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Older
" <tr>\n",
" <th>Male</th>\n",
" <td>2626</td>\n",
" <td>29</td>\n",
" <td>1621</td>\n",
" <td>427</td>\n",
" <td>9</td>\n",
" <td>285</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"race African-American Asian Caucasian Hispanic Native American Other\n",
"sex \n",
"Female 549 2 482 82 2 58\n",
"Male 2626 29 1621 427 9 285"
]
},
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tab = compas.groupby(['sex', 'race']).size()\n",
"tab.unstack()"
]
},
{
"cell_type": "code",
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
"metadata": {
"scrolled": false
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x504 with 2 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.bar(range(1, 11), compas.decile_score.value_counts(), ec='black')\n",
"plt.title(\"Decile scores of all defendants\")\n",
"plt.ylabel(\"Frequency\")\n",
"plt.xlabel(\"Decile score\")\n",
"plt.xticks(range(1, 11))\n",
"plt.show()\n",
"\n",
"fig, ax = compas.query(\"race in ['Caucasian', 'African-American']\").hist(\n",
" \"decile_score\",\n",
" by=\"race\",\n",
" figsize=(14, 7),\n",
" sharey=True,\n",
" xrot='horizontal',\n",
" ec='black',\n",
" bins=np.arange(0.5, 11.5, 1.0),\n",
" rwidth=0.8)\n",
"\n",
"fig.text(-1.5, 350, \"Frequency\", rotation='vertical')\n",
"fig.text(11.5, -60, \"Decile score\", horizontalalignment='center')\n",
"plt.tight_layout(w_pad=-2)\n",
"plt.show()"
]
},
{
"cell_type": "code",
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"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
" return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"sns.distplot(compas.age)\n",
"plt.title(\"Histogram of defendants' ages\")\n",
"plt.xlabel(\"Age of defendant\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": false
},
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"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>is_recid</th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" </tr>\n",
" <tr>\n",
" <th>age_cat</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>25 - 45</th>\n",
" <td>1784</td>\n",
" <td>1748</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Greater than 45</th>\n",
" <td>847</td>\n",
" <td>446</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Less than 25</th>\n",
" <td>551</td>\n",
" <td>796</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"is_recid 0 1\n",
"age_cat \n",
"25 - 45 1784 1748\n",
"Greater than 45 847 446\n",
"Less than 25 551 796"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"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>is_recid</th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" </tr>\n",
" <tr>\n",
" <th>sex</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Female</th>\n",
" <td>740</td>\n",
" <td>435</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Male</th>\n",
" <td>2442</td>\n",
" <td>2555</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"is_recid 0 1\n",
"sex \n",
"Female 740 435\n",
"Male 2442 2555"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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" 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>is_recid</th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" </tr>\n",
" <tr>\n",
" <th>race</th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th rowspan=\"3\" valign=\"top\">African-American</th>\n",
" <th>25 - 45</th>\n",
" <td>847.0</td>\n",
" <td>1051.0</td>\n",
" <th>Greater than 45</th>\n",
" <td>261.0</td>\n",
" <td>207.0</td>\n",
" <th>Less than 25</th>\n",
" <td>294.0</td>\n",
" <td>515.0</td>\n",
" <th rowspan=\"3\" valign=\"top\">Asian</th>\n",
" <th>25 - 45</th>\n",
" <td>10.0</td>\n",
" <td>4.0</td>\n",
" <th>Greater than 45</th>\n",
" <td>7.0</td>\n",
" <td>4.0</td>\n",
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" <th>Less than 25</th>\n",
" <td>4.0</td>\n",
" <td>2.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th rowspan=\"3\" valign=\"top\">Caucasian</th>\n",
" <th>25 - 45</th>\n",
" <td>620.0</td>\n",
" <td>508.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Greater than 45</th>\n",
