EDA_Pandas.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# w261 Final Project EDA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Description:\n",
    "\n",
    "This notebook shows the EDA performed for the w261 final project. This EDA started with taking a small random sample of the raw data and performing exploratory analysis with pandas packages."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Objectives for final project:\n",
    "Determine 2-3 relevant EDA tasks that will help you make decisions about how you implement the algorithm to be scalable. Discuss any challenges that you anticipate based on the EDA you perform."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The EDA comprises the following tasks:\n",
    "- Understanding the data structure and composition of the features in the dataset.\n",
    "- Plotting the target and numerical variables to understand their distributions in order to make decisions about the type of transformations required. \n",
    "    - For instance, if numerical variables are ordinal in nature, performing appropriate bucketing of the variables or one-hot encoding to ensure each value is captured in the data for analysis.\n",
    "- Displaying the distribution of the categorical variables to understand their distributions in order to make decision about the bucketing or one-hot encoding required."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# General tools & operations libraries\n",
    "import re\n",
    "import ast\n",
    "import time\n",
    "import csv\n",
    "import itertools\n",
    "import math\n",
    "from statsmodels.stats.stattools import durbin_watson\n",
    "\n",
    "# Mathematical operations and dataframes libraries\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# Plotting and visualization libraries\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# store path to notebook\n",
    "PWD = !pwd\n",
    "PWD = PWD[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Spark is not required for this analysis, no the following codeblock is commented out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# # start Spark Session (RUN THIS CELL AS IS)\n",
    "# from pyspark.sql import SparkSession\n",
    "# app_name = \"finalproject_notebook\"\n",
    "# master = \"local[*]\"\n",
    "# spark = SparkSession\\\n",
    "#         .builder\\\n",
    "#         .appName(app_name)\\\n",
    "#         .master(master)\\\n",
    "#         .getOrCreate()\n",
    "# sc = spark.sparkContext"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# # Spark configuration Information (RUN THIS CELL AS IS)\n",
    "# sc.getConf().getAll()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# spark"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Note about the dataset\n",
    "\n",
    "The datasets for the Kaggle Display Advertising Competition are downloaded from the Criteo Labs competition site and are hosted as a compressed `.tar` file in an `S3` bucket here:\n",
    "https://s3-eu-west-1.amazonaws.com/kaggle-display-advertising-challenge-dataset/dac.tar.gz\n",
    "\n",
    "The full raw `train.txt` dataset is 11.15GB in size and is too large to read into conventional Jupyter Notebooks to perform analysis. Moreover, as we will discuss later, there are significant dimensionality constraints that inhibit loading the entire dataset and performing conventional one-hot encoding on the entire dataset. A solution is required to analyze the data and perform an algorithm implementation at scale.\n",
    "\n",
    "Therefore, we load a random sample of the dataset representing just 0.1% of the dataset. While this represents a small portion of the entire raw dataset, we believe this gives us a representative sample that will allow us to understand the dataset's features, data structure and distributions in preparation for an analysis and predictive modeling at scale."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Full dataset to be used for analysis:\n",
    "\n",
    "http://labs.criteo.com/2014/02/kaggle-display-advertising-challenge-dataset//\n",
    "\n",
    "https://s3-eu-west-1.amazonaws.com/kaggle-display-advertising-challenge-dataset/dac.tar.gz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Change directory"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "/Volumes/LaCie/dac\n"
     ]
    }
   ],
   "source": [
    "cd '/Volumes/LaCie/dac'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# assign parameters\n",
    "!BUCKET=danielalvarez_w261projects"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following command line snippet is shown for exposition as to how we took a 0.1% random sample. This data is 11.4MB in size. It is commented out since it was just needed to produce the toy example one time. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "!cat train.txt | awk 'BEGIN {srand()} !/^$/ { if (rand() <= .001) print $0}' > data/sample.txt\n",
    "#!gzip -cd data/dac.tar.gz | awk 'BEGIN {srand()} !/^$/ { if (rand() <= .001) print $0}' > data/sample.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we inspect the sample .`txt` data. We note that there are 46,048 lines in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   46048 1586737 11196195 data/sample.txt\r\n"
     ]
    }
   ],
   "source": [
    "# check number of lines, byte and characters count\n",
    "!wc data/sample.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\t1\t2\t2\t2\t292\t2\t1\t2\t2\t1\t1\t\t2\t05db9164\t0a519c5c\tb00d1501\td16679b9\t25c83c98\t7e0ccccf\t1683df22\t0b153874\ta73ee510\t3b08e48b\t89073265\te0d76380\t8b266858\tb28479f6\tb760dcb7\t1203a270\td4bb7bd8\t2efa89c6\t\t\t73d06dde\t\t3a171ecb\taee52b6f\t\t\r\n"
     ]
    }
   ],
   "source": [
    "# inspect first line to get a sense of the overall schema\n",
    "!head -n 1 data/sample.txt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we impose a schema structure over the 40 variables. We note that:\n",
    "\n",
    "- feature in position 0 is the target label, `y`\n",
    "- feature in the 13th position is numeric (`n13`)\n",
    "- features in the 14th through 39th position are categorical"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# convert txt file into a csv file\n",
    "with open('data/sample.txt', 'r') as in_file:\n",
    "    stripped = (line.strip() for line in in_file)\n",
    "    lines = (line.split(\",\") for line in stripped if line)\n",
    "    with open('data/sample.csv', 'w') as out_file:\n",
    "        writer = csv.writer(out_file)\n",
    "        writer.writerow(('title', 'intro'))\n",
    "        writer.writerows(lines)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# Assign parameters\n",
    "chunksize = 327433\n",
    "file = 'data/sample.csv'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Read in dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "column_names = ['y','n1','n2','n3','n4','n5','n6',\n",
    "                'n7','n8','n9','n10','n11', 'n12', 'n13',\n",
    "                'cat14','cat15','cat16','cat17','cat18',\n",
    "                'cat19','cat20','cat21','cat22','cat23','cat24',\n",
    "                'cat25','cat26','cat27','cat28','cat29','cat30',\n",
    "                'cat31','cat32','cat33','cat34','cat35','cat36',\n",
    "                'cat37','cat38','cat39']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "df = pd.read_csv('data/sample.csv', sep=\"\\t\", names=column_names, chunksize=chunksize, engine='python')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(46049, 40)"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_sample = df.get_chunk()\n",
    "df_sample.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we assess the data structure, data types and non-null values for each feature"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 46049 entries, 0 to 46048\n",
      "Data columns (total 40 columns):\n",
      "y        46049 non-null object\n",
      "n1       25374 non-null float64\n",
      "n2       46048 non-null float64\n",
      "n3       36219 non-null float64\n",
      "n4       36054 non-null float64\n",
      "n5       44940 non-null float64\n",
      "n6       35770 non-null float64\n",
      "n7       44042 non-null float64\n",
      "n8       46018 non-null float64\n",
      "n9       44042 non-null float64\n",
      "n10      25374 non-null float64\n",
      "n11      44042 non-null float64\n",
      "n12      10829 non-null float64\n",
      "n13      36054 non-null float64\n",
      "cat14    46048 non-null object\n",
      "cat15    46048 non-null object\n",
      "cat16    44475 non-null object\n",
      "cat17    44475 non-null object\n",
      "cat18    46048 non-null object\n",
