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{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"toc": true
},
"source": [
"<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
"<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Causal-model\" data-toc-modified-id=\"Causal-model-1\"><span class=\"toc-item-num\">1 </span>Causal model</a></span><ul class=\"toc-item\"><li><span><a href=\"#Notes\" data-toc-modified-id=\"Notes-1.1\"><span class=\"toc-item-num\">1.1 </span>Notes</a></span></li></ul></li><li><span><a href=\"#Data-sets\" data-toc-modified-id=\"Data-sets-2\"><span class=\"toc-item-num\">2 </span>Data sets</a></span><ul class=\"toc-item\"><li><span><a href=\"#Synthetic-data-with-unobservables\" data-toc-modified-id=\"Synthetic-data-with-unobservables-2.1\"><span class=\"toc-item-num\">2.1 </span>Synthetic data with unobservables</a></span></li><li><span><a href=\"#Data-without-unobservables\" data-toc-modified-id=\"Data-without-unobservables-2.2\"><span class=\"toc-item-num\">2.2 </span>Data without unobservables</a></span></li></ul></li><li><span><a href=\"#Algorithms\" data-toc-modified-id=\"Algorithms-3\"><span class=\"toc-item-num\">3 </span>Algorithms</a></span><ul class=\"toc-item\"><li><span><a href=\"#Contraction-algorithm\" data-toc-modified-id=\"Contraction-algorithm-3.1\"><span class=\"toc-item-num\">3.1 </span>Contraction algorithm</a></span></li><li><span><a href=\"#Causal-algorithm\" data-toc-modified-id=\"Causal-algorithm-3.2\"><span class=\"toc-item-num\">3.2 </span>Causal algorithm</a></span></li></ul></li><li><span><a href=\"#Performance-comparison\" data-toc-modified-id=\"Performance-comparison-4\"><span class=\"toc-item-num\">4 </span>Performance comparison</a></span><ul class=\"toc-item\"><li><span><a href=\"#With-unobservables-in-the-data\" data-toc-modified-id=\"With-unobservables-in-the-data-4.1\"><span class=\"toc-item-num\">4.1 </span>With unobservables in the data</a></span><ul class=\"toc-item\"><li><span><a href=\"#Predictive-models\" data-toc-modified-id=\"Predictive-models-4.1.1\"><span class=\"toc-item-num\">4.1.1 </span>Predictive models</a></span></li><li><span><a href=\"#Visual-comparison\" data-toc-modified-id=\"Visual-comparison-4.1.2\"><span class=\"toc-item-num\">4.1.2 </span>Visual comparison</a></span></li></ul></li><li><span><a href=\"#Without-unobservables\" data-toc-modified-id=\"Without-unobservables-4.2\"><span class=\"toc-item-num\">4.2 </span>Without unobservables</a></span><ul class=\"toc-item\"><li><span><a href=\"#Predictive-model\" data-toc-modified-id=\"Predictive-model-4.2.1\"><span class=\"toc-item-num\">4.2.1 </span>Predictive model</a></span></li></ul></li></ul></li></ul></div>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Causal model\n",
"\n",
"Our model is defined by the probabilistic expression \n",
"\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",
"\\end{equation}\n",
"\n",
"which is equal to \n",
"\n",
"\\begin{equation}\\label{model_cont}\n",
"P(Y=0 | \\text{do}(R=r)) = \\int_x P(Y=0|X=x, T=1)P(T=1|R=r, X=x)P(X=x)\n",
"\\end{equation}\n",
"\n",
"for continuous $x$. Model as a graph (Z is a latent variable, and can be excluded from the expression with do-calculus by showing that $X$ is admissible for adjustment):\n",
"\n",
"![Model as picture](../figures/intervention_model.png \"Intervention model\")\n",
"\n",
"For predicting the probability of negative outcome the following should hold because by Pearl $P(Y=0 | \\text{do}(R=r), X=x) = P(Y=0 | R=r, X=x)$ when $X$ is an admissible set:\n",
"\n",
"\\begin{equation} \\label{model_pred}\n",
"P(Y=0 | \\text{do}(R=r), X=x) = P(Y=0|X=x, T=1)P(T=1|R=r, X=x).\n",
"\\end{equation}\n",
"\n",
"Still it should be noted that this prediction takes into account the probability of the individual to be given a positive decision ($T=1$), see second term in \\ref{model_pred}.\n",
"\n",
"----\n",
"\n",
"### Notes\n",
"\n",
"* Equations \\ref{model_disc} and \\ref{model_cont} describe the whole causal effect in the population (the causal effect of changing $r$ over all strata $X$).\n",
"* Prediction should be possible with \\ref{model_pred}. Both terms can be learned from the data. NB: the probability $P(Y=0 | \\text{do}(R=r), X=x)$ is lowest when the individual $x$ is the most dangerous or the least dangerous. How could we infer/predict the counterfactual \"what is the probability of $Y=0$ if we were to let this individual go?\" has yet to be calculated.\n",
"* Is the effect of R learned/estimated correctly if it is just plugged in to a predictive model (e.g. logistic regression)?\n",
"* $P(Y=0 | do(R=0)) = 0$ only in this application. My predictive models say that when $r=0$ the probability $P(Y=0) \\approx 0.027$ which would be a natural estimate in another application/scenario (e.g. in medicine the probability of an adverse event when a stronger medicine is distributed to everyone. Then the probability will be close to zero but not exactly zero.)"
