = 0.9\n",
    "n_est = 16\n",
    "clf_ADA = AdaBoostClassifier(learning_rate = lr, n_estimators = n_est)\n",
    "test_classifier(clf_ADA, enron_data, initial_selection_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the feature importances importances on the training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "salary: 0.13\n",
      "total_payments: 0.19\n",
      "exercised_stock_options: 0.13\n",
      "bonus: 0.25\n",
      "restricted_stock: 0.13\n",
      "total_stock_value: 0.0\n",
      "expenses: 0.06\n",
      "other: 0.06\n",
      "share_shared_receipt_with_poi: 0.06\n",
      "share_from_this_person_to_poi: 0.0\n",
      "share_from_poi_to_this_person: 0.0\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(initial_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(round(imp,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how the performance compares if we drop the features with 0 importance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "second_selection_features = initial_selection_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "second_selection_features.remove('share_from_this_person_to_poi')\n",
    "second_selection_features.remove('share_from_poi_to_this_person')\n",
    "second_selection_features.remove('total_stock_value')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'salary', 'total_payments', 'exercised_stock_options', 'bonus', 'restricted_stock', 'expenses', 'other', 'share_shared_receipt_with_poi']\n",
      "\n",
      " Numbers of features: 9\n"
     ]
    }
   ],
   "source": [
    "print  second_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(second_selection_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Re-create relevant variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, second_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and test performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
      "          learning_rate=0.9, n_estimators=16, random_state=None)\n",
      "\tAccuracy: 0.87247\tPrecision: 0.52921\tRecall: 0.39400\tF1: 0.45171\tF2: 0.41522\n",
      "\tTotal predictions: 15000\tTrue positives:  788\tFalse positives:  701\tFalse negatives: 1212\tTrue negatives: 12299\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_classifier(clf_ADA, enron_data, second_selection_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "salary: 0.13\n",
      "total_payments: 0.19\n",
      "exercised_stock_options: 0.13\n",
      "bonus: 0.25\n",
      "restricted_stock: 0.13\n",
      "expenses: 0.06\n",
      "other: 0.06\n",
      "share_shared_receipt_with_poi: 0.06\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(second_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(round(imp,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The performance is roughly the same, with slightly better *Recall* and *F1*. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's double check the tuning."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=10, error_score='raise',\n",
       "       estimator=AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
       "          learning_rate=1.0, n_estimators=50, random_state=None),\n",
       "       fit_params={}, iid=True, n_jobs=1,\n",
       "       param_grid={'n_estimators': [1, 5, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 50, 100, 1000, 2000], 'learning_rate': [0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9, 1, 2, 3, 5, 10]},\n",
       "       pre_dispatch='2*n_jobs', refit=True, return_train_score=True,\n",
       "       scoring='f1', verbose=0)"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf_ADA = AdaBoostClassifier()\n",
    "clf = GridSearchCV(clf_ADA, parameters, scoring = 'f1', cv = 10 )\n",
    "clf.fit(features, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'n_estimators': 11, 'learning_rate': 0.5}\n",
      "0.428904428904\n"
     ]
    }
   ],
   "source": [
    "print clf.best_params_\n",
    "print clf.best_score_ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double check performance of the best model, and obtain the other metrics:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
      "          learning_rate=0.5, n_estimators=11, random_state=None)\n",
      "\tAccuracy: 0.88767\tPrecision: 0.63496\tRecall: 0.37050\tF1: 0.46795\tF2: 0.40417\n",
      "\tTotal predictions: 15000\tTrue positives:  741\tFalse positives:  426\tFalse negatives: 1259\tTrue negatives: 12574\n",
      "\n"
     ]
    }
   ],
   "source": [
    "lr = 0.5\n",
    "n_est = 11\n",
    "clf_ADA = AdaBoostClassifier(learning_rate = lr, n_estimators = n_est)\n",
    "test_classifier(clf_ADA, enron_data, second_selection_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a clear improvement, particularly in Precision. Let's check the importance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "salary: 0.0\n",
      "total_payments: 0.09\n",
      "exercised_stock_options: 0.18\n",
      "bonus: 0.27\n",
      "restricted_stock: 0.27\n",
      "expenses: 0.09\n",
      "other: 0.0\n",