      "cat19    40458 non-null object\n",
      "cat20    46048 non-null object\n",
      "cat21    46048 non-null object\n",
      "cat22    46048 non-null object\n",
      "cat23    46048 non-null object\n",
      "cat24    46048 non-null object\n",
      "cat25    44475 non-null object\n",
      "cat26    46048 non-null object\n",
      "cat27    46048 non-null object\n",
      "cat28    46048 non-null object\n",
      "cat29    44475 non-null object\n",
      "cat30    46048 non-null object\n",
      "cat31    46048 non-null object\n",
      "cat32    25768 non-null object\n",
      "cat33    25768 non-null object\n",
      "cat34    44475 non-null object\n",
      "cat35    10831 non-null object\n",
      "cat36    46048 non-null object\n",
      "cat37    44475 non-null object\n",
      "cat38    25768 non-null object\n",
      "cat39    25768 non-null object\n",
      "dtypes: float64(13), object(27)\n",
      "memory usage: 14.1+ MB\n"
     ]
    }
   ],
   "source": [
    "df_sample.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inspect top 5 rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>n1</th>\n",
       "      <th>n2</th>\n",
       "      <th>n3</th>\n",
       "      <th>n4</th>\n",
       "      <th>n5</th>\n",
       "      <th>n6</th>\n",
       "      <th>n7</th>\n",
       "      <th>n8</th>\n",
       "      <th>n9</th>\n",
       "      <th>...</th>\n",
       "      <th>cat30</th>\n",
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       "      <th>cat32</th>\n",
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       "      <th>cat37</th>\n",
       "      <th>cat38</th>\n",
       "      <th>cat39</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>title,intro</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>...</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>292.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>...</td>\n",
       "      <td>d4bb7bd8</td>\n",
       "      <td>2efa89c6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>73d06dde</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3a171ecb</td>\n",
       "      <td>aee52b6f</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>86.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6147.0</td>\n",
       "      <td>875.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>96.0</td>\n",
       "      <td>...</td>\n",
       "      <td>e5ba7672</td>\n",
       "      <td>47e4d79e</td>\n",
       "      <td>9437f62f</td>\n",
       "      <td>a458ea53</td>\n",
       "      <td>d2bc432c</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bcdee96c</td>\n",
       "      <td>b0a08858</td>\n",
       "      <td>c9f3bea7</td>\n",
       "      <td>553d46e8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>...</td>\n",
       "      <td>e5ba7672</td>\n",
       "      <td>e88ffc9d</td>\n",
       "      <td>efa3470f</td>\n",
       "      <td>b1252a9d</td>\n",
       "      <td>65229b6e</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bcdee96c</td>\n",
       "      <td>3fdb382b</td>\n",
       "      <td>cb079c2d</td>\n",
       "      <td>64f08cc6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>3195.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>...</td>\n",
       "      <td>e5ba7672</td>\n",
       "      <td>9dde83ca</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>831d5286</td>\n",
       "      <td>NaN</td>\n",
       "      <td>32c7478e</td>\n",
       "      <td>9e9a60e4</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 40 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             y   n1   n2    n3   n4      n5     n6    n7    n8     n9  ...  \\\n",
       "0  title,intro  NaN  NaN   NaN  NaN     NaN    NaN   NaN   NaN    NaN  ...   \n",
       "1            0  1.0  2.0   2.0  2.0   292.0    2.0   1.0   2.0    2.0  ...   \n",
       "2            0  NaN -1.0  86.0  1.0  6147.0  875.0   3.0   1.0   96.0  ...   \n",
       "3            0  1.0  1.0  16.0  2.0     0.0    2.0  24.0   2.0   13.0  ...   \n",
       "4            0  0.0  1.0   3.0  9.0  3195.0   57.0   3.0  35.0  120.0  ...   \n",
       "\n",
       "      cat30     cat31     cat32     cat33     cat34 cat35     cat36     cat37  \\\n",
       "0      None      None      None      None      None  None      None      None   \n",
       "1  d4bb7bd8  2efa89c6       NaN       NaN  73d06dde   NaN  3a171ecb  aee52b6f   \n",
       "2  e5ba7672  47e4d79e  9437f62f  a458ea53  d2bc432c   NaN  bcdee96c  b0a08858   \n",
       "3  e5ba7672  e88ffc9d  efa3470f  b1252a9d  65229b6e   NaN  bcdee96c  3fdb382b   \n",
       "4  e5ba7672  9dde83ca       NaN       NaN  831d5286   NaN  32c7478e  9e9a60e4   \n",
       "\n",
       "      cat38     cat39  \n",
       "0      None      None  \n",
       "1      None      None  \n",
       "2  c9f3bea7  553d46e8  \n",
       "3  cb079c2d  64f08cc6  \n",
       "4      None      None  \n",
       "\n",
       "[5 rows x 40 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_sample.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>n1</th>\n",
       "      <th>n2</th>\n",
       "      <th>n3</th>\n",
       "      <th>n4</th>\n",
       "      <th>n5</th>\n",
       "      <th>n6</th>\n",
       "      <th>n7</th>\n",
       "      <th>n8</th>\n",
       "      <th>n9</th>\n",
       "      <th>...</th>\n",
       "      <th>cat30</th>\n",
       "      <th>cat31</th>\n",
       "      <th>cat32</th>\n",
       "      <th>cat33</th>\n",
       "      <th>cat34</th>\n",
       "      <th>cat35</th>\n",
       "      <th>cat36</th>\n",
       "      <th>cat37</th>\n",
       "      <th>cat38</th>\n",
       "      <th>cat39</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>292.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>...</td>\n",
       "      <td>d4bb7bd8</td>\n",
       "      <td>2efa89c6</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>73d06dde</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3a171ecb</td>\n",
       "      <td>aee52b6f</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>-1.0</td>\n",
       "      <td>86.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6147.0</td>\n",
       "      <td>875.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>96.0</td>\n",
       "      <td>...</td>\n",
       "      <td>e5ba7672</td>\n",
       "      <td>47e4d79e</td>\n",
       "      <td>9437f62f</td>\n",
       "      <td>a458ea53</td>\n",
       "      <td>d2bc432c</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bcdee96c</td>\n",
       "      <td>b0a08858</td>\n",
       "      <td>c9f3bea7</td>\n",
       "      <td>553d46e8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>...</td>\n",
       "      <td>e5ba7672</td>\n",
       "      <td>e88ffc9d</td>\n",
       "      <td>efa3470f</td>\n",
       "      <td>b1252a9d</td>\n",
       "      <td>65229b6e</td>\n",
       "      <td>NaN</td>\n",
       "      <td>bcdee96c</td>\n",
       "      <td>3fdb382b</td>\n",
       "      <td>cb079c2d</td>\n",
       "      <td>64f08cc6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>3195.0</td>\n",
       "      <td>57.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>35.0</td>\n",
       "      <td>120.0</td>\n",
       "      <td>...</td>\n",
       "      <td>e5ba7672</td>\n",
       "      <td>9dde83ca</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>831d5286</td>\n",
       "      <td>NaN</td>\n",
       "      <td>32c7478e</td>\n",
       "      <td>9e9a60e4</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>21.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>7460.0</td>\n",
       "      <td>192.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>24.0</td>\n",
       "      <td>153.0</td>\n",
       "      <td>...</td>\n",
       "      <td>07c540c4</td>\n",
       "      <td>7b49e3d2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>73d06dde</td>\n",
       "      <td>NaN</td>\n",
       "      <td>3a171ecb</td>\n",
       "      <td>aee52b6f</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 40 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   y   n1    n2    n3   n4      n5     n6    n7    n8     n9  ...     cat30  \\\n",
       "1  0  1.0   2.0   2.0  2.0   292.0    2.0   1.0   2.0    2.0  ...  d4bb7bd8   \n",
       "2  0  NaN  -1.0  86.0  1.0  6147.0  875.0   3.0   1.0   96.0  ...  e5ba7672   \n",
       "3  0  1.0   1.0  16.0  2.0     0.0    2.0  24.0   2.0   13.0  ...  e5ba7672   \n",
       "4  0  0.0   1.0   3.0  9.0  3195.0   57.0   3.0  35.0  120.0  ...  e5ba7672   \n",
       "5  0  0.0  21.0   5.0  6.0  7460.0  192.0   2.0  24.0  153.0  ...  07c540c4   \n",
       "\n",