" <td>442.0</td>\n",
" <td>186.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Less than 25</th>\n",
" <td>167.0</td>\n",
" <td>180.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th rowspan=\"3\" valign=\"top\">Hispanic</th>\n",
" <th>25 - 45</th>\n",
" <td>180.0</td>\n",
" <td>111.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Greater than 45</th>\n",
" <td>81.0</td>\n",
" <td>28.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Less than 25</th>\n",
" <td>51.0</td>\n",
" <td>58.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th rowspan=\"3\" valign=\"top\">Native American</th>\n",
" <th>25 - 45</th>\n",
" <td>5.0</td>\n",
" <td>2.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Greater than 45</th>\n",
" <td>NaN</td>\n",
" <td>2.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Less than 25</th>\n",
" <td>NaN</td>\n",
" <td>2.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th rowspan=\"3\" valign=\"top\">Other</th>\n",
" <th>25 - 45</th>\n",
" <td>122.0</td>\n",
" <td>72.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Greater than 45</th>\n",
" <td>56.0</td>\n",
" <td>19.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Less than 25</th>\n",
" <td>35.0</td>\n",
" <td>39.0</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"is_recid 0 1\n",
"race age_cat \n",
"African-American 25 - 45 847.0 1051.0\n",
" Greater than 45 261.0 207.0\n",
" Less than 25 294.0 515.0\n",
"Asian 25 - 45 10.0 4.0\n",
" Greater than 45 7.0 4.0\n",
" Less than 25 4.0 2.0\n",
"Caucasian 25 - 45 620.0 508.0\n",
" Greater than 45 442.0 186.0\n",
" Less than 25 167.0 180.0\n",
"Hispanic 25 - 45 180.0 111.0\n",
" Greater than 45 81.0 28.0\n",
" Less than 25 51.0 58.0\n",
"Native American 25 - 45 5.0 2.0\n",
" Greater than 45 NaN 2.0\n",
" Less than 25 NaN 2.0\n",
"Other 25 - 45 122.0 72.0\n",
" Greater than 45 56.0 19.0\n",
" Less than 25 35.0 39.0"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tab = compas.groupby(['age_cat', 'is_recid']).size()\n",
"display(tab.unstack())\n",
"\n",
"tab = compas.groupby(['sex', 'is_recid']).size()\n",
"display(tab.unstack())\n",
"\n",
"tab = compas.groupby(['race', 'age_cat', 'is_recid']).size()\n",
{
"cell_type": "markdown",
"metadata": {},
"source": [
"From above it is clear that there are no Native American recidivists of age over 45 or under 25. There are some other value combinations that might be problematic. Therefore the procedure of estimating $P(X=x)$ has to be considered carefully."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Synthetic data\n",
"In the chunk below, we generate the synthetic data as described by Lakkaraju et al. The default values and definitions of $Y$ and $T$ values follow their description.\n",
"* M = `nJudges_M`, number of judges\n",
"* N = `nSubjects_N`, number of subjects assigned to each judge\n",
"* betas $\\beta_i$ = `beta_i`, where $i \\in \\{X, Z, W\\}$ are coefficients for the respected variables\n",
"* R = `acceptanceRate_R`, acceptance rates\n",
"* X = `X`, invidual's features observable to all (models and judges)\n",
"* Z = `Z`, information observable for judges only\n",
"* W = `W`, unobservable / inaccessible information\n",
"* T = `decision_T`, bail-or-jail decisions where $T=0$ represents jail decision and $T=1$ bail decision.\n",
"* Y = `result_Y`, result variable, if $Y=0$ person will or would recidivate and if $Y=1$ person will or would not commit a crime."
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": false
},
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{
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" <th></th>\n",
" <th>count</th>\n",
" <th>mean</th>\n",
" <th>std</th>\n",
" <th>min</th>\n",
" <th>25%</th>\n",
" <th>50%</th>\n",
" <th>75%</th>\n",
" <th>max</th>\n",
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" </thead>\n",
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" <tr>\n",
" <th>judgeID_J</th>\n",
" <td>50000.0</td>\n",
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" <td>28.866359</td>\n",
" <td>0.000000</td>\n",
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" <td>49.500000</td>\n",
