week-5/week-5-1-machine-bias-class.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Week 5-1: Breaking down Machine Bias\n",
    "\n",
    "This notebook explores the classic ProPublica story [Machine Bias](https://www.propublica.org/article/machine-bias-risk-assessments-in-criminal-sentencing). It uses the original data that the reporters collected for the story, through FOIA requests to Broward County, Florida.\n",
    "\n",
    "The COMPAS score uses answers to [137 questions](https://www.documentcloud.org/documents/2702103-Sample-Risk-Assessment-COMPAS-CORE.html) to assign a risk score to defendents -- essentially a probability of re-arrest. The actual output is two-fold: a risk rating of 1-10 and a \"low\", \"medium\", or \"high\" risk label\n",
    "\n",
    "This analysis is based on ProPublica's [original notebook](https://github.com/propublica/compas-analysis/blob/master/Compas%20Analysis.ipynb)\n",
    "\n",
    "There has been a lot of discussion about this story and its particular definition of fairness. The best overall reference is the [Fairness in Machine Learning\n",
    "NIPS 2017 Tutorial](http://fairml.how) by Solon Barocas and Moritz Hardt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from pandas.plotting import scatter_matrix\n",
    "from sklearn import metrics\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook is designed to let you select between data on arrests for non-violent or violent crimes. This allows quick comparisons of the difference between these two data sets.\n",
    "\n",
    "\n",
    "There is some reason to suspect that arrest data for violent crime is both more accurate and less biased than non-violent crime data. See e.g. [Skeem and Lowenkamp](https://www.law.berkeley.edu/wp-content/uploads/2015/04/SSRN-id2687339.pdf). Also, we do get more accurate predictors wih the violent data (including COMPAS).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "violent = False\n",
    "\n",
    "if violent:\n",
    "    fname ='compas-scores-two-years-violent.csv'\n",
    "    decile_col = 'v_decile_score'\n",
    "    score_col = 'v_score_text'\n",
    "else:\n",
    "    fname ='compas-scores-two-years.csv'\n",
    "    decile_col = 'decile_score'\n",
    "    score_col = 'score_text'\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>name</th>\n",
       "      <th>first</th>\n",
       "      <th>last</th>\n",
       "      <th>compas_screening_date</th>\n",
       "      <th>sex</th>\n",
       "      <th>dob</th>\n",
       "      <th>age</th>\n",
       "      <th>age_cat</th>\n",
       "      <th>race</th>\n",
       "      <th>...</th>\n",
       "      <th>v_decile_score</th>\n",
       "      <th>v_score_text</th>\n",
       "      <th>v_screening_date</th>\n",
       "      <th>in_custody</th>\n",
       "      <th>out_custody</th>\n",
       "      <th>priors_count.1</th>\n",
       "      <th>start</th>\n",
       "      <th>end</th>\n",
       "      <th>event</th>\n",
       "      <th>two_year_recid</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>miguel hernandez</td>\n",
       "      <td>miguel</td>\n",
       "      <td>hernandez</td>\n",
       "      <td>2013-08-14</td>\n",
       "      <td>Male</td>\n",
       "      <td>1947-04-18</td>\n",
       "      <td>69</td>\n",
       "      <td>Greater than 45</td>\n",
       "      <td>Other</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>Low</td>\n",
       "      <td>2013-08-14</td>\n",
       "      <td>2014-07-07</td>\n",
       "      <td>2014-07-14</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>327</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>3</td>\n",
       "      <td>kevon dixon</td>\n",
       "      <td>kevon</td>\n",
       "      <td>dixon</td>\n",
       "      <td>2013-01-27</td>\n",
       "      <td>Male</td>\n",
       "      <td>1982-01-22</td>\n",
       "      <td>34</td>\n",
       "      <td>25 - 45</td>\n",
       "      <td>African-American</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>Low</td>\n",
       "      <td>2013-01-27</td>\n",
       "      <td>2013-01-26</td>\n",
       "      <td>2013-02-05</td>\n",
       "      <td>0</td>\n",
       "      <td>9</td>\n",
       "      <td>159</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4</td>\n",
       "      <td>ed philo</td>\n",
       "      <td>ed</td>\n",
       "      <td>philo</td>\n",
       "      <td>2013-04-14</td>\n",
       "      <td>Male</td>\n",
       "      <td>1991-05-14</td>\n",
       "      <td>24</td>\n",
       "      <td>Less than 25</td>\n",
       "      <td>African-American</td>\n",
       "      <td>...</td>\n",
       "      <td>3</td>\n",
       "      <td>Low</td>\n",
       "      <td>2013-04-14</td>\n",