      "share_shared_receipt_with_poi: 0.09\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(second_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(round(imp,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see how the performance compares if we drop the features with 0 importance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "third_selection_features = second_selection_features"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "third_selection_features.remove('other')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'salary', 'total_payments', 'exercised_stock_options', 'bonus', 'restricted_stock', 'expenses', 'share_shared_receipt_with_poi']\n",
      "\n",
      " Numbers of features: 8\n"
     ]
    }
   ],
   "source": [
    "print  third_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(third_selection_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Re-create relevant variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, third_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and test performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
      "          learning_rate=0.5, n_estimators=11, random_state=None)\n",
      "\tAccuracy: 0.89007\tPrecision: 0.66924\tRecall: 0.34700\tF1: 0.45703\tF2: 0.38398\n",
      "\tTotal predictions: 15000\tTrue positives:  694\tFalse positives:  343\tFalse negatives: 1306\tTrue negatives: 12657\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_classifier(clf_ADA, enron_data, third_selection_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Performance is slightly improved in *Precision* but drops in *Recall* and *F1*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We stop this investigation and stick with the *second_selection_features* list, with the *learning rate* = 0.5 and *n_estimators* = 11."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Alternative Feature Selection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this case I will start with the full list of features including the created festures, and use recursive feature elimination (RFE) to select the 8 best features from the full list and compare performance the performance against my manually selected features. I'll start the RFE using the tuned parameters from above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.feature_selection import RFE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, all_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "rfe = RFE(clf_ADA,8)\n",
    "selector = rfe.fit(features,labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "salary (15)\n",
      "to_messages (14)\n",
      "deferral_payments (13)\n",
      "total_payments (1)\n",
      "exercised_stock_options (1)\n",
      "bonus (1)\n",
      "restricted_stock (1)\n",
      "shared_receipt_with_poi (9)\n",
      "restricted_stock_deferred (8)\n",
      "total_stock_value (7)\n",
      "expenses (1)\n",
      "loan_advances (11)\n",
      "from_messages (12)\n",
      "other (1)\n",
      "from_this_person_to_poi (6)\n",
      "director_fees (5)\n",
      "deferred_income (4)\n",
      "long_term_incentive (3)\n",
      "from_poi_to_this_person (2)\n",
      "share_shared_receipt_with_poi (1)\n",
      "share_from_this_person_to_poi (1)\n",
      "share_from_poi_to_this_person (10)\n"
     ]
    }
   ],
   "source": [
    "for feature, rank in zip(all_features[1:], selector.ranking_ ):\n",
    "    print feature +\" (\" + str(rank) +\")\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "alternative_selection_features = ['poi']\n",
    "for feature, rank in zip(all_features[1:], selector.ranking_ ):\n",
    "    if rank == 1:\n",
    "        alternative_selection_features.append(feature)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'total_payments', 'exercised_stock_options', 'bonus', 'restricted_stock', 'expenses', 'other', 'share_shared_receipt_with_poi', 'share_from_this_person_to_poi']\n",
      "\n",
      " Numbers of features: 9\n"
     ]
    }
   ],
   "source": [
    "print  alternative_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(alternative_selection_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Re-create relevant variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, alternative_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and test performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
      "          learning_rate=0.5, n_estimators=11, random_state=None)\n",
      "\tAccuracy: 0.88933\tPrecision: 0.64912\tRecall: 0.37000\tF1: 0.47134\tF2: 0.40481\n",
      "\tTotal predictions: 15000\tTrue positives:  740\tFalse positives:  400\tFalse negatives: 1260\tTrue negatives: 12600\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_classifier(clf_ADA, enron_data, alternative_selection_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We notice an increase in performance, particularly in *Recall* and *F1*, therefore we proceed in this path. Let's check the importance of features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "total_payments: 0.09\n",
      "exercised_stock_options: 0.18\n",
      "bonus: 0.27\n",
      "restricted_stock: 0.27\n",
      "expenses: 0.09\n",
      "other: 0.0\n",
      "share_shared_receipt_with_poi: 0.09\n",