       "      cat31     cat32     cat33     cat34 cat35     cat36     cat37     cat38  \\\n",
       "1  2efa89c6       NaN       NaN  73d06dde   NaN  3a171ecb  aee52b6f      None   \n",
       "2  47e4d79e  9437f62f  a458ea53  d2bc432c   NaN  bcdee96c  b0a08858  c9f3bea7   \n",
       "3  e88ffc9d  efa3470f  b1252a9d  65229b6e   NaN  bcdee96c  3fdb382b  cb079c2d   \n",
       "4  9dde83ca       NaN       NaN  831d5286   NaN  32c7478e  9e9a60e4      None   \n",
       "5  7b49e3d2       NaN       NaN  73d06dde   NaN  3a171ecb  aee52b6f      None   \n",
       "\n",
       "      cat39  \n",
       "1      None  \n",
       "2  553d46e8  \n",
       "3  64f08cc6  \n",
       "4      None  \n",
       "5      None  \n",
       "\n",
       "[5 rows x 40 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Drop first row\n",
    "df_sample.drop(df_sample.index[0]).head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0              0.745554\n",
       "1              0.254425\n",
       "title,intro    0.000022\n",
       "Name: y, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Assess percentage of label categories\n",
    "df_sample.y.value_counts(dropna=False)/len(df_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>y</th>\n",
       "      <th>n1</th>\n",
       "      <th>n2</th>\n",
       "      <th>n3</th>\n",
       "      <th>n4</th>\n",
       "      <th>n5</th>\n",
       "      <th>n6</th>\n",
       "      <th>n7</th>\n",
       "      <th>n8</th>\n",
       "      <th>n9</th>\n",
       "      <th>...</th>\n",
       "      <th>cat30</th>\n",
       "      <th>cat31</th>\n",
       "      <th>cat32</th>\n",
       "      <th>cat33</th>\n",
       "      <th>cat34</th>\n",
       "      <th>cat35</th>\n",
       "      <th>cat36</th>\n",
       "      <th>cat37</th>\n",
       "      <th>cat38</th>\n",
       "      <th>cat39</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>title,intro</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>...</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "      <td>None</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 40 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "             y  n1  n2  n3  n4  n5  n6  n7  n8  n9  ...  cat30  cat31  cat32  \\\n",
       "0  title,intro NaN NaN NaN NaN NaN NaN NaN NaN NaN  ...   None   None   None   \n",
       "\n",
       "   cat33 cat34 cat35 cat36 cat37 cat38 cat39  \n",
       "0   None  None  None  None  None  None  None  \n",
       "\n",
       "[1 rows x 40 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Examine row with `label` value `title,intro`\n",
    "df_sample[df_sample['y']=='title,intro']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Row with `label` value 'title,empty' is empty, so proceed to drop the row. Drop rows with label values not equal to `0` or `1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Drop row with `label` value `title,intro`\n",
    "df_sample = df_sample[(df_sample.y == '0') | (df_sample.y == '1')]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#convert `label` value to an integer value\n",
    "df_sample['y'] = df_sample['y'].astype(str).astype(int)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Sparseness of features (null values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe the number of null values for each feature to assess sparseness."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature\t| Null values\t| Null Values as a Percent of Total\n",
      "====================================================================================================\n",
      " y\t|      0\t| 0.000000\n",
      " n1\t|  20674\t| 44.896630\n",
      " n2\t|      0\t| 0.000000\n",
      " n3\t|   9829\t| 21.345118\n",
      " n4\t|   9994\t| 21.703440\n",
      " n5\t|   1108\t| 2.406185\n",
      " n6\t|  10278\t| 22.320188\n",
      " n7\t|   2006\t| 4.356324\n",
      " n8\t|     30\t| 0.065149\n",
      " n9\t|   2006\t| 4.356324\n",
      " n10\t|  20674\t| 44.896630\n",
      " n11\t|   2006\t| 4.356324\n",
      " n12\t|  35219\t| 76.483235\n",
      " n13\t|   9994\t| 21.703440\n",
      " cat14\t|      0\t| 0.000000\n",
      " cat15\t|      0\t| 0.000000\n",
      " cat16\t|   1573\t| 3.416001\n",
      " cat17\t|   1573\t| 3.416001\n",
      " cat18\t|      0\t| 0.000000\n",
      " cat19\t|   5590\t| 12.139507\n",
      " cat20\t|      0\t| 0.000000\n",
      " cat21\t|      0\t| 0.000000\n",
      " cat22\t|      0\t| 0.000000\n",
      " cat23\t|      0\t| 0.000000\n",
      " cat24\t|      0\t| 0.000000\n",
      " cat25\t|   1573\t| 3.416001\n",
      " cat26\t|      0\t| 0.000000\n",
      " cat27\t|      0\t| 0.000000\n",
      " cat28\t|      0\t| 0.000000\n",
      " cat29\t|   1573\t| 3.416001\n",
      " cat30\t|      0\t| 0.000000\n",
      " cat31\t|      0\t| 0.000000\n",
      " cat32\t|  20280\t| 44.041001\n",
      " cat33\t|  20280\t| 44.041001\n",
      " cat34\t|   1573\t| 3.416001\n",
      " cat35\t|  35217\t| 76.478892\n",
      " cat36\t|      0\t| 0.000000\n",
      " cat37\t|   1573\t| 3.416001\n",
      " cat38\t|  20280\t| 44.041001\n",
      " cat39\t|  20280\t| 44.041001\n"
     ]
    }
   ],
   "source": [
    "# Number of null values for each feature and percentage of null values for each feature\n",
    "print(\"{}\\t| {:10s}\\t| {:10s}\".format(\"Feature\",\"Null values\",\"Null Values as a Percent of Total\"))\n",
    "print(\"=\"*100)\n",
    "for col in df_sample.columns:\n",
    "    null_values = df_sample[col].isnull().sum(axis=0)\n",
    "    null_values_pct = df_sample[col].isnull().sum(axis=0)/len(df_sample) * 100\n",
    "    print(\" {}\\t| {:6d}\\t| {:6f}\".format(str(col),null_values,null_values_pct))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that there are several features with a large percentage of null values. Particularly, the features: `n1`, `n3`, `n4`, `n6`, `n10`, `n12`, `n13`, `cat32`, `cat33`, `cat35`, `cat38` and `cat39` each have over 20% of their values being null. We will have to make analytical choices about how we treat these null values."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Imbalance in target label"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we assess the label values to observe class imbalance. This may affect the behavior of tree algorithms in particular, since it imposes a bias for the majority class in each tree split."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    34332\n",
       "1    11716\n",
       "Name: y, dtype: int64"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Assess label categories\n",
    "df_sample.y.value_counts(dropna=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    0.74557\n",
       "1    0.25443\n",
       "Name: y, dtype: float64"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Assess percentage of label categories\n",
    "df_sample.y.value_counts(dropna=False)/len(df_sample)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/anaconda3/lib/python3.6/site-packages/seaborn/categorical.py:1460: FutureWarning: remove_na is deprecated and is a private function. Do not use.\n",
      "  stat_data = remove_na(group_data)\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot distribution of label counts\n",
    "sns.set(style=\"whitegrid\")\n",
    "ax = sns.countplot(x=\"y\", data=df_sample)\n",
    "ax.set(title=\"Label counts\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that `y` target values equal to 0 are dominant, corresponding to around three-quarters of the dataset labels. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## EDA - Mean and median values with respect to target label categories"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we explore mean values of numeric variables with respect to label target categories. This is important for creating recursive partitions of regions into homogeneous zones in tree-based algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>n1</th>\n",
       "      <th>n2</th>\n",
       "      <th>n3</th>\n",
       "      <th>n4</th>\n",
       "      <th>n5</th>\n",
       "      <th>n6</th>\n",
       "      <th>n7</th>\n",
       "      <th>n8</th>\n",
       "      <th>n9</th>\n",
       "      <th>n10</th>\n",
       "      <th>n11</th>\n",
       "      <th>n12</th>\n",
       "      <th>n13</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.890596</td>\n",
       "      <td>94.917977</td>\n",
       "      <td>21.962752</td>\n",
       "      <td>7.587890</td>\n",
       "      <td>22193.431860</td>\n",
       "      <td>137.943265</td>\n",
       "      <td>12.421027</td>\n",
       "      <td>12.756712</td>\n",
       "      <td>102.552015</td>\n",
       "      <td>0.538505</td>\n",