       "      <td>2013-06-16</td>\n",
       "      <td>2013-06-16</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>63</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5</td>\n",
       "      <td>marcu brown</td>\n",
       "      <td>marcu</td>\n",
       "      <td>brown</td>\n",
       "      <td>2013-01-13</td>\n",
       "      <td>Male</td>\n",
       "      <td>1993-01-21</td>\n",
       "      <td>23</td>\n",
       "      <td>Less than 25</td>\n",
       "      <td>African-American</td>\n",
       "      <td>...</td>\n",
       "      <td>6</td>\n",
       "      <td>Medium</td>\n",
       "      <td>2013-01-13</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1174</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>6</td>\n",
       "      <td>bouthy pierrelouis</td>\n",
       "      <td>bouthy</td>\n",
       "      <td>pierrelouis</td>\n",
       "      <td>2013-03-26</td>\n",
       "      <td>Male</td>\n",
       "      <td>1973-01-22</td>\n",
       "      <td>43</td>\n",
       "      <td>25 - 45</td>\n",
       "      <td>Other</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>Low</td>\n",
       "      <td>2013-03-26</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>1102</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 53 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   id                name   first         last compas_screening_date   sex  \\\n",
       "0   1    miguel hernandez  miguel    hernandez            2013-08-14  Male   \n",
       "1   3         kevon dixon   kevon        dixon            2013-01-27  Male   \n",
       "2   4            ed philo      ed        philo            2013-04-14  Male   \n",
       "3   5         marcu brown   marcu        brown            2013-01-13  Male   \n",
       "4   6  bouthy pierrelouis  bouthy  pierrelouis            2013-03-26  Male   \n",
       "\n",
       "          dob  age          age_cat              race      ...        \\\n",
       "0  1947-04-18   69  Greater than 45             Other      ...         \n",
       "1  1982-01-22   34          25 - 45  African-American      ...         \n",
       "2  1991-05-14   24     Less than 25  African-American      ...         \n",
       "3  1993-01-21   23     Less than 25  African-American      ...         \n",
       "4  1973-01-22   43          25 - 45             Other      ...         \n",
       "\n",
       "   v_decile_score  v_score_text  v_screening_date  in_custody  out_custody  \\\n",
       "0               1           Low        2013-08-14  2014-07-07   2014-07-14   \n",
       "1               1           Low        2013-01-27  2013-01-26   2013-02-05   \n",
       "2               3           Low        2013-04-14  2013-06-16   2013-06-16   \n",
       "3               6        Medium        2013-01-13         NaN          NaN   \n",
       "4               1           Low        2013-03-26         NaN          NaN   \n",
       "\n",
       "   priors_count.1 start   end event two_year_recid  \n",
       "0               0     0   327     0              0  \n",
       "1               0     9   159     1              1  \n",
       "2               4     0    63     0              1  \n",
       "3               1     0  1174     0              0  \n",
       "4               2     0  1102     0              0  \n",
       "\n",
       "[5 rows x 53 columns]"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv = pd.read_csv(fname)\n",
    "cv.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['id', 'name', 'first', 'last', 'compas_screening_date', 'sex', 'dob',\n",
       "       'age', 'age_cat', 'race', 'juv_fel_count', 'decile_score',\n",
       "       'juv_misd_count', 'juv_other_count', 'priors_count',\n",
       "       'days_b_screening_arrest', 'c_jail_in', 'c_jail_out', 'c_case_number',\n",
       "       'c_offense_date', 'c_arrest_date', 'c_days_from_compas',\n",
       "       'c_charge_degree', 'c_charge_desc', 'is_recid', 'r_case_number',\n",
       "       'r_charge_degree', 'r_days_from_arrest', 'r_offense_date',\n",
       "       'r_charge_desc', 'r_jail_in', 'r_jail_out', 'violent_recid',\n",
       "       'is_violent_recid', 'vr_case_number', 'vr_charge_degree',\n",
       "       'vr_offense_date', 'vr_charge_desc', 'type_of_assessment',\n",
       "       'decile_score.1', 'score_text', 'screening_date',\n",
       "       'v_type_of_assessment', 'v_decile_score', 'v_score_text',\n",
       "       'v_screening_date', 'in_custody', 'out_custody', 'priors_count.1',\n",
       "       'start', 'end', 'event', 'two_year_recid'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Following ProPublica, we filter out certain rows which are missing data. As they put it:\n",
    "\n",