      "share_from_this_person_to_poi: 0.0\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(alternative_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(round(imp,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since there are features with close to 0 importance, we investigate if we can drop features."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, all_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "rfe = RFE(clf_ADA,6)\n",
    "selector = rfe.fit(features,labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "salary (17)\n",
      "to_messages (16)\n",
      "deferral_payments (15)\n",
      "total_payments (3)\n",
      "exercised_stock_options (1)\n",
      "bonus (1)\n",
      "restricted_stock (2)\n",
      "shared_receipt_with_poi (11)\n",
      "restricted_stock_deferred (10)\n",
      "total_stock_value (9)\n",
      "expenses (1)\n",
      "loan_advances (13)\n",
      "from_messages (14)\n",
      "other (1)\n",
      "from_this_person_to_poi (8)\n",
      "director_fees (7)\n",
      "deferred_income (6)\n",
      "long_term_incentive (5)\n",
      "from_poi_to_this_person (4)\n",
      "share_shared_receipt_with_poi (1)\n",
      "share_from_this_person_to_poi (1)\n",
      "share_from_poi_to_this_person (12)\n"
     ]
    }
   ],
   "source": [
    "for feature, rank in zip(all_features[1:], selector.ranking_ ):\n",
    "    print feature +\" (\" + str(rank) +\")\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "second_alternative_selection_features = ['poi']\n",
    "for feature, rank in zip(all_features[1:], selector.ranking_ ):\n",
    "    if rank == 1:\n",
    "        second_alternative_selection_features.append(feature)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'exercised_stock_options', 'bonus', 'expenses', 'other', 'share_shared_receipt_with_poi', 'share_from_this_person_to_poi']\n",
      "\n",
      " Numbers of features: 7\n"
     ]
    }
   ],
   "source": [
    "print  second_alternative_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(second_alternative_selection_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Re-create relevant variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, second_alternative_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and test performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
      "          learning_rate=0.5, n_estimators=11, random_state=None)\n",
      "\tAccuracy: 0.88943\tPrecision: 0.72027\tRecall: 0.36950\tF1: 0.48843\tF2: 0.40937\n",
      "\tTotal predictions: 14000\tTrue positives:  739\tFalse positives:  287\tFalse negatives: 1261\tTrue negatives: 11713\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_classifier(clf_ADA, enron_data, second_alternative_selection_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Performance is again improved, therefore we can investigate further. Let's see the importance again."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exercised_stock_options: 0.27\n",
      "bonus: 0.18\n",
      "expenses: 0.18\n",
      "other: 0.18\n",
      "share_shared_receipt_with_poi: 0.0\n",
      "share_from_this_person_to_poi: 0.18\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(second_alternative_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(round(imp,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are still features with close to 0 importance. Let's see what happens if we drop an additional feature."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, all_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "rfe = RFE(clf_ADA,5)\n",
    "selector = rfe.fit(features,labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "salary (18)\n",
      "to_messages (17)\n",
      "deferral_payments (16)\n",
      "total_payments (4)\n",
      "exercised_stock_options (1)\n",
      "bonus (1)\n",
      "restricted_stock (3)\n",
      "shared_receipt_with_poi (12)\n",
      "restricted_stock_deferred (11)\n",
      "total_stock_value (10)\n",
      "expenses (2)\n",
      "loan_advances (14)\n",
      "from_messages (15)\n",
      "other (1)\n",
      "from_this_person_to_poi (9)\n",
      "director_fees (8)\n",
      "deferred_income (7)\n",
      "long_term_incentive (6)\n",
      "from_poi_to_this_person (5)\n",
      "share_shared_receipt_with_poi (1)\n",
      "share_from_this_person_to_poi (1)\n",
      "share_from_poi_to_this_person (13)\n"
     ]
    }
   ],
   "source": [
    "for feature, rank in zip(all_features[1:], selector.ranking_ ):\n",
    "    print feature +\" (\" + str(rank) +\")\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "third_alternative_selection_features = ['poi']\n",
    "for feature, rank in zip(all_features[1:], selector.ranking_ ):\n",
    "    if rank == 1:\n",
    "        third_alternative_selection_features.append(feature)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'exercised_stock_options', 'bonus', 'other', 'share_shared_receipt_with_poi', 'share_from_this_person_to_poi']\n",
      "\n",
      " Numbers of features: 6\n"
     ]
    }
   ],
   "source": [
    "print  third_alternative_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(third_alternative_selection_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Re-create relevant variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, third_alternative_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and test performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