]
},
{
"cell_type": "code",
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"metadata": {},
"outputs": [],
"source": [
"# Imports\n",
"\n",
"import numpy as np\n",
"import pandas as pd\n",
"from datetime import datetime\n",
"import matplotlib.pyplot as plt\n",
"import scipy.stats as scs\n",
"import scipy.integrate as si\n",
"import seaborn as sns\n",
"import numpy.random as npr\n",
"from sklearn.preprocessing import OneHotEncoder\n",
"from sklearn.linear_model import LogisticRegression\n",
"from sklearn.ensemble import RandomForestClassifier\n",
"\n",
"# Settings\n",
"\n",
"%matplotlib inline\n",
"\n",
"plt.rcParams.update({'font.size': 16})\n",
"plt.rcParams.update({'figure.figsize': (14, 7)})\n",
"\n",
"# Suppress deprecation warnings.\n",
"\n",
"import warnings\n",
"\n",
"def fxn():\n",
" warnings.warn(\"deprecated\", DeprecationWarning)\n",
"\n",
"with warnings.catch_warnings():\n",
" warnings.simplefilter(\"ignore\")\n",
" fxn()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Data sets\n",
"\n",
"### Synthetic data with unobservables\n",
"\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",
"\n",
"**Parameters**\n",
"\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",
"\n",
"**Columns of the data:**\n",
"\n",
"* `judgeID_J` = judge IDs as running numbering from 0 to `nJudges_M - 1`\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."
]
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{
"cell_type": "code",
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" <th>result_Y</th>\n",
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" <th>All</th>\n",
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"text/plain": [
"result_Y 0.0 1.0 All\n",
"decision_T \n",
"0 16884 6985 23869\n",
"1 8128 18003 26131\n",
"All 25012 24988 50000"
"\n",
"def sigmoid(x):\n",
" return 1 / (1 + np.exp(-x))\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 = sigmoid(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",
" # For the conditional probabilities of T we add noise ~ N(0, 0.1)\n",
" probabilities_T += npr.normal(0, np.sqrt(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(np.column_stack(\n",
" (judgeID_J, acceptanceRate_R, X, Z, W, result_Y, probabilities_T,\n",
" decision_T)),\n",
" columns=[\n",
" \"judgeID_J\", \"acceptanceRate_R\", \"X\", \"Z\", \"W\",\n",
" \"result_Y\", \"probabilities_T\", \"decision_T\"\n",
" ])\n",
"\n",
" # Sort by judges then probabilities in decreasing order\n",
" data = df_init.sort_values(by=[\"judgeID_J\", \"probabilities_T\"],\n",
" 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",
"pd.crosstab(df.decision_T, df.result_Y, margins=True)"
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"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(25000, 8)\n",
"(25000, 8)\n",
"(25000, 8)\n",
"(25000, 8)\n"
]
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" <tr style=\"text-align: right;\">\n",
" <th>decision_T</th>\n",
" <th>1</th>\n",
" </tr>\n",
" <tr>\n",
" <th>result_Y</th>\n",
" <th></th>\n",
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"text/plain": [
"decision_T 1\n",
"result_Y \n",
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"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.copy()\n",
"test_labeled = test.copy()\n",
"\n",
"# Set results as NA if decision is negative.\n",
"train_labeled.result_Y = np.where(train.decision_T == 0, np.nan, train.result_Y)\n",
"test_labeled.result_Y = np.where(test.decision_T == 0, np.nan, test.result_Y)\n",
"\n",
"print(train_labeled.shape)\n",
"print(test_labeled.shape)\n",
"\n",
"tab = train_labeled.groupby(['result_Y', 'decision_T']).size()\n",
"tab.unstack()"
]
},
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Data without unobservables\n",
"\n",
"In the chunk below, we generate a simplified data. The default values and definitions of $Y$ and $T$ values follow the previous description.\n",
"\n",