       "      <td>2.216218</td>\n",
       "      <td>0.617135</td>\n",
       "      <td>8.978133</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.853875</td>\n",
       "      <td>136.881188</td>\n",
       "      <td>27.669818</td>\n",
       "      <td>6.604589</td>\n",
       "      <td>9251.656253</td>\n",
       "      <td>64.945327</td>\n",
       "      <td>26.966072</td>\n",
       "      <td>11.939042</td>\n",
       "      <td>117.708464</td>\n",
       "      <td>0.804193</td>\n",
       "      <td>4.204704</td>\n",
       "      <td>1.765704</td>\n",
       "      <td>6.037941</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         n1          n2         n3        n4            n5          n6  \\\n",
       "y                                                                        \n",
       "0  2.890596   94.917977  21.962752  7.587890  22193.431860  137.943265   \n",
       "1  4.853875  136.881188  27.669818  6.604589   9251.656253   64.945327   \n",
       "\n",
       "          n7         n8          n9       n10       n11       n12       n13  \n",
       "y                                                                            \n",
       "0  12.421027  12.756712  102.552015  0.538505  2.216218  0.617135  8.978133  \n",
       "1  26.966072  11.939042  117.708464  0.804193  4.204704  1.765704  6.037941  "
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_sample.groupby(df_sample.y)['n1', 'n2', 'n3', 'n4', 'n5', 'n6', 'n7', 'n8', 'n9', 'n10',\n",
    "                               'n11', 'n12', 'n13'].mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Explore median values of numeric variables with respect to label target categories. This may allow us to more evenly split the numeric variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>n1</th>\n",
       "      <th>n2</th>\n",
       "      <th>n3</th>\n",
       "      <th>n4</th>\n",
       "      <th>n5</th>\n",
       "      <th>n6</th>\n",
       "      <th>n7</th>\n",
       "      <th>n8</th>\n",
       "      <th>n9</th>\n",
       "      <th>n10</th>\n",
       "      <th>n11</th>\n",
       "      <th>n12</th>\n",
       "      <th>n13</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3208.0</td>\n",
       "      <td>41.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1342.0</td>\n",
       "      <td>14.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>38.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    n1   n2   n3   n4      n5    n6   n7   n8    n9  n10  n11  n12  n13\n",
       "y                                                                      \n",
       "0  1.0  3.0  7.0  4.0  3208.0  41.0  2.0  8.0  38.0  0.0  1.0  0.0  5.0\n",
       "1  2.0  3.0  5.0  4.0  1342.0  14.0  6.0  7.0  38.0  1.0  2.0  0.0  3.0"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_sample.groupby(df_sample.y)['n1', 'n2', 'n3', 'n4', 'n5', 'n6', 'n7', 'n8', 'n9', 'n10',\n",
    "                               'n11', 'n12', 'n13'].median()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Correlation Heat Map of Numeric Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Correlation heat map of the numeric variables allows us to visualize whether there are non-orthogonal variables and whether we can reduce the dimensionality of our data in the modeling analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hytCuj2/fJ/KnP9N/rzZ3EPcPnEH79MWfBnRs64ZFGQdurd9v8oy2pR2IC83+2jPLkBHg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+RKHBuFqlXiFPmsWbOYO3cuFhYWJZVVmtTamuwnT7SP1U+eIDU2RmJoWGCa3HTWLFKPHSMzKKjI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\nsaHR7PH0x7J2DUasnsgKF+9ia1ITU1j80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/x8mz224yeadm+hV93ti39yYM03aLVatOnp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\n",
      "text/plain": [
       "<Figure size 864x864 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_integers = df_sample.iloc[:,1:14]\n",
    "\n",
    "var_corr = df_integers.corr()\n",
    "var_corr = var_corr.round(3)\n",
    "# plot the heatmap and annotation on it\n",
    "fig, ax = plt.subplots(figsize=(12,12))         # Sample figsize\n",
    "sns.heatmap(var_corr, xticklabels=var_corr.columns, yticklabels=var_corr.columns, annot=True)\n",
    "\n",
    "# Fix axes\n",
    "b, t = plt.ylim() # discover the values for bottom and top\n",
    "b += 0.5 # Add 0.5 to the bottom\n",
    "t -= 0.5 # Subtract 0.5 from the top\n",
    "plt.ylim(b, t) # update the ylim(bottom, top) values\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most positively correlated feature pairs from this sample are:\n",
    "- `n7` and `n11` (_p_ = .74 in this sample);\n",
    "- `n4` and `n13` (_p_ = .6 in this sample);\n",
    "- `n4` and `n8` (_p_ = .53 in this sample);\n",
    "- `n7` and `n1` (_p_ = .4 in this sample);\n",
    "- `n10` and `n1` (_p_ = .4 in this sample);\n",
    "\n",
    "The most negatively correlated feature pairs from this sample are:\n",
    "- `n5` and `n10` (_p_ = -.34 in this sample);\n",
    "- `n6` and `n10` (_p_ = -.28 in this sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following this correlation analysis, since we did not consider these features to be strongly correlated, we were not concerned with effects of multicollinearity and chose to keep these features for the modeling implementation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Considering binning the integer variables to find the best split. Plot the histograms of each variable and see if equal-width lengths can be extracted. After, can be treated as an ordered categorical attribute. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n1\n",
      "[  0.   36.3  72.6 108.9 145.2 181.5 217.8 254.1 290.4 326.7 363. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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AgABjtKdRp04dPffcc3ruued8nQcAEMCMSiM6Olo2m63Sst/97nfKycnxSSgAQGAyKo19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\nrkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n2\n",
      "[-2.00000e+00  1.43330e+03  2.86860e+03  4.30390e+03  5.73920e+03\n",
      "  7.17450e+03  8.60980e+03  1.00451e+04  1.14804e+04  1.29157e+04\n",
      "  1.43510e+04]\n"
     ]
    },
    {
     "data": {
      "image/png": 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9+/a1mBUREe/xammcOXMGwzBYvXq1e+2uu+5i2bJldO/enfvuu48PP/yQw4cP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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n3\n",
      "[    0.   3724.3  7448.6 11172.9 14897.2 18621.5 22345.8 26070.1 29794.4\n",
      " 33518.7 37243. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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AcXExSUlJ3zkrIiLBE5ArjRdffJEvv/ySVatWsWrVKgAyMjJYsmQJ4eHh9OjRg7y8PJxO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\nQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n4\n",
      "[  0.   25.3  50.6  75.9 101.2 126.5 151.8 177.1 202.4 227.7 253. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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3iYiIYQoNERExTKEhIiKGKTRERMQwhYaIiBim0BAREcMUGiIiYphCQ0REDFNoiIiIYQoN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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n5\n",
      "[      0.   181315.8  362631.6  543947.4  725263.2  906579.  1087894.8\n",
      " 1269210.6 1450526.4 1631842.2 1813158. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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PG9pjT61Rn96lPr1LfZ6fX0OjU6dOTJs2jXHjxrF//37uv/9+QkJCPK8HBQXx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\nNERExLT/A2BXggZR5XE/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n6\n",
      "[    0.   2158.5  4317.   6475.5  8634.  10792.5 12951.  15109.5 17268.\n",
      " 19426.5 21585. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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IiBhTaIiIiDGFhoiIGAvox722Fo9mv+R1/Hf5TwZ4JiIigaUzDRERMabQEBER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\nbJpfdrW1i9UAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n7\n",
      "[   0.   344.9  689.8 1034.7 1379.6 1724.5 2069.4 2414.3 2759.2 3104.1\n",
      " 3449. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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Gdmc9KY6amppO3Y/O3l5n8uds7VFe7+tqmZXXuzojr0+Lo0ePHsyYMYOJEydy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\nGPL/AcYdG5nrfyriAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n8\n",
      "[  0.   71.6 143.2 214.8 286.4 358.  429.6 501.2 572.8 644.4 716. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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vGD9+PM888wxpaWkAxMfHU1paCkBRUREJCQl0796d4uJiPB4PJ06cwOPxEBkZeVVzRUTE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\n93JozwyXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n9\n",