    "- If the charge date of a defendants Compas scored crime was not within 30 days from when the person was arrested, we assume that because of data quality reasons, that we do not have the right offense.\n",
    "- We coded the recidivist flag -- is_recid -- to be -1 if we could not find a compas case at all.\n",
    "- In a similar vein, ordinary traffic offenses -- those with a c_charge_degree of 'O' -- will not result in Jail time are removed\n",
    "- We filtered the underlying data from Broward county to include only those rows representing people who had either recidivated in two years, or had at least two years outside of a correctional facility."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(6172, 53)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cv = cv[\n",
    "    (cv.days_b_screening_arrest <= 30) &  \n",
    "    (cv.days_b_screening_arrest >= -30) &  \n",
    "    (cv.is_recid != -1) &\n",
    "    (cv.c_charge_degree != 'O') &\n",
    "    (cv[score_col] != 'N/A')\n",
    "]\n",
    "\n",
    "cv.reset_index(inplace=True, drop=True) # renumber the rows from 0 again\n",
    "cv.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. A first look at the data \n",
    "\n",
    "Let's do some basic analysis on the demographics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "25 - 45            3532\n",
       "Less than 25       1347\n",
       "Greater than 45    1293\n",
       "Name: age_cat, dtype: int64"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# age value coutns\n",
    "cv.age_cat.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "African-American    3175\n",
       "Caucasian           2103\n",
       "Hispanic             509\n",
       "Other                343\n",
       "Asian                 31\n",
       "Native American       11\n",
       "Name: race, dtype: int64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# race value counts\n",
    "cv.race.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The COMPAS model predictions are in `v_decile_score` from 1 to 10, and low/med/high in `v_score_text`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1     1286\n",
       "2      822\n",
       "4      666\n",
       "3      647\n",
       "5      582\n",
       "6      529\n",
       "7      496\n",
       "9      420\n",
       "8      420\n",
       "10     304\n",
       "Name: decile_score, dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# COMPAS decile score value counts\n",
    "cv[decile_col].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Low       3421\n",
       "Medium    1607\n",
       "High      1144\n",
       "Name: score_text, dtype: int64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# COMPAS text score value counts\n",
    "cv[score_col].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can look at the decile scores white and black to get our first look at how the COMPAS algorithm handles different races."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x112c640f0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram of decile scores for White\n",
    "cv[cv.race == 'Caucasian'][decile_col].plot(kind='hist', title='White Defendant\\'s Decile Scores ')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11307b080>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lOSDMzCzLAWFmZlkNBYSk91ddiJmZNZdGtyD+XdJDkr4oafdKKzIzs6bQUEBExIeAT1Nc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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Histogram of decile scores for Black\n",
    "cv[cv.race == 'African-American'][decile_col].plot(kind='hist', title='Black Defendant\\'s Decile Scores')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Meanwhile the `two_year_recid` field records whether or not each person was re-arrested for a violent offense within two years, which is what COMPAS is trying to predict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    3363\n",
       "1    2809\n",
       "Name: two_year_recid, dtype: int64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# recidivism value counts\n",
    "cv.two_year_recid.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can start looking at the relationships between these variables. First, recidivism by race.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>two_year_recid</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>race</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>African-American</th>\n",
       "      <td>1514</td>\n",
       "      <td>1661</td>\n",
       "      <td>0.523150</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Asian</th>\n",
       "      <td>23</td>\n",
       "      <td>8</td>\n",
       "      <td>0.258065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Caucasian</th>\n",