" <td>74.250000</td>\n",
" <td>99.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>acceptanceRate_R</th>\n",
" <td>50000.0</td>\n",
" <td>0.478235</td>\n",
" <td>0.230644</td>\n",
" <td>0.103756</td>\n",
" <td>0.264643</td>\n",
" <td>0.473985</td>\n",
" <td>0.647587</td>\n",
" <td>0.890699</td>\n",
" </tr>\n",
" <tr>\n",
" <th>X</th>\n",
" <td>50000.0</td>\n",
" <td>-0.003875</td>\n",
" <td>0.996715</td>\n",
" <td>-4.659953</td>\n",
" <td>-0.671782</td>\n",
" <td>-0.001726</td>\n",
" <td>0.668077</td>\n",
" <td>3.831790</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Z</th>\n",
" <td>50000.0</td>\n",
" <td>0.006964</td>\n",
" <td>0.998001</td>\n",
" <td>-4.852118</td>\n",
" <td>-0.666258</td>\n",
" <td>0.004730</td>\n",
" <td>0.679477</td>\n",
" <td>4.241772</td>\n",
" </tr>\n",
" <tr>\n",
" <th>W</th>\n",
" <td>50000.0</td>\n",
" <td>0.010863</td>\n",
" <td>0.996944</td>\n",
" <td>-4.029138</td>\n",
" <td>-0.666574</td>\n",
" <td>0.012306</td>\n",
" <td>0.679578</td>\n",
" <td>4.285856</td>\n",
" </tr>\n",
" <tr>\n",
" <th>result_Y</th>\n",
" <td>50000.0</td>\n",
" <td>0.496500</td>\n",
" <td>0.499993</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>probabilities_T</th>\n",
" <td>50000.0</td>\n",
" <td>0.500794</td>\n",
" <td>0.279762</td>\n",
" <td>-0.335627</td>\n",
" <td>0.276723</td>\n",
" <td>0.501317</td>\n",
" <td>0.723352</td>\n",
" <td>1.295719</td>\n",
" </tr>\n",
" <tr>\n",
" <th>decision_T</th>\n",
" <td>50000.0</td>\n",
" <td>0.477260</td>\n",
" <td>0.499488</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>1.000000</td>\n",
" <td>1.000000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" count mean std min 25% \\\n",
"judgeID_J 50000.0 49.500000 28.866359 0.000000 24.750000 \n",
"acceptanceRate_R 50000.0 0.478235 0.230644 0.103756 0.264643 \n",
"X 50000.0 -0.003875 0.996715 -4.659953 -0.671782 \n",
"Z 50000.0 0.006964 0.998001 -4.852118 -0.666258 \n",
"W 50000.0 0.010863 0.996944 -4.029138 -0.666574 \n",
"result_Y 50000.0 0.496500 0.499993 0.000000 0.000000 \n",
"probabilities_T 50000.0 0.500794 0.279762 -0.335627 0.276723 \n",
"decision_T 50000.0 0.477260 0.499488 0.000000 0.000000 \n",
"\n",
" 50% 75% max \n",
"judgeID_J 49.500000 74.250000 99.000000 \n",
"acceptanceRate_R 0.473985 0.647587 0.890699 \n",
"X -0.001726 0.668077 3.831790 \n",
"Z 0.004730 0.679477 4.241772 \n",
"W 0.012306 0.679578 4.285856 \n",
"result_Y 0.000000 1.000000 1.000000 \n",
"probabilities_T 0.501317 0.723352 1.295719 \n",
"decision_T 0.000000 1.000000 1.000000 "
]
},
"metadata": {},
"output_type": "display_data"
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"name": "stdout",
"output_type": "stream",
"text": [
"0 26137\n",
"1 23863\n",
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"Name: decision_T, dtype: int64\n"
]
},
{
"data": {
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" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>decision_T</th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" </tr>\n",
" <tr>\n",
" <th>result_Y</th>\n",
" <th></th>\n",
" <th></th>\n",
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" <tbody>\n",
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"text/plain": [
"0.0 20083 5092\n",
"1.0 6054 18771"
"output_type": "display_data"
"# Set seed for reproducibility\n",
"npr.seed(0)\n",
"\n",
"def generateData(nJudges_M=100,\n",
" nSubjects_N=500,\n",
" beta_X=1.0,\n",
" beta_Z=1.0,\n",
" beta_W=0.2):\n",
"\n",
" # Assign judge IDs as running numbering from 0 to nJudges_M - 1\n",
" judgeID_J = np.repeat(np.arange(0, nJudges_M, dtype=np.int32), nSubjects_N)\n",
"\n",
" # Sample acceptance rates uniformly from a closed interval\n",
" # from 0.1 to 0.9 and round to tenth decimal place.\n",
" acceptance_rates = np.round(npr.uniform(.1, .9, nJudges_M), 10)\n",
"\n",
" # Replicate the rates so they can be attached to the corresponding judge ID.\n",
" acceptanceRate_R = np.repeat(acceptance_rates, nSubjects_N)\n",
"\n",
" # Sample the variables from standard Gaussian distributions.\n",
" X = npr.normal(size=nJudges_M * nSubjects_N)\n",