      "[   0.   916.5 1833.  2749.5 3666.  4582.5 5499.  6415.5 7332.  8248.5\n",
      " 9165. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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EjCk0RETEmEJDRESMKTRERMSYQkNERIwpNERExJhCQ0REjCk0RETEmEJDRESM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\nRMSYQkNERIwpNERExNj/A4/NYj5RAXcKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n10\n",
      "[0.  0.8 1.6 2.4 3.2 4.  4.8 5.6 6.4 7.2 8. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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drs4lIiJeyOiYxsCBAxk4cCA//PADpaWlPPjggwQHB5OUlERKSgr+/v6uzikiIl7A+EB4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\nxlQaIiJiTKUhIiLG/j/y1kfh61MbqAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n11\n",
      "[  0.   13.5  27.   40.5  54.   67.5  81.   94.5 108.  121.5 135. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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eTnRlmzdvNpYsWWIYhmGcOXPGGDZsmDFjxgzj448/NgzDMPLz8413333XmxFb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\nlAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n12\n",
      "[  0.  14.  28.  42.  56.  70.  84.  98. 112. 126. 140.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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JEydi5MiR3d6Yl5cX/Pz84OLiAj8/P7i6uuL06dOmxw0GAzw9PeHu7g6DwWA27uHhAbVa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\nICIiaf8PRco6AzQtO/YAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n13\n",
      "[  0.  93. 186. 279. 372. 465. 558. 651. 744. 837. 930.]\n"
     ]
    },
    {
     "data": {
      "image/png": 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EV1RU8OCDD/LII4+QkpLCAw88wKlTp1i0aFGH9fX19cyePZvx48czbtw47Pb/fyqPx0NE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\nQFWDAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in df_integers:\n",
    "    # The leftmost and rightmost bin edges\n",
    "    first_edge, last_edge = df_sample[i].min(), df_sample[i].max()\n",
    "\n",
    "    n_equal_bins = 10  # NumPy's default\n",
    "    bin_edges = np.linspace(start=first_edge, stop=last_edge, num=n_equal_bins + 1, endpoint=True)\n",
    "    print(i)\n",
    "    print(bin_edges)\n",
    "    \n",
    "    # An \"interface\" to matplotlib.axes.Axes.hist() method\n",
    "    df_sample[i].plot.hist(grid=True, bins=50, rwidth=0.9,color='#607c8e')\n",
    "    plt.grid(axis='y', alpha=0.75)\n",
    "    plt.xlabel('Value')\n",
    "    plt.ylabel('Frequency')\n",
    "    plt.title('Histogram of '+ str(i))\n",
    "    #plt.text(23, 45, r'$\\mu=15, b=3$')\n",
    "    maxfreq = df_sample[i].max()\n",
    "    # Set a clean upper y-axis limit.\n",
    "    #plt.ylim(ymax=np.ceil(maxfreq / 10) * 10 if maxfreq % 10 else maxfreq + 10)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Assessment of class dominance (imbalance) across features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, we examine the distribution of value counts (in percentage terms) for each of the variables. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top percentage value counts for variable y\n",
      "0    74.556984\n",
      "1    25.443016\n",
      "Name: y, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n1\n",
      "NaN    44.896630\n",
      "0.0    23.269197\n",
      "1.0     9.670344\n",
      "2.0     5.555073\n",
      "3.0     3.296560\n",
      "Name: n1, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n2\n",
      " 0.0    17.273280\n",
      " 1.0    15.477328\n",
      "-1.0    10.343555\n",
      " 2.0     5.850417\n",
      " 3.0     3.118485\n",
      "Name: n2, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n3\n",
      "NaN    21.345118\n",
      "1.0    12.350156\n",
      "2.0     8.595379\n",
      "3.0     6.289090\n",
      "4.0     5.255386\n",
      "Name: n3, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n4\n",
      "NaN    21.703440\n",
      "1.0    12.825747\n",
      "2.0     9.870136\n",
      "3.0     7.622481\n",
      "4.0     6.130559\n",
      "Name: n4, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n5\n",
      "NaN    2.406185\n",
      "1.0    2.269371\n",
      "0.0    1.854587\n",
      "2.0    1.587474\n",
      "4.0    1.144458\n",
      "Name: n5, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n6\n",
      "NaN    22.320188\n",
      "0.0     4.949183\n",
      "1.0     2.803596\n",
      "2.0     2.347550\n",
      "3.0     2.084781\n",
      "Name: n6, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n7\n",
      "0.0    21.494962\n",
      "1.0    12.919128\n",
      "2.0     8.656185\n",
      "3.0     5.911223\n",
      "4.0     5.114229\n",
      "Name: n7, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n8\n",
      "0.0    11.409833\n",
      "1.0     8.082870\n",
      "2.0     6.918867\n",
      "3.0     5.752693\n",
      "4.0     5.476894\n",
      "Name: n8, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n9\n",
      "NaN    4.356324\n",
      "1.0    3.722203\n",
      "0.0    3.062022\n",
      "2.0    2.840514\n",
      "3.0    2.529969\n",
      "Name: n9, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n10\n",
      "NaN    44.896630\n",
      "0.0    26.096682\n",
      "1.0    24.652536\n",
      "2.0     3.665740\n",
      "3.0     0.560285\n",
      "Name: n10, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n11\n",
      "1.0    33.367356\n",
      "0.0    22.296300\n",
      "2.0    13.946317\n",
      "3.0     7.548645\n",
      "4.0     4.384555\n",
      "Name: n11, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n12\n",
      "NaN    76.483235\n",
      "0.0    17.655490\n",
      "1.0     3.483322\n",
      "2.0     0.803509\n",
      "3.0     0.367008\n",
      "Name: n12, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable n13\n",
      "NaN    21.703440\n",
      "1.0    12.460910\n",
      "2.0     9.576963\n",
      "3.0     7.225069\n",
      "4.0     5.876477\n",
      "Name: n13, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat14\n",
      "05db9164    49.767634\n",
      "68fd1e64    16.756428\n",
      "5a9ed9b0     8.460737\n",
      "8cf07265     5.001303\n",
      "be589b51     3.372568\n",
      "Name: cat14, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat15\n",
      "38a947a1    11.448923\n",
      "207b2d81     4.321577\n",
      "38d50e09     3.822099\n",
      "1cfdf714     3.641852\n",
      "287130e0     3.437717\n",
      "Name: cat15, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat16\n",
      "NaN         3.416001\n",
      "d032c263    2.427901\n",
      "aa8c1539    1.059764\n",
      "9143c832    1.038047\n",
      "02cf9876    1.011987\n",
      "Name: cat16, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat17\n",
      "c18be181    3.439889\n",
      "NaN         3.416001\n",
      "d16679b9    2.189020\n",
      "29998ed1    2.184677\n",
      "85dd697c    2.084781\n",
      "Name: cat17, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat18\n",
      "25c83c98    66.878040\n",
      "4cf72387    15.740097\n",
      "43b19349     6.475851\n",
      "384874ce     3.363881\n",
      "30903e74     1.830698\n",
      "Name: cat18, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat19\n",
      "7e0ccccf    39.467512\n",
      "fbad5c96    22.022672\n",
      "fe6b92e5    18.535007\n",
      "NaN         12.139507\n",
      "13718bbd     3.164090\n",
      "Name: cat19, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat20\n",
      "1c86e0eb    1.987057\n",
      "dc7659bd    1.198749\n",
      "7195046d    0.877345\n",
      "468a0854    0.814368\n",
      "5e64ce5f    0.801338\n",
      "Name: cat20, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat21\n",
      "0b153874    59.249044\n",
      "5b392875    16.715167\n",
      "1f89b562     7.498697\n",
      "37e4aa92     4.249913\n",
      "062b5529     2.666782\n",
      "Name: cat21, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat22\n",
      "a73ee510    89.958304\n",
      "7cc72ec2    10.013464\n",
      "a18233ea     0.028231\n",
      "Name: cat22, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat23\n",
      "3b08e48b    21.896716\n",
      "efea433b     1.502780\n",
      "fbbf2c95     0.783965\n",
      "fa7d0797     0.560285\n",
      "03e48276     0.475591\n",
      "Name: cat23, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat24\n",
      "755e4a50    3.075052\n",
      "e51ddf94    2.037005\n",
      "7f8ffe57    1.485407\n",
      "4d8549da    1.296473\n",
      "8b94178b    1.150973\n",