       "      <td>1281</td>\n",
       "      <td>822</td>\n",
       "      <td>0.390870</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hispanic</th>\n",
       "      <td>320</td>\n",
       "      <td>189</td>\n",
       "      <td>0.371316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Native American</th>\n",
       "      <td>6</td>\n",
       "      <td>5</td>\n",
       "      <td>0.454545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Other</th>\n",
       "      <td>219</td>\n",
       "      <td>124</td>\n",
       "      <td>0.361516</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "two_year_recid       0     1      rate\n",
       "race                                  \n",
       "African-American  1514  1661  0.523150\n",
       "Asian               23     8  0.258065\n",
       "Caucasian         1281   822  0.390870\n",
       "Hispanic           320   189  0.371316\n",
       "Native American      6     5  0.454545\n",
       "Other              219   124  0.361516"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# recidivism rates by race\n",
    "recid_race = pd.crosstab(cv.race, cv.two_year_recid)\n",
    "recid_race['rate'] = recid_race[1] / recid_race.sum(axis=1)\n",
    "recid_race"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Similarly for sex:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>two_year_recid</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sex</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Female</th>\n",
       "      <td>762</td>\n",
       "      <td>413</td>\n",
       "      <td>0.351489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>2601</td>\n",
       "      <td>2396</td>\n",
       "      <td>0.479488</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "two_year_recid     0     1      rate\n",
       "sex                                 \n",
       "Female           762   413  0.351489\n",
       "Male            2601  2396  0.479488"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# recidivism rates by sex\n",
    "recid_sex = pd.crosstab(cv.sex, cv.two_year_recid)\n",
    "recid_sex['rate'] = recid_sex[1] / recid_sex.sum(axis=1)\n",
    "recid_sex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are significant differences in recidivisim in this population by race and gender. These are the \"base rates\" we will talk about more. However, there may also be significant differences in the composition of these populations -- they may have different age, criminal histories, etc.\n",
    "\n",
    "Let's see how the COMPAS risk scores break down by race and gender."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>score_text</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Medium</th>\n",
       "      <th>High risk rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>race</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>African-American</th>\n",
       "      <td>845</td>\n",
       "      <td>1346</td>\n",
       "      <td>984</td>\n",
       "      <td>0.266142</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Asian</th>\n",
       "      <td>3</td>\n",
       "      <td>24</td>\n",
       "      <td>4</td>\n",
       "      <td>0.096774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Caucasian</th>\n",
       "      <td>223</td>\n",
       "      <td>1407</td>\n",
       "      <td>473</td>\n",
       "      <td>0.106039</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Hispanic</th>\n",
       "      <td>47</td>\n",
       "      <td>368</td>\n",
       "      <td>94</td>\n",
       "      <td>0.092338</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Native American</th>\n",
       "      <td>4</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>0.363636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Other</th>\n",
       "      <td>22</td>\n",
       "      <td>273</td>\n",
       "      <td>48</td>\n",
       "      <td>0.064140</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "score_text        High   Low  Medium  High risk rate\n",
       "race                                                \n",
       "African-American   845  1346     984        0.266142\n",
       "Asian                3    24       4        0.096774\n",
       "Caucasian          223  1407     473        0.106039\n",
       "Hispanic            47   368      94        0.092338\n",
       "Native American      4     3       4        0.363636\n",
       "Other               22   273      48        0.064140"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# high risk rates by race\n",
    "score_race = pd.crosstab(cv.race, cv[score_col])\n",
    "score_race['High risk rate'] = score_race['High'] / score_race.sum(axis=1)\n",