" Z = npr.normal(size=nJudges_M * nSubjects_N)\n",
" W = npr.normal(size=nJudges_M * nSubjects_N)\n",
"\n",
" probabilities_Y = 1 / (1 + np.exp(-(beta_X * X + beta_Z * Z + beta_W * W)))\n",
"\n",
" # 0 if P(Y = 0| X = x; Z = z; W = w) >= 0.5 , 1 otherwise\n",
" result_Y = 1 - probabilities_Y.round()\n",
"\n",
" probabilities_T = 1 / (1 + np.exp(-(beta_X * X + beta_Z * Z)))\n",
" probabilities_T += npr.normal(0, .1, nJudges_M * nSubjects_N)\n",
"\n",
" # Initialize decision values as 1\n",
" decision_T = np.ones(nJudges_M * nSubjects_N)\n",
"\n",
" # Initialize the dataframe\n",
" df_init = pd.DataFrame(\n",
" np.column_stack((judgeID_J, acceptanceRate_R, X, Z, W, result_Y,\n",
" probabilities_T, decision_T)),\n",
" columns=[\n",
" \"judgeID_J\", \"acceptanceRate_R\", \"X\", \"Z\", \"W\", \"result_Y\",\n",
" \"probabilities_T\", \"decision_T\"\n",
" ])\n",
"\n",
" # Sort by judges then probabilities\n",
" data = df_init.sort_values(\n",
" by=[\"judgeID_J\", \"probabilities_T\"], ascending=False)\n",
"\n",
" # Iterate over the data. Subject is in the top (1-r)*100% if\n",
" # his within-judge-index is over acceptance threshold times\n",
" # the number of subjects assigned to each judge. If subject\n",
" # is over the limit they are assigned a zero, else one.\n",
" data.reset_index(drop=True, inplace=True)\n",
"\n",
" data['decision_T'] = np.where(\n",
" (data.index.values % nSubjects_N) <\n",
" ((1 - data['acceptanceRate_R']) * nSubjects_N), 0, 1)\n",
"\n",
" return data\n",
"\n",
"\n",
"df = generateData()\n",
"\n",
"# Basic stats of the created data set.\n",
"display(df.describe().T)\n",
"print(df.decision_T.value_counts())\n",
"\n",
"tab = df.groupby(['result_Y', 'decision_T']).size()\n",
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(25000, 8)\n",
"(25000, 8)\n",
"(11866, 8)\n",
"(11997, 8)\n"
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" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th>decision_T</th>\n",
" </tr>\n",
" <tr>\n",
" <th>result_Y</th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
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"0.0 2495\n",
"1.0 9371"
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Split the data set to test and train\n",
"from sklearn.model_selection import train_test_split\n",
"train, test = train_test_split(df, test_size=0.5, random_state=0)\n",
"\n",
"print(train.shape)\n",
"print(test.shape)\n",
"\n",
"train_labeled = train[train.decision_T == 1]\n",
"\n",
"print(train_labeled.shape)\n",
"\n",
"tab = train_labeled.groupby(['result_Y', 'decision_T']).size()\n",
"tab.unstack()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Contraction algorithm\n",
"Below is an implementation of Lakkaraju's team's algorithm presented in [their paper](https://helka.finna.fi/PrimoRecord/pci.acm3098066). Relevant parameters to be passed to the function are presented in the description."
]
},
{
"cell_type": "code",
"def contraction(df,\n",
" judgeIDJ_col,\n",
" decisionT_col,\n",
" resultY_col,\n",
" modelProbS_col,\n",
" accRateR_col,\n",
" r,\n",
" binning=False):\n",
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" '''\n",
" This is an implementation of the algorithm presented by Lakkaraju\n",
" et al. in their paper \"The Selective Labels Problem: Evaluating \n",
" Algorithmic Predictions in the Presence of Unobservables\" (2017).\n",
" \n",
" Parameters:\n",
" df = The (Pandas) data frame containing the data, judge decisions,\n",
" judge IDs, results and probability scores.\n",
" judgeIDJ_col = String, the name of the column containing the judges' IDs\n",
" in df.\n",
" decisionT_col = String, the name of the column containing the judges' decisions\n",
" resultY_col = String, the name of the column containing the realization\n",
" modelProbS_col = String, the name of the column containing the probability\n",
" scores from the black-box model B.\n",
" accRateR_col = String, the name of the column containing the judges' \n",
" acceptance rates\n",
" r = Float between 0 and 1, the given acceptance rate.\n",
" binning = Boolean, should judges with same acceptance rate be binned\n",
" \n",