      "Name: cat24, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat25\n",
      "NaN         3.416001\n",
      "dfbb09fb    2.427901\n",
      "6aaba33c    2.184677\n",
      "d8c29807    1.059764\n",
      "ae1bb660    1.038047\n",
      "Name: cat25, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat26\n",
      "5978055e    3.075052\n",
      "3516f6e6    2.280229\n",
      "46f42a63    1.648280\n",
      "025225f2    1.457175\n",
      "1aa94af3    1.335563\n",
      "Name: cat26, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat27\n",
      "b28479f6    35.087300\n",
      "07d13a8f    34.466209\n",
      "1adce6ef    15.195014\n",
      "64c94865     4.449705\n",
      "cfef1c29     2.966470\n",
      "Name: cat27, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat28\n",
      "2d0bb053    1.496265\n",
      "d345b1a0    1.038047\n",
      "3628a186    0.925122\n",
      "10040656    0.901233\n",
      "42b3012c    0.853457\n",
      "Name: cat28, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat29\n",
      "NaN         3.416001\n",
      "84898b2a    2.427901\n",
      "b041b04a    2.184677\n",
      "c64d548f    1.059764\n",
      "bad5ee18    1.038047\n",
      "Name: cat29, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat30\n",
      "e5ba7672    46.236536\n",
      "07c540c4    13.055942\n",
      "d4bb7bd8    11.685632\n",
      "3486227d     8.276147\n",
      "776ce399     5.320535\n",
      "Name: cat30, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat31\n",
      "e88ffc9d    3.146716\n",
      "891589e7    2.716730\n",
      "2804effd    2.566887\n",
      "c21c3e4c    2.419215\n",
      "5aed7436    2.149931\n",
      "Name: cat31, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat32\n",
      "NaN         44.041001\n",
      "21ddcdc9    34.607366\n",
      "55dd3565     1.878475\n",
      "5b885066     0.833912\n",
      "9437f62f     0.697099\n",
      "Name: cat32, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat33\n",
      "NaN         44.041001\n",
      "b1252a9d    19.036657\n",
      "5840adea    18.817321\n",
      "a458ea53    18.105021\n",
      "Name: cat33, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat34\n",
      "NaN         3.416001\n",
      "0014c32a    2.427901\n",
      "723b4dfd    2.184677\n",
      "5f957280    1.059764\n",
      "0429f84b    1.038047\n",
      "Name: cat34, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat35\n",
      "NaN         76.478892\n",
      "ad3062eb    13.587995\n",
      "c9d4222a     8.165393\n",
      "78e2e389     0.766591\n",
      "8ec974f4     0.505994\n",
      "Name: cat35, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat36\n",
      "32c7478e    44.090949\n",
      "3a171ecb    20.018242\n",
      "423fab69    12.189454\n",
      "bcdee96c     6.775539\n",
      "be7c41b4     5.594163\n",
      "Name: cat36, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat37\n",
      "3fdb382b    5.025191\n",
      "b34f3128    4.803683\n",
      "3b183c5c    4.482279\n",
      "1793a828    4.477936\n",
      "NaN         3.416001\n",
      "Name: cat37, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat38\n",
      "NaN         44.041001\n",
      "001f3601    14.391505\n",
      "e8b83407    10.977675\n",
      "ea9a246c     7.939541\n",
      "cb079c2d     3.976286\n",
      "Name: cat38, dtype: float64\n",
      "\n",
      "Top percentage value counts for variable cat39\n",
      "NaN         44.041001\n",
      "49d68486     3.898106\n",
      "c84c4aec     1.908878\n",
      "2fede552     1.622220\n",
      "c27f155b     1.446317\n",
      "Name: cat39, dtype: float64\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# Show top value counts for each variable\n",
    "for col in df_sample.columns:\n",
    "    print(\"Top percentage value counts for variable\", col)\n",
    "    print((df_sample[col].value_counts(dropna=False)/len(df_sample) * 100).head())\n",
    "    print(\"\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Several variables are dominated by select few variables (where the threshold is more than 20% dominated by one value):\n",
    "- n1 is dominated by `null` values (~44% of category values);\n",
    "- n3 is dominated by `null` values (~22% of category values);\n",
    "- n4 is dominated by `null` values (~22% of category values);\n",
    "- n6 is dominated by `null` values (~23% of category values);\n",
    "- n7 is dominated by 0.0 values (~22% of category values);\n",
    "- n10 is dominated by `null` values (~44% of category values);\n",
    "- n11 is dominated by 1.0 values (~34% of category values);\n",
    "- n12 is dominated by `null` values (~77% of category values);\n",
    "- n13 is dominated by `null` values (~22% of category values);\n",
    "- cat14 is dominated by `05db9164` (~50% of category values);\n",
    "- cat18 is dominated by `25c83c98` (~67% of category values);\n",
    "- cat20 is dominated by `0b153874` (~59% of category values); \n",
    "- cat21 is dominated by `a73ee510` (~90% of category values);\n",
    "- cat30 is dominated by `e5ba7672` (~47% of category values);\n",
    "- cat32 is dominated by `null` values (~44% of category values);\n",
    "- cat33 is dominated by `null` values (~44% of category values);\n",
    "- cat35 is dominated by `null` values (~77% of category values);\n",
    "- cat36 is dominated by `32c7478e` (~44% of category values);\n",
    "- cat38 is dominated by `null` values (~44% of category values);\n",
    "- cat39 is dominated by `null` values (~44% of category values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observed that there are several features that contain a high percentage of `null` values (at least 33% `null` values). Namely, the are the features `n1`, `n10`, `n12`, `cat32`, `cat33`, `cat35`, `cat38` and `cat39`. How we treated these presented a potential challenge. For the purpose of the algorithm implemented in the subsequent section, we kept the features with high percentage null values given the predictive importance these may have. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "source": [
    "## Assessment of under-represented values across features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We then assess the number of distinct unique values associated with each feature in the sample dataframe. We do this in order to assess how we will perform the discretization of the categorical features and mitigate the dimensionality problem. We note that features `cat32`, `cat33`, `cat35`, `cat38` and `cat39` are particularly troublesome to produce distinct values for given the large percentage of null values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Feature\t| Distinct Values\t| Distinct Values as a Percent of Total\n",
      "====================================================================================================\n",
      " y\t|      2\t\t| 0.004343\n",
      " n1\t|    111\t\t| 0.241053\n",
      " n2\t|   1920\t\t| 4.169562\n",
      " n3\t|    441\t\t| 0.957696\n",
      " n4\t|     84\t\t| 0.182418\n",
      " n5\t|  15279\t\t| 33.180594\n",
      " n6\t|   1400\t\t| 3.040306\n",
      " n7\t|    491\t\t| 1.066279\n",
      " n8\t|     66\t\t| 0.143329\n",
      " n9\t|   1287\t\t| 2.794910\n",
      " n10\t|      9\t\t| 0.019545\n",
      " n11\t|     86\t\t| 0.186762\n",
      " n12\t|     64\t\t| 0.138985\n",
      " n13\t|    133\t\t| 0.288829\n",
      " cat14\t|    361\t\t| 0.783965\n",
      " cat15\t|    493\t\t| 1.070622\n",
      " cat16\t|  23414\t\t| 50.846942\n",
      " cat17\t|  14182\t\t| 30.798297\n",
      " cat18\t|    102\t\t| 0.221508\n",
      " cat19\t|     10\t\t| 0.021716\n",
      " cat20\t|   6375\t\t| 13.844249\n",
      " cat21\t|    180\t\t| 0.390896\n",
      " cat22\t|      3\t\t| 0.006515\n",
      " cat23\t|   8075\t\t| 17.536049\n",
      " cat24\t|   3407\t\t| 7.398801\n",
      " cat25\t|  21721\t\t| 47.170344\n",
      " cat26\t|   2612\t\t| 5.672342\n",
      " cat27\t|     24\t\t| 0.052120\n",
      " cat28\t|   4036\t\t| 8.764767\n",
      " cat29\t|  18585\t\t| 40.360059\n",
      " cat30\t|     10\t\t| 0.021716\n",
      " cat31\t|   2075\t\t| 4.506167\n",
      " cat34\t|  20394\t\t| 44.288568\n",
      " cat36\t|     13\t\t| 0.028231\n",
      " cat37\t|   7427\t\t| 16.128822\n"
     ]
    }
   ],
   "source": [
    "# the number of distinct features associated with each feature\n",
    "# use forward fill to account for missing values in some categorical variables\n",
    "\n",
    "\n",
    "print(\"{}\\t| {:10s}\\t| {:10s}\".format(\"Feature\",\"Distinct Values\",\"Distinct Values as a Percent of Total\"))\n",
    "print(\"=\"*100)\n",