    "score_race"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>score_text</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Medium</th>\n",
       "      <th>High risk rate</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>sex</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Female</th>\n",
       "      <td>151</td>\n",
       "      <td>699</td>\n",
       "      <td>325</td>\n",
       "      <td>0.128511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Male</th>\n",
       "      <td>993</td>\n",
       "      <td>2722</td>\n",
       "      <td>1282</td>\n",
       "      <td>0.198719</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "score_text  High   Low  Medium  High risk rate\n",
       "sex                                           \n",
       "Female       151   699     325        0.128511\n",
       "Male         993  2722    1282        0.198719"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# high risk rates by sex\n",
    "score_sex = pd.crosstab(cv.sex, cv[score_col])\n",
    "score_sex['High risk rate'] = score_sex['High'] / score_sex.sum(axis=1)\n",
    "score_sex"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generally, the fraction of people assigned a `high` risk is greater where the recidivism rates are also higher. \n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Predictive calibration and accuracy\n",
    "Being \"accurate\" in a predictive sense is only one type of \"fairness,\" as we shall see, but it's still a desirable characteristic.\n",
    "\n",
    "Let's start by looking at the proportion of people who are re-arrested in each decile score."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x112f9e940>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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sjRxLIQMsjRxLIQMsjRwjyzDrC6qSpFOPn1CVpAZZ7pLUIMtdkhpkuZ+ikqxL8vLu8dok\n1yd53SJn+p3FXF+LL8nyJG9Oclm3/aYk/ynJ25P80GLn+5vEF1TnKMmPAecC91TVN/vG11fVJ0eU\n4d/Qu9bP6cAfABcBnwYuB3ZX1b8fQYbpb4cN8NPAXQBVtWGhM8wkySvpXTLjkaq6c0RrXgTsq6pv\nJPlhYCtwIfAo8GtV9fUR5bgW+HhVHRrFesfJ8F/o/b08E/gr4FnA7wGvodc3bznBbx9mjr8D/Cy9\nz998D/gicGtVfWMU6y8FTZR7kn9WVR8ewTrXAm8H9gEXANdV1X/r9t1XVRcudIZurYe79c8A/hJY\n0Vcs91TV+SPIcB+98vogUPTK/Xfp3gZbVX+40Bm6HH9SVeu6x2+l9/35OPBa4PeratsIMuwFfrJ7\n2/AO4Nt011jqxn92oTN0Ob4OfAv4c3rfi49V1dQo1u7L8FBVnd99mPEI8MKq+l53rakHR/R381rg\nHwF3A68D7qf3g+ZngH9RVZ9Z6AxLQlWd8l/A4yNa52HgWd3jVcAkvYIHuH+E/733z/S4235gRBlO\nA36Z3r8cLujGDi7C977/z2IPMNY9fibw8Igy7Ot7fN9ifD+O/Vl035fX0vvsyRTwSXofMHz2iDI8\nAiwHngv8H+B53fgz+v+cFjjDw8Cy7vGZwGe6x+eN+P/Ts4BtwJ/S+/zPE/QODLcBz1no9Ud6bZn5\nSPLQ8XYB54woxmnVnYqpqseSXArcnuRFXY5ReSrJmVX1beBlxwaTnAV8fxQBqur7wPuTfKz79cuM\n+FpFndOSPJdeqaW6I9Wq+laSoyPK8Ejfvx4fTDJeVZNJXgx8d0QZAKr7vtwJ3Nmd474CuAr4D8Cs\nF5sagg/RK7NlwLuAjyU5CPwUvSvKjsrp9E7HnEHv1BBV9fiIz/vfRu805aVV9ZcASf42vR+2t9H7\nIbxgTpnTMl15/EPgyem7gD+uqheOIMNdwPVV9UDf2OnAzcDPV9Wyhc7QrXlGVX1nhvGzgRdU1cOj\nyDFt7SuBi6vqX4943cfo/UALvdNDF1fV/07yLOCzVXXBCDKcBfwG8Cp6V/y7EDjUfV1bVQ8udIYu\nx/1V9dLj7Dt2MDCKHC8EqKq/SPIc4DJ6/7r+kxGtfx29e0zcQ+978p6q+nCSMeC/VtUlI8qxv6pe\nMtd9Q1v/FCr3DwEfrqrPzrDv1qp60wgyrACOHvspPG3fxVX1uYXOoMEkORM4p6q+NMI1fwRYTe+o\n8XBVfXlUa3frv7iqvjjKNZeqJH8P+HF6L6z/6SJluBP4n8BHjv1dSHIOcDVweVVdtqDrnyrlLkmn\nku504VZ6NzN6fjf8ZXoXWtxWVdPPQgx3fctdkkZrFO/ws9wlacSSPF5V5y3kGqfMu2Uk6VSy2O/w\ns9wlaWGcwwne4bfQi1vukrQw/ju9Dz0+MH1Hks8s9OKec5ekBnlVSElqkOUuSQ2y3CWpQZa7ThlJ\nbkzyL0/i9/1x9+uqJI8MP5m09Fjual5VvWKxM/TrLjYnLSjLXUtakncl+WKSzwIv6cZ+NMknk9yb\n5I+6u2OR5JwkH0/yYPf1im78mzM877Ik702yJ8lDSf75CTK8IMndSR5I8kiSV3Xj65Pc1631qW7s\neUk+0T3nF5Kc343fmOSWJJ8DbpnL+tLJ8AhCS1aSl9G7s9MF9P6u3gfcC+wAfqmq/qy7xd1/Bl4N\n/EfgD6vqZ5Iso7uO93FcA3y9ql6e5Azgc0nuPM5VJN9Ed/vC7nnP7C4f+wHgkqr6UpLndXP/Lb0b\nQrw+yauB3+nyA6wFXllVf51k8xzWl+bMctdS9ip69wT9Nvzgvq3PAF5B7yYQx+ad0f36auDNAFX1\nPeBE9y59LXB+kjd222cBa4CZynUPcHN3o4dPVNUD3Y1a7j5WxlX1tW7uK4E3dGN3Jflb3aWAASaq\n6q9PYn1pzix3nWpOA/5qCDfhCPCOqto928SqujvJJcCVwG8neR9P/0j5IL51MutLJ8Nz7lrK7gZe\nn+SHkzwb+Mf0bj79pSQ/B5Cen+zmfwp4Wze+rLtD0vHsBt527LZrSV6c5JkzTexuo/jlqvoAvRuC\nXwh8AbgkyepuzrHTMn8E/Hw3dinw1ar6xnzWl06GR+5asqrqviQfBR4EvkLv9Aj0yvM3k7wb+CF6\n9+Z8ELgO2JHkGnr3z3wb8PnjPP0H6d3k/L70zu9MAa8/ztxLgV9N8l3gm8Cbq2qqO2/+e0lO6/Jd\nDtxI7xTOQ/R+EL1lCOtLc+a1ZSSpQZ6WkaQGeVpG6iT5CeCWacPfqaqLFiOPNB+elpGkBnlaRpIa\nZLlLUoMsd0lqkOUuSQ36f+9OtqS2EX7cAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# probability of recidivism by decile\n",
    "cv.groupby(decile_col).mean()['two_year_recid'].plot(kind='bar')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1132dd908>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# probability of recidivism by decile and race\n",
    "b = cv[cv.race=='African-American'].groupby([decile_col]).mean()['two_year_recid']\n",
    "w = cv[cv.race=='Caucasian'].groupby([decile_col]).mean()['two_year_recid']\n",
    "\n",