      "          learning_rate=0.5, n_estimators=11, random_state=None)\n",
      "\tAccuracy: 0.84331\tPrecision: 0.47919\tRecall: 0.21300\tF1: 0.29491\tF2: 0.23962\n",
      "\tTotal predictions: 13000\tTrue positives:  426\tFalse positives:  463\tFalse negatives: 1574\tTrue negatives: 10537\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_classifier(clf_ADA, enron_data, third_alternative_selection_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Performance is clearly reduced. Let's check the importance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exercised_stock_options: 0.18\n",
      "bonus: 0.09\n",
      "other: 0.36\n",
      "share_shared_receipt_with_poi: 0.18\n",
      "share_from_this_person_to_poi: 0.18\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(third_alternative_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(round(imp,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Final thing we can do is to manually remove the features with near 0 importance and compare performance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "forth_alternative_selection_features = second_alternative_selection_features\n",
    "forth_alternative_selection_features.remove('share_shared_receipt_with_poi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'exercised_stock_options', 'bonus', 'expenses', 'other', 'share_from_this_person_to_poi']\n",
      "\n",
      " Numbers of features: 6\n"
     ]
    }
   ],
   "source": [
    "print  forth_alternative_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(forth_alternative_selection_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Re-create relevant variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, forth_alternative_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and test performance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
      "          learning_rate=0.5, n_estimators=11, random_state=None)\n",
      "\tAccuracy: 0.86864\tPrecision: 0.57285\tRecall: 0.31650\tF1: 0.40773\tF2: 0.34761\n",
      "\tTotal predictions: 14000\tTrue positives:  633\tFalse positives:  472\tFalse negatives: 1367\tTrue negatives: 11528\n",
      "\n"
     ]
    }
   ],
   "source": [
    "test_classifier(clf_ADA, enron_data, forth_alternative_selection_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see the importance:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exercised_stock_options: 0.09\n",
      "bonus: 0.18\n",
      "expenses: 0.27\n",
      "other: 0.27\n",
      "share_from_this_person_to_poi: 0.18\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(forth_alternative_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(round(imp,2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far, *second_alternative_selection_features* seems the best option."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Best option"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'exercised_stock_options', 'bonus', 'expenses', 'other', 'share_shared_receipt_with_poi', 'share_from_this_person_to_poi']\n",
      "\n",
      " Numbers of features: 7\n"
     ]
    }
   ],
   "source": [
    "second_alternative_selection_features = ['poi', 'exercised_stock_options', 'bonus', 'expenses', 'other', 'share_shared_receipt_with_poi', 'share_from_this_person_to_poi']\n",
    "\n",
    "print  second_alternative_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(second_alternative_selection_features))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Double Check tune"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, second_alternative_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GridSearchCV(cv=10, error_score='raise',\n",
       "       estimator=AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None,\n",
       "          learning_rate=1.0, n_estimators=50, random_state=None),\n",
       "       fit_params={}, iid=True, n_jobs=1,\n",
       "       param_grid={'n_estimators': [1, 5, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 50, 100, 1000, 2000], 'learning_rate': [0.1, 0.2, 0.3, 0.5, 0.7, 0.8, 0.9, 1, 2, 3, 5, 10]},\n",
       "       pre_dispatch='2*n_jobs', refit=True, return_train_score=True,\n",
       "       scoring='f1', verbose=0)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "clf_ADA = AdaBoostClassifier()\n",
    "clf = GridSearchCV(clf_ADA, parameters, scoring = 'f1', cv = 10 )\n",
    "clf.fit(features, labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'n_estimators': 13, 'learning_rate': 2}\n",
      "0.500241545894\n"
     ]
    }
   ],
   "source": [
    "print clf.best_params_\n",
    "print clf.best_score_ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Double check performance with the optimal parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None, learning_rate=2,\n",
      "          n_estimators=13, random_state=None)\n",
      "\tAccuracy: 0.87736\tPrecision: 0.58408\tRecall: 0.49150\tF1: 0.53380\tF2: 0.50759\n",