" Returns:\n",
" u = The estimated failure rate at acceptance rate r.\n",
" '''\n",
" # Sort first by acceptance rate and judge ID.\n",
" sorted_df = df.sort_values(\n",
" by=[accRateR_col, judgeIDJ_col], ascending=False)\n",
"\n",
" if binning:\n",
" # Get maximum leniency\n",
" max_leniency = sorted_df[accRateR_col].values[0].round(1)\n",
"\n",
" # Get list of judges that are the most lenient\n",
" most_lenient_list = sorted_df.loc[sorted_df[accRateR_col].round(1) ==\n",
" max_leniency, judgeIDJ_col]\n",
"\n",
" # Subset to obtain D_q\n",
" D_q = sorted_df[sorted_df[judgeIDJ_col].isin(\n",
" most_lenient_list.unique())]\n",
" else:\n",
" # Get most lenient judge\n",
" most_lenient_ID = sorted_df[judgeIDJ_col].values[0]\n",
" # Subset\n",
" D_q = sorted_df[sorted_df[judgeIDJ_col] == most_lenient_ID]\n",
" R_q = D_q[D_q[decisionT_col] == 1]\n",
"\n",
" number_to_remove = int(\n",
" np.round((1 - r) * D_q.shape[0] - (D_q.shape[0] - R_q.shape[0])))\n",
"\n",
" R_B = R_sort_q[number_to_remove:R_sort_q.shape[0]]\n",
"\n",
" return np.sum(R_B[resultY_col] == 0) / D_q.shape[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our model is defined by the probabilistic expression \n",
"P(Y=0 | \\text{do}(R=r)) = \\sum_x \\underbrace{P(Y=0|X=x, T=1)}_\\text{1} \n",
"\\overbrace{P(T=1|R=r, X=x)}^\\text{2} \n",
"\\underbrace{P(X=x)}_\\text{3}\n",
"As a picture (Z not in model):\n",
"\n",
"![Model as picture](../figures/intervention_model.png \"Intervention model\")\n",
"\n",
"Our model will be constructed sequentially.\n",
"Input: Training and test data sets $(\\mathbf{x}, t, y) \\in \\mathcal{D}$ and acceptance rate $r$. \n",
"Returns: $P(Y=0 | \\text{do}(R=r))$\n",
"1. Model $P(X=x)$ in a suitable way and assign to $\\mathcal{M}_0$\n",
"* Build model $\\mathcal{M}_1$ predicting response $Y$ with predictors $X$ from the labeled observations (where $T=1$) in training data.\n",
"* Predict $P(Y=0|X=x)$ for every observation in the test data using model $\\mathcal{M}_1$.\n",
"* Initialize `sum = 0`\n",
"* For every point in the parameter space (for every $x$ in $X$)\n",
" 1. $p_x \\leftarrow P(X=x)$ from $\\mathcal{M}_0$\n",
" * $\\mathcal{D_x} \\leftarrow \\{\\mathcal{D} | X = x\\}$\n",
" * Assign first $r\\cdot 100\\%$ observations from $\\mathcal{D_x}$ to $\\mathcal{D}_{rx}$\n",
" * $p_t \\leftarrow \\dfrac{|\\{\\mathcal{D}_{rx}|T=1\\}|}{|\\mathcal{D}_{rx}|}$ (part 2 of eq. $\\ref{model}$) Pitääkö tähänkin treenaa joku oma luokittelija?\n",
" * $p_y$ will be predicted from the model $\\mathcal{M}_1$\n",
" * `sum +=` $p_y \\cdot p_t \\cdot p_x$\n",
"* Return `sum`\n",
"**Constructing $\\mathcal{M}_0$, preliminary ideas:**\n",
"* Approximate $P(X=x)$ with frequencies (makes independence assumption, make variables factors first)\n",
"* Construct Bayesian network.\n",
"\n",
"Functions:\n",
"\n",
"* $f(x)$ gives probability of recidivism given personal properties and predictive model.\n",
"* `ep` counts performance of the predictive model given a data, model and leniency rate like Michael's pdf."
]
},
{
"cell_type": "code",
"def causal(x_list, df_test, df_train, result_col, feature_cols, x_model, y_model,\n",
" Gives probability of negative event given a leniency r.\n",
" \n",
" Parameters:\n",
" x_list = list of all possible x values\n",
" df_test = pandas dataframe, test data\n",
" df_train = pandas dataframe, training data\n",
" feature_cols = String (list), name of columns containing individual features.\n",
" y_cols = String, name of column containgn the result variable\n",
" x_model = model predicting probability of given combination of private features\n",
" y_model = model predicting probability of recidivism given private features\n",
" leniency_r = float, leniency level between .0.0 and 1.0\n",
" '''\n",
" probability = 0\n",
" for x in x_list:\n",
"\n",
" D_tx = df_test[(y_model(df_test[feature_cols]) < leniency_r)\n",
" & (df_test[feature_cols] == x)]\n",
" if D_tx.shape[0] == 0:\n",
" continue\n",
" p_t = np.sum(D_tx.decision_T == 1) / D_tx.shape[0]\n",
" probability += p_y[0, 0] * p_t * p_x\n",
" return probability\n",
"\n",
"\n",
"def f(x, model):\n",