    "a = pd.concat([w,b], axis=1)\n",
    "a.columns = ['White','Black']\n",
    "a.plot.bar()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The outcome variable `two_year_recid` is the actually observed results in the world, and it is binary -- was this person re-arrested within two years of their initial arrest and risk score assignment? To work with this data further we're going to simplify the COMPAS classifier scores  it by thresholding them into a binary variable as well. ProPublica splits \"low\" from \"medium or high\" risk, according to their [methodology](https://www.propublica.org/article/how-we-analyzed-the-compas-recidivism-algorithm). \n",
    "\n",
    "Using this binary prediction variable lets us compute a confusion matrix for the COMPAS algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>guessed_recid</th>\n",
       "      <th>False</th>\n",
       "      <th>True</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>actual_recid</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>2345</td>\n",
       "      <td>1018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>1076</td>\n",
       "      <td>1733</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "guessed_recid  False  True \n",
       "actual_recid               \n",
       "False           2345   1018\n",
       "True            1076   1733"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# COMPAS recidivism confusion matrix\n",
    "cv['guessed_recid'] = cv[score_col] != 'Low'\n",
    "cv['actual_recid'] = cv.two_year_recid == 1\n",
    "cm = pd.crosstab(cv.actual_recid, cv.guessed_recid)\n",
    "cm # for \"confusion matrix\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "All of the information about binary classifier performance and error (for a particular group) is in a 2x2 confusion matrix (also called a contingency table.) But we're usually interested in rates as opposed to raw numbers, so we're going to convert this table into the following values:\n",
    "\n",
    "- Accuracy: the fraction of guesses that were correct\n",
    "- Precision or Positive Predictive Value: of the people we guessed would recidivate, what fraction did?\n",
    "- False Positive Rate: of the people who didn't recidivate, how many did we guess would?\n",
    "- False Negative Rate: of the people who did recidivate, how many did we guess would not?\n",
    "\n",
    "There's a wonderful little [diagram on the qauntitative definitions of fairness](https://speak-statistics-to-power.github.io/fairness/#definitions-metric-parities) page that shows how all of these relate, and Wikipedia is also a [good reference](https://en.wikipedia.org/wiki/Confusion_matrix)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# The usual definitions. First index is predicted, second is actual\n",
    "TN = cm[False][False]\n",
    "TP = cm[True][True]\n",
    "FN = cm[False][True]\n",
    "FP = cm[True][False]\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "About 63% of those scored as medium or high risk end up getting arrested again within two years. This is the **Positive Predictive Value (PPV)** or **Precision**. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.62995274445656124"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# PPV\n",
    "TP / (TP + FP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Of those who did not go on to be re-arrested, about 30% were classified as medium or high risk. This is the **False Positive Rate (FPR)**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.30270591733571217"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# FPR\n",
    "FP / (FP + TN)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It may help to understand many of these formulas if we define variables for the total number of true positive and negative cases:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "P = TP + FN\n",
    "N = TN + FP"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.30270591733571217"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Equivalent definition of FPR that might be easier to understand, N in denominator\n",
    "FP / N"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also calculate the **False Negative Rate (FNR)** which counts those who were  classified as low risk, as a fraction of those who were re-arrested.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.38305446778212887"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# FNR\n",
    "FN / (FN + TP)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.38305446778212887"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Alternate form with P in denominator\n",