    "for col in df_sample.columns[0:32]:\n",
    "    unique_values = len(np.unique(df_sample[col].ffill()))\n",
    "    unique_values_pct = len(np.unique(df_sample[col].ffill()))/len(df_sample) * 100\n",
    "    print(\" {}\\t| {:6d}\\t\\t| {:6f}\".format(str(col),unique_values,unique_values_pct))\n",
    "\n",
    "print(\" {}\\t| {:6d}\\t\\t| {:6f}\".format(str('cat34'),len(np.unique(df_sample['cat34'].ffill())),len(np.unique(df_sample['cat34'].ffill()))/len(df_sample)* 100)) \n",
    "print(\" {}\\t| {:6d}\\t\\t| {:6f}\".format(str('cat36'),len(np.unique(df_sample['cat36'].ffill())),len(np.unique(df_sample['cat36'].ffill()))/len(df_sample)* 100)) \n",
    "print(\" {}\\t| {:6d}\\t\\t| {:6f}\".format(str('cat37'),len(np.unique(df_sample['cat37'].ffill())),len(np.unique(df_sample['cat37'].ffill()))/len(df_sample)* 100)) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that the features `n5`, `cat16`, `cat17`, `cat20`, `cat23`, `cat25`, `cat29`, `cat34` and `cat37` are comprised of distinct values that are over 20% of total values. In other words, these features contain a large number of under-represented values. This is another potential challenge to be addressed in the algorithm implementation as it would cause high dimensionality if we were to treat each value as its own feature through non-discretionary one-hot encoding. \n",
    "\n",
    "In order to mitigate the dimensionality issue, we impose a criteria for one-hot encoding features for a certain threshold of distinct values. Following the reference paper, de Wit (2014), we attempt an approach of applying one-hot encoding to features with less than 3,000 and another approach applying one-hot encoding to features with over 10,000 distinct values. For features with over 3K+ and 10K+ unique values, we decide to create a stash variable that comprises the least represented values for each original feature."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can also account for the number of distinct values of the dataframe series as follows. This will give you the column name and the cardinality (the number of elements of the set or number of distinct values for each feature)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Distinct_values</th>\n",
       "      <th>Distinct_values_as_pct_of_total</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>2</td>\n",
       "      <td>0.000043</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n1</th>\n",
       "      <td>111</td>\n",
       "      <td>0.002411</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n2</th>\n",
       "      <td>1920</td>\n",
       "      <td>0.041696</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n3</th>\n",
       "      <td>441</td>\n",
       "      <td>0.009577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n4</th>\n",
       "      <td>84</td>\n",
       "      <td>0.001824</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n5</th>\n",
       "      <td>15279</td>\n",
       "      <td>0.331806</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n6</th>\n",
       "      <td>1400</td>\n",
       "      <td>0.030403</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n7</th>\n",
       "      <td>491</td>\n",
       "      <td>0.010663</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n8</th>\n",
       "      <td>66</td>\n",
       "      <td>0.001433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n9</th>\n",
       "      <td>1287</td>\n",
       "      <td>0.027949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n10</th>\n",
       "      <td>9</td>\n",
       "      <td>0.000195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n11</th>\n",
       "      <td>86</td>\n",
       "      <td>0.001868</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n12</th>\n",
       "      <td>60</td>\n",
       "      <td>0.001303</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>n13</th>\n",
       "      <td>133</td>\n",
       "      <td>0.002888</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat14</th>\n",
       "      <td>361</td>\n",
       "      <td>0.007840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat15</th>\n",
       "      <td>493</td>\n",
       "      <td>0.010706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat16</th>\n",
       "      <td>23414</td>\n",
       "      <td>0.508469</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat17</th>\n",
       "      <td>14182</td>\n",
       "      <td>0.307983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat18</th>\n",
       "      <td>102</td>\n",
       "      <td>0.002215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat19</th>\n",
       "      <td>10</td>\n",
       "      <td>0.000217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat20</th>\n",
       "      <td>6375</td>\n",
       "      <td>0.138442</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat21</th>\n",
       "      <td>180</td>\n",
       "      <td>0.003909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat22</th>\n",
       "      <td>3</td>\n",
       "      <td>0.000065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat23</th>\n",
       "      <td>8075</td>\n",
       "      <td>0.175360</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat24</th>\n",
       "      <td>3407</td>\n",
       "      <td>0.073988</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat25</th>\n",
       "      <td>21721</td>\n",
       "      <td>0.471703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat26</th>\n",
       "      <td>2612</td>\n",
       "      <td>0.056723</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat27</th>\n",
       "      <td>24</td>\n",
       "      <td>0.000521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat28</th>\n",
       "      <td>4036</td>\n",
       "      <td>0.087648</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat29</th>\n",
       "      <td>18585</td>\n",
       "      <td>0.403601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat30</th>\n",
       "      <td>10</td>\n",
       "      <td>0.000217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat31</th>\n",
       "      <td>2075</td>\n",
       "      <td>0.045062</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat32</th>\n",
       "      <td>985</td>\n",
       "      <td>0.021391</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat33</th>\n",
       "      <td>3</td>\n",
       "      <td>0.000065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat34</th>\n",
       "      <td>20394</td>\n",
       "      <td>0.442886</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat35</th>\n",
       "      <td>9</td>\n",
       "      <td>0.000195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat36</th>\n",
       "      <td>13</td>\n",
       "      <td>0.000282</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat37</th>\n",
       "      <td>7428</td>\n",
       "      <td>0.161310</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat38</th>\n",
       "      <td>50</td>\n",
       "      <td>0.001086</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cat39</th>\n",
       "      <td>5713</td>\n",
       "      <td>0.124066</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Distinct_values  Distinct_values_as_pct_of_total\n",
       "y                    2                         0.000043\n",
       "n1                 111                         0.002411\n",
       "n2                1920                         0.041696\n",
       "n3                 441                         0.009577\n",
       "n4                  84                         0.001824\n",
       "n5               15279                         0.331806\n",
       "n6                1400                         0.030403\n",
       "n7                 491                         0.010663\n",
       "n8                  66                         0.001433\n",
       "n9                1287                         0.027949\n",
       "n10                  9                         0.000195\n",
       "n11                 86                         0.001868\n",
       "n12                 60                         0.001303\n",
       "n13                133                         0.002888\n",
       "cat14              361                         0.007840\n",
       "cat15              493                         0.010706\n",
       "cat16            23414                         0.508469\n",
       "cat17            14182                         0.307983\n",
       "cat18              102                         0.002215\n",
       "cat19               10                         0.000217\n",
