fico.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "from math import inf\n",
    "\n",
    "from gurobipy import *\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "\n",
    "from implementation import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set_context(\"notebook\", font_scale=1.25, rc={\"lines.linewidth\": 1.8})\n",
    "blue=\"#3F51B5\"; green=\"#43A047\"; orange=\"#FF9800\"\n",
    "sns.set_palette(sns.color_palette([blue, green, orange]))\n",
    "plt.rc('font', **{'family': 'serif', 'serif': ['CMU Serif', 'computer modern']})\n",
    "plt.rc('text', usetex=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Academic license - for non-commercial use only\n"
     ]
    }
   ],
   "source": [
    "setParam(\"OutputFlag\", False)\n",
    "EPS = 0.0001"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To replicate the results, the three csv files at https://github.com/fairmlbook/fairmlbook.github.io/tree/master/code/creditscore/data must be downloaded as `transrisk_performance_by_race_ssa.csv`, `totals.csv`, and `transrisk_cdf_by_race_ssa.csv` in the same directory."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cleanup_frame(frame):\n",
    "    \"\"\"Rename and re-order columns\"\"\"\n",
    "    # (c) Moritz Hardt, https://github.com/fairmlbook/fairmlbook.github.io/blob/master/code/creditscore/creditscore.ipynb\n",
    "    frame = frame.rename(columns={'Non- Hispanic white': 'White'})\n",
    "    frame = frame.reindex(['Asian', 'Black', 'Hispanic', 'White'], axis=1)\n",
    "    return frame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "risk = cleanup_frame(pd.read_csv(\"transrisk_performance_by_race_ssa.csv\"))\n",
    "totals = cleanup_frame(pd.read_csv(\"totals.csv\"))\n",
    "cdf = cleanup_frame(pd.read_csv(\"transrisk_cdf_by_race_ssa.csv\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "174047"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = sum(totals[race][0] for race in totals.columns)\n",
    "N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "buckets_by_group = []\n",
    "for race in risk.columns:\n",
    "    tot = totals[race][0]\n",
    "    buckets = []\n",
    "    old_cd = 0\n",
    "    for default_percent, cd in zip(risk[race], cdf[race]):\n",
    "        buckets.append((1 - float(default_percent)/100, int(cd * tot / 100) - int(old_cd * tot / 100))) #(cd - old_cd) / 100 * tot))\n",
    "        old_cd = cd\n",
    "    buckets = [(b1, b2) for b1, b2 in buckets if b2 > 0]\n",
    "    buckets.sort(reverse=True)\n",
    "    buckets_by_group.append(buckets)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def _setup_constraints(classifications, cardinality):\n",
    "    num_groups = len(classifications)\n",
    "    \n",
    "    m = Model()\n",
    "\n",
    "    allocations = [[] for _ in range(num_groups)]\n",
    "    allocation_sum = 0\n",
    "    will_pay_back = [0 for _ in range(num_groups)]\n",
    "    wont_pay_back = [0 for _ in range(num_groups)]\n",
    "    will_pay_back_and_received = [0 for _ in range(num_groups)]\n",
    "    wont_pay_back_and_received = [0 for _ in range(num_groups)]\n",
    "\n",
    "    for group in range(num_groups):\n",
    "        for prob, group_size in classifications[group]:\n",
    "            var = m.addVar(ub=group_size)\n",
    "            allocation_sum += var\n",
    "            allocations[group].append((prob, var))\n",
    "            will_pay_back[group] += group_size * prob\n",
    "            wont_pay_back[group] += group_size * (1 - prob)\n",
    "            will_pay_back_and_received[group] += var * prob\n",
    "            wont_pay_back_and_received[group] += var * (1 - prob)\n",
    "\n",
    "    m.addConstr(allocation_sum == cardinality)\n",
    "\n",
    "    for group in range(num_groups):\n",
    "        m.addConstr(will_pay_back_and_received[0] * will_pay_back[group] == will_pay_back_and_received[group] * will_pay_back[0])\n",
    "        m.addConstr(wont_pay_back_and_received[0] * wont_pay_back[group] == wont_pay_back_and_received[group] * wont_pay_back[0])\n",
    "\n",
    "    return m, allocations, will_pay_back_and_received\n",
    "\n",
    "\n",
    "def maximize_efficiency_given_necessary_popmonotonicity(classifications, cardinality):\n",
    "    m, allocations, will_pay_back_and_received = _setup_constraints(classifications, cardinality)\n",
    "    \n",
    "    num_groups = len(classifications)\n",
    "    group_sizes = [sum(group_size for _, group_size in clf) for clf in classifications]\n",
    "    for group in range(num_groups):\n",
    "        for (prob, group_size), (prob2, var) in zip(classifications[group], allocations[group]):\n",
    "            assert prob == prob2\n",
    "            agents_after_removal = group_size + sum(group_sizes[:group]) + sum(group_sizes[group+1:])\n",
    "            m.addConstr(var * agents_after_removal <= cardinality * group_size)\n",
    "            # var / group_size <= cardinality / agents_after_removal\n",
    "    \n",
    "    m.setObjective(sum(will_pay_back_and_received), GRB.MAXIMIZE)\n",
    "    m.optimize()\n",
    "    assert m.status == 2\n",
    "    return m"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "data_pop = []\n",
    "for k in range(1, int(N + 1), 10):\n",
    "    unfair_eff = optimal_nonfair_efficiency(k, buckets_by_group)\n",
    "    eff = sum(get_pos(alloc) for alloc in find_opt_fair(k, buckets_by_group))\n",
    "    datum = {\"$k$\": k, \"efficiency\": eff, \"efficiency fraction of unfair\": eff / unfair_eff, \"algorithm\": \"equalized odds\"}\n",
    "    data_pop.append(datum)\n",
    "    eff = maximize_efficiency_given_necessary_popmonotonicity(buckets_by_group, k).objVal\n",
    "    datum = {\"$k$\": k, \"efficiency\": eff, \"efficiency fraction of unfair\": eff / unfair_eff, \"algorithm\": \"upper bound\"}\n",
    "    data_pop.append(datum)\n",
    "    eff = k / N * sum(get_pos(bucket) for bucket in buckets_by_group)\n",
    "    datum = {\"$k$\": k, \"efficiency\": eff, \"efficiency fraction of unfair\": eff / unfair_eff, \"algorithm\": \"uniform\"}\n",
    "    data_pop.append(datum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 711.269x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_pop = pd.DataFrame(data_pop)\n",
    "f = sns.relplot(data=df_pop[-(df_pop[\"algorithm\"].isin([\"no fairness\"]))], x=\"$k$\", y=\"efficiency fraction of unfair\", hue=\"algorithm\", kind=\"line\", aspect=1.6)\n",
    "f.savefig(\"efficiency_ratios.pdf\")"
   ]
  }
 ],
 "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": "3.6.6rc1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}