    "FN / P"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To study the difference betwen races, let's define a few helper functions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# cm is a confusion matrix. The rows are guessed, the columns are actual \n",
    "def print_ppv_fpv(cm):\n",
    "    # the indices here are [col][row] or [actual][guessed]\n",
    "    TN = cm[False][False]   \n",
    "    TP = cm[True][True]\n",
    "    FN = cm[True][False]\n",
    "    FP = cm[False][True]\n",
    "    print('Accuracy: ', (TN+TP)/(TN+TP+FN+FP))\n",
    "    print('PPV: ', TP / (TP + FP))\n",
    "    print('FPR: ', FP / (FP + TN))\n",
    "    print('FNR: ', FN / (FN + TP))\n",
    "    print()\n",
    "\n",
    "def print_metrics(guessed, actual):\n",
    "    cm = pd.crosstab(guessed, actual, rownames=['guessed'], colnames=['actual'])\n",
    "    print(cm)\n",
    "    print()\n",
    "    print_ppv_fpv(cm)    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "White\n",
      "actual   False  True \n",
      "guessed              \n",
      "False      999    408\n",
      "True       282    414\n",
      "\n",
      "Accuracy:  0.671897289586\n",
      "PPV:  0.594827586207\n",
      "FPR:  0.220140515222\n",
      "FNR:  0.496350364964\n",
      "\n",
      "Black\n",
      "actual   False  True \n",
      "guessed              \n",
      "False      873    473\n",
      "True       641   1188\n",
      "\n",
      "Accuracy:  0.649133858268\n",
      "PPV:  0.649535265172\n",
      "FPR:  0.423381770145\n",
      "FNR:  0.284768211921\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('White')\n",
    "subset = cv[cv.race == 'Caucasian']\n",
    "print_metrics(subset.guessed_recid, subset.actual_recid)\n",
    "\n",
    "print('Black')\n",
    "subset = cv[cv.race == 'African-American']\n",
    "print_metrics(subset.guessed_recid, subset.actual_recid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is the statistical core of ProPublica's story: the False Positive Rate is substantially higher for black defendants. \n",
    "\n",
    "However, also note that the PPV is similar between black and white. In fact the lower PPV for white means the score is has greater predictive accuracy for black defendants. Here \"accurate\" measures the proportion of people that actually were re-arrested, as a proportion of the people that COMPAS guessed would be."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Logistic regression to build our own predictor\n",
    "\n",
    "We are going to use logistic regression to try to build our own predictor, just from the information we we have. This is actually quite a lot:\n",
    "- Age\n",
    "- Sex\n",
    "- Felony or Misdemeanor charge (`c_charge_degree`)\n",
    "- Number of prior arrests (`c_priors_count`)\n",
    "\n",
    "And we'll try this both with and without race as a predictive factor, too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# build up dummy variables for age, race, gender\n",
    "features = pd.concat(\n",
    "    [pd.get_dummies(cv.age_cat, prefix='age'),\n",
    "     pd.get_dummies(cv.sex, prefix='sex'),\n",
    "     pd.get_dummies(cv.c_charge_degree, prefix='degree'), # felony or misdemeanor charge ('f' or 'm')\n",
    "     cv.priors_count],\n",
    "    axis=1)\n",
    "\n",
    "# We should have one less dummy variable than the number of categories, to avoid the \"dummy variable trap\"\n",
    "# See https://www.quora.com/When-do-I-fall-in-the-dummy-variable-trap\n",
    "features.drop(['age_25 - 45', 'sex_Female', 'degree_M'], axis=1, inplace=True)\n",
    "\n",
    "# Try to predict whether someone is re-arrested\n",
    "target = cv.two_year_recid\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = features.values\n",
    "y = target.values\n",
    "lr = LogisticRegression()\n",
    "lr.fit(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a logistic regression, so the coefficients are odds ratios (after undoing the logarithm.) Let's look at them to see what weights it used to make its predictions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>age_Greater than 45</th>\n",
       "      <th>age_Less than 25</th>\n",
       "      <th>sex_Male</th>\n",
       "      <th>degree_F</th>\n",
       "      <th>priors_count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.504745</td>\n",
       "      <td>2.105168</td>\n",
       "      <td>1.397191</td>\n",
       "      <td>1.250864</td>\n",
       "      <td>1.185331</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   age_Greater than 45  age_Less than 25  sex_Male  degree_F  priors_count\n",
       "0             0.504745          2.105168  1.397191  1.250864      1.185331"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Examine regression coefficients\n",
    "coeffs = pd.DataFrame(np.exp(lr.coef_), columns=features.columns)\n",