      "\tTotal predictions: 14000\tTrue positives:  983\tFalse positives:  700\tFalse negatives: 1017\tTrue negatives: 11300\n",
      "\n"
     ]
    }
   ],
   "source": [
    "lr = 2\n",
    "n_est = 13\n",
    "clf_ADA = AdaBoostClassifier(learning_rate = lr, n_estimators = n_est)\n",
    "test_classifier(clf_ADA, enron_data, second_alternative_selection_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and the importance of features:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exercised_stock_options: 0.692307692308\n",
      "bonus: 0.230769230769\n",
      "expenses: 0.0769230769231\n",
      "other: 0.0\n",
      "share_shared_receipt_with_poi: 0.0\n",
      "share_from_this_person_to_poi: 0.0\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(second_alternative_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(imp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's see what happens if we drop the features with near 0 importance"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'exercised_stock_options', 'bonus', 'expenses']\n",
      "\n",
      " Numbers of features: 4\n"
     ]
    }
   ],
   "source": [
    "final_selection_features = ['poi', 'exercised_stock_options', 'bonus', 'expenses']\n",
    "\n",
    "print  final_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(final_selection_features))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = featureFormat(enron_data, final_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None, learning_rate=2,\n",
      "          n_estimators=13, random_state=None)\n",
      "\tAccuracy: 0.85129\tPrecision: 0.46645\tRecall: 0.28500\tF1: 0.35382\tF2: 0.30904\n",
      "\tTotal predictions: 14000\tTrue positives:  570\tFalse positives:  652\tFalse negatives: 1430\tTrue negatives: 11348\n",
      "\n"
     ]
    }
   ],
   "source": [
    "clf_ADA = AdaBoostClassifier(learning_rate = lr, n_estimators = n_est)\n",
    "test_classifier(clf_ADA, enron_data, final_selection_features)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Clearly not an improvement"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Impact of created features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to access the impact of the created features, we compare the performance of the classifier with and without it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'exercised_stock_options', 'bonus', 'expenses', 'other', 'share_shared_receipt_with_poi', 'share_from_this_person_to_poi']\n",
      "\n",
      " Numbers of features: 7\n",
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None, learning_rate=2,\n",
      "          n_estimators=13, random_state=None)\n",
      "\tAccuracy: 0.87700\tPrecision: 0.58264\tRecall: 0.49000\tF1: 0.53232\tF2: 0.50609\n",
      "\tTotal predictions: 14000\tTrue positives:  980\tFalse positives:  702\tFalse negatives: 1020\tTrue negatives: 11298\n",
      "\n"
     ]
    }
   ],
   "source": [
    "data = featureFormat(enron_data, second_alternative_selection_features, sort_keys = True)\n",
    "labels, features = targetFeatureSplit(data)\n",
    "\n",
    "features_train, features_test, labels_train, labels_test = \\\n",
    "    train_test_split(features, labels, test_size=0.3, random_state=42)\n",
    "\n",
    "print  second_alternative_selection_features\n",
    "print \"\\n Numbers of features: \" + str(len(second_alternative_selection_features))\n",
    "\n",
    "lr = 2\n",
    "n_est = 13\n",
    "clf_ADA = AdaBoostClassifier(learning_rate = lr, n_estimators = n_est)\n",
    "test_classifier(clf_ADA, enron_data, second_alternative_selection_features)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "exercised_stock_options: 0.69\n",
      "bonus: 0.23\n",
      "expenses: 0.08\n",
      "other: 0.0\n",
      "share_shared_receipt_with_poi: 0.0\n",
      "share_from_this_person_to_poi: 0.0\n"
     ]
    }
   ],
   "source": [
    "clf_ADA.fit(features_train,labels_train)\n",
    "for feature, imp in zip(second_alternative_selection_features[1:],clf_ADA.feature_importances_):\n",
    "    print feature +\": \" + str(round(imp,2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['poi', 'exercised_stock_options', 'bonus', 'expenses', 'other']\n",
      "\n",
      " Numbers of features: 5\n",
      "AdaBoostClassifier(algorithm='SAMME.R', base_estimator=None, learning_rate=2,\n",
      "          n_estimators=13, random_state=None)\n",
      "\tAccuracy: 0.85186\tPrecision: 0.47068\tRecall: 0.29700\tF1: 0.36419\tF2: 0.32067\n",
      "\tTotal predictions: 14000\tTrue positives:  594\tFalse positives:  668\tFalse negatives: 1406\tTrue negatives: 11332\n",
      "\n"
     ]
    }
   ],
   "source": [
    "second_alternative_selection_features_without = ['poi', 'exercised_stock_options', 'bonus', 'expenses', 'other']\n",
    "print  second_alternative_selection_features_without\n",
    "print \"\\n Numbers of features: \" + str(len(second_alternative_selection_features_without))\n",
    "\n",
    "lr = 2\n",
    "n_est = 13\n",
    "clf_ADA = AdaBoostClassifier(learning_rate = lr, n_estimators = n_est)\n",
    "test_classifier(clf_ADA, enron_data, second_alternative_selection_features_without)"
   ]
  }
 ],
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