       "cat20             6375                         0.138442\n",
       "cat21              180                         0.003909\n",
       "cat22                3                         0.000065\n",
       "cat23             8075                         0.175360\n",
       "cat24             3407                         0.073988\n",
       "cat25            21721                         0.471703\n",
       "cat26             2612                         0.056723\n",
       "cat27               24                         0.000521\n",
       "cat28             4036                         0.087648\n",
       "cat29            18585                         0.403601\n",
       "cat30               10                         0.000217\n",
       "cat31             2075                         0.045062\n",
       "cat32              985                         0.021391\n",
       "cat33                3                         0.000065\n",
       "cat34            20394                         0.442886\n",
       "cat35                9                         0.000195\n",
       "cat36               13                         0.000282\n",
       "cat37             7428                         0.161310\n",
       "cat38               50                         0.001086\n",
       "cat39             5713                         0.124066"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get feature and cardinality\n",
    "cardinality = df_sample.apply(pd.Series.nunique)\n",
    "cardinality_df = pd.DataFrame(cardinality)\n",
    "cardinality_df.columns = ['Distinct_values']\n",
    "cardinality_df['Distinct_values_as_pct_of_total'] = cardinality_df['Distinct_values']/len(df_sample) \n",
    "cardinality_df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Logistic regression implementation (on numeric variables)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Perform naive logistic regression on numeric variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# Assign variables\n",
    "y = df_sample['y']\n",
    "X = df_integers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>n11</th>\n",
       "      <th>n12</th>\n",
       "      <th>n13</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
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       "      <td>292.0</td>\n",
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       "      <td>86.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6147.0</td>\n",
       "      <td>875.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>96.0</td>\n",
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       "      <td>13.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2.0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    n1   n2    n3   n4      n5     n6    n7   n8    n9  n10  n11  n12  n13\n",
       "1  1.0  2.0   2.0  2.0   292.0    2.0   1.0  2.0   2.0  1.0  1.0  NaN  2.0\n",
       "2  NaN -1.0  86.0  1.0  6147.0  875.0   3.0  1.0  96.0  NaN  1.0  NaN  1.0\n",
       "3  1.0  1.0  16.0  2.0     0.0    2.0  24.0  2.0  13.0  1.0  6.0  NaN  2.0"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/anaconda3/lib/python3.6/site-packages/sklearn/linear_model/logistic.py:432: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.\n",
      "  FutureWarning)\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-3.33092837e-03 -3.53417775e-05 -1.37208171e-05 -1.15863678e-02\n",
      "  -8.75823610e-06 -4.26960077e-03  1.40318311e-03 -1.67462019e-02\n",
      "   3.76431631e-04 -8.16314789e-04  5.76304544e-04 -5.62253456e-04\n",
      "  -1.56564765e-02]]\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/anaconda/anaconda3/lib/python3.6/site-packages/sklearn/svm/base.py:929: ConvergenceWarning: Liblinear failed to converge, increase the number of iterations.\n",
      "  \"the number of iterations.\", ConvergenceWarning)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "m = LogisticRegression()\n",
    "X = X.fillna(X.mean())\n",
    "m.fit(X, y)\n",
    "\n",
    "# The estimated coefficients will all be around 1:\n",
    "print(m.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Order the features by coefficient weight contributions from naive logistic regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature</th>\n",
       "      <th>Weight</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>n8</td>\n",
       "      <td>0.016746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>n13</td>\n",
       "      <td>0.015656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>n4</td>\n",
       "      <td>0.011586</td>\n",
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       "      <th>5</th>\n",
       "      <td>n6</td>\n",
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       "      <th>0</th>\n",
       "      <td>n1</td>\n",
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       "      <th>6</th>\n",
       "      <td>n7</td>\n",
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       "      <th>9</th>\n",
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       "    </tr>\n",
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       "      <th>11</th>\n",
       "      <td>n12</td>\n",
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       "      <th>2</th>\n",
       "      <td>n3</td>\n",
       "      <td>0.000014</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>n5</td>\n",
       "      <td>0.000009</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Feature    Weight\n",
       "7       n8  0.016746\n",
       "12     n13  0.015656\n",
       "3       n4  0.011586\n",
       "5       n6  0.004270\n",
       "0       n1  0.003331\n",
       "6       n7  0.001403\n",
       "9      n10  0.000816\n",
       "10     n11  0.000576\n",
       "11     n12  0.000562\n",
       "8       n9  0.000376\n",
       "1       n2  0.000035\n",
       "2       n3  0.000014\n",
       "4       n5  0.000009"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs_weights = np.abs(m.coef_)\n",
    "int_col_names = ['n1', 'n2', 'n3', 'n4', 'n5', 'n6', 'n7', 'n8', 'n9', 'n10', 'n11', 'n12', 'n13']\n",
    "weights_df = pd.DataFrame(list(zip(int_col_names, abs_weights[0])), columns =['Feature', 'Weight']) \n",
    "weights_df.sort_values('Weight', ascending=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Load files to GCP bucket and convert to RDDs for Spark analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `train.txt` and `test.txt` files were downloaded to an external hard drive and subsequently loaded into a GCP bucket. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# This command streams the main data set from dropbox directly to your GCP bucket - this may take a little time (RUN THIS CELL AS IS)\n",
    "#!curl -L \"https://s3-eu-west-1.amazonaws.com/kaggle-display-advertising-challenge-dataset/dac.tar.gz\" | gsutil cp - gs://{BUCKET}/finalproject/train.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# Do not run in the Docker container. This command puts a local file on GCP\n",
    "#!gsutil cp 'train.txt' gs://{BUCKET}/finalproject/train.txt\n",
    "#!gsutil cp 'train.txt' gs://danielalvarez_w261projects/finalproject/train.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# Do not run in the Docker container. This command puts a local file on GCP\n",
    "#!gsutil cp 'test.txt' gs://{BUCKET}/finalproject/test.txt\n",
    "#!gsutil cp 'test.txt' gs://danielalvarez_w261projects/finalproject/test.txt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# load the data into Spark RDDs for convenience of use later (RUN THIS CELL AS IS)\n",
    "# trainRDD = sc.textFile(f'gs://danielalvarez_w261projects/finalproject/train.txt')\n",
    "# testRDD = sc.textFile(f'gs://danielalvarez_w261projects/finalproject/test.txt')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# print the class\n",
    "# print(type(trainRDD))\n",
    "# print(type(testRDD))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# number of rows and shape of the files\n",
    "# !cat trainRDD | wc -l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": [
    "# convert to RDDs to DataFrames\n",
    "#DF = trainRDD.map(lambda x: (x.split('\\t')[0], ast.literal_eval(x.split('\\t')[1]))).toDF()\n",
    "# from pyspark.sql.types import Row\n",
    "\n",
    "# #here you are going to create a function\n",
    "# def f(x):\n",
    "#     d = {}\n",
    "#     for i in range(len(x)):\n",
    "#         d[str(i)] = x[i]\n",
    "#     return d\n",
    "\n",
    "# #Now populate that\n",
    "# df = trainRDD.map(lambda x: Row(**f(x))).toDF()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [],
   "source": []
  }
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