    "coeffs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model thinks that (for the non-violent data set):\n",
    "\n",
    "- being young (<25) more than doubles your odds of recidivism\n",
    "- but being >45 years old makes half as likely\n",
    "- being male increases your odds by 40%\n",
    "- every prior arrest increases your odds by 18%\n",
    "\n",
    "Now let's put our model through the same tests as we used on the COMPAS score to see how well this predictor does."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>actual</th>\n",
       "      <th>False</th>\n",
       "      <th>True</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>guessed</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>2568</td>\n",
       "      <td>1239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>795</td>\n",
       "      <td>1570</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "actual   False  True \n",
       "guessed              \n",
       "False     2568   1239\n",
       "True       795   1570"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Crosstab for our predictive model\n",
    "y_pred = lr.predict(x)\n",
    "guessed=pd.Series(y_pred)==1\n",
    "\n",
    "actual=cv.two_year_recid==1\n",
    "\n",
    "cm = pd.crosstab(guessed, actual, rownames=['guessed'], colnames=['actual'])\n",
    "cm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Accuracy:  0.670447180817\n",
      "PPV:  0.663847780127\n",
      "FPR:  0.236396074933\n",
      "FNR:  0.441082235671\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print_ppv_fpv(cm)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Once again, we can compare between White and Black."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "White\n",
      "actual   False  True \n",
      "guessed              \n",
      "False     1068    494\n",
      "True       213    328\n",
      "\n",
      "Accuracy:  0.66381359962\n",
      "PPV:  0.606284658041\n",
      "FPR:  0.166276346604\n",
      "FNR:  0.60097323601\n",
      "\n",
      "Black\n",
      "actual   False  True \n",
      "guessed              \n",
      "False     1026    564\n",
      "True       488   1097\n",
      "\n",
      "Accuracy:  0.668661417323\n",
      "PPV:  0.692113564669\n",
      "FPR:  0.322324966975\n",
      "FNR:  0.33955448525\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print('White')\n",
    "subset = cv.race == 'Caucasian'\n",
    "print_metrics(guessed[subset], actual[subset])\n",
    "\n",
    "print('Black')\n",
    "subset = cv.race == 'African-American'\n",
    "print_metrics(guessed[subset], actual[subset])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. The limits of prediction\n",
    "Both COMPAS and our logistic regression classifier only get about 65% accuracy overall. Would it be possible to do better with are more sophisticated classifier or feature encoding? We can take a look at two variables at a time to try to see what's happening here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1176abf28>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Af11r/QdKqQHwdaXUbwP/KfB/aK3/jlLqbwB/A/jl8zP1nOn3jZqiaL5L8nI8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sx++gG2sey9fg+hPN7+RxM2gjl739zCOPjBH2l0lfCt3wkIVMX0J4ZTNnnlrQFmXtC1GdH+BsH1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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatterpolot of age vs. priors, colored by two_year_recid\n",
    "colors = cv.two_year_recid.apply(lambda x: 'red' if x else 'blue')\n",
    "plt.scatter(cv.age, cv.priors_count, c=colors, alpha=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# add a  noise to the values in the array\n",
    "def jitter(arr):\n",
    "    # pick a standard deviation for the jitter of 3% of the data range\n",
    "    stdev = .02*(max(arr)-min(arr))\n",
    "    return arr + np.random.randn(len(arr)) * stdev"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1177d1fd0>"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lB4CDDC0eTRUDR/OiilmkgtFaoxrIK5eLc40fCopFztmJ5iYfYtcunSMZJjlN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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatterpolot of age vs. sex, colored by two_year_recid\n",
    "plt.scatter(cv.age, jitter(features.sex_Male), c=colors, alpha=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is no way to draw a line (even a curved line) that cleanly separates the red (recidivated) and blue (did not recidivate) dots. We can do a little better by looking at more than two axes at a time, and might be able to imagine fitting a curved plane, but it's still not possible to separate red and blue enough to give us a very accurate classifier."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}