"**Parameters**\n",
"\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",
"\n",
"**Columns of the data:**\n",
"\n",
"* `judgeID_J` = judge IDs as running numbering from 0 to `nJudges_M - 1`\n",
"* R = `acceptanceRate_R`, acceptance rates\n",
"* X = `X`, invidual's features observable to all (models and judges), now $X \\sim \\mathcal{N}(0, 1)$\n",
"* T = `decision_T`, bail-or-jail decisions where $T=0$ represents jail decision and $T=1$ bail decision.\n",
"* $p_y$ = `probabilities_Y`, variable where $p_y = P(Y=1)$\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. Here $Y \\sim \\text{Bernoulli}(1/exp(\\beta_X \\cdot X))$"
]
},
{
"cell_type": "code",
"execution_count": 195,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"['judgeID_J' 'acceptanceRate_R' 'X' 'probabilities_Y' 'result_Y'\n",
" 'decision_T']\n"
]
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"result_Y 0 1 All\n",
"decision_T \n",
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"decision_T \n",
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" }\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>result_Y</th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>All</th>\n",
" </tr>\n",
" <tr>\n",
" <th>decision_T</th>\n",
" <th></th>\n",
" <th></th>\n",
" <th></th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>7757</td>\n",
" <td>4197</td>\n",
" <td>11954</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>4703</td>\n",
" <td>8343</td>\n",
" <td>13046</td>\n",
" </tr>\n",
" <tr>\n",
" <th>All</th>\n",
" <td>12460</td>\n",
" <td>12540</td>\n",
" <td>25000</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
"result_Y 0 1 All\n",
"decision_T \n",
"0 7757 4197 11954\n",
"1 4703 8343 13046\n",
"All 12460 12540 25000"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# Set seed for reproducibility\n",
"#npr.seed(0)\n",
"\n",
"def generateDataNoUnobservables(nJudges_M=100, nSubjects_N=500, beta_X=1.0):\n",
"\n",
" df = pd.DataFrame()\n",
"\n",
" # Assign judge IDs as running numbering from 0 to nJudges_M - 1\n",
" df = df.assign(judgeID_J=np.repeat(np.arange(0, nJudges_M, dtype=np.int32),\n",
" 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",
" df = df.assign(acceptanceRate_R=np.repeat(acceptance_rates, nSubjects_N))\n",
"\n",
" # Sample the variables from standard Gaussian distributions.\n",
" df = df.assign(X=npr.normal(size=nJudges_M * nSubjects_N))\n",
"\n",
" df = df.assign(probabilities_Y=sigmoid(beta_X * df.X))\n",
"\n",
" # Y ~ Bernoulli(sigmoid(beta_X * x))\n",
" df = df.assign(result_Y=npr.binomial(\n",
" n=1, p=df.probabilities_Y, size=nJudges_M * nSubjects_N))\n",
"\n",
" # Sort by judges then probabilities in decreasing order.\n",
" # I.e. most dangerous are last.\n",
" df = df.sort_values(by=[\"judgeID_J\", \"probabilities_Y\"], ascending=True)\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",
" df.reset_index(drop=True, inplace=True)\n",
"\n",
" df['decision_T'] = np.where((df.index.values % nSubjects_N) <\n",
" ((1 - df['acceptanceRate_R']) * nSubjects_N),\n",
" 0, 1)\n",
"\n",
" return df\n",
"\n",
"simple_data = generateDataNoUnobservables()\n",
"\n",
"# Split the data set to test and train\n",
"s_train, s_test = train_test_split(simple_data, test_size=0.5, random_state=0)\n",
"\n",
"s_train_labeled = s_train.copy()\n",
"s_test_labeled = s_test.copy()\n",
"\n",
"# Set results as NA if decision is negative.\n",
"s_train_labeled.result_Y = np.where(s_train.decision_T == 0, np.nan, s_train.result_Y)\n",
"s_test_labeled.result_Y = np.where(s_test.decision_T == 0, np.nan, s_test.result_Y)\n",
"\n",
"#display(simple_data.head(20))\n",
"\n",
"print(simple_data.columns.values)\n",
"\n",
"display(pd.crosstab(simple_data.decision_T, simple_data.result_Y,\n",
" margins=True))\n",
"\n",
"display(pd.crosstab(s_train.decision_T, s_train.result_Y,\n",
" margins=True))\n",
"\n",
"display(pd.crosstab(s_test.decision_T, s_test.result_Y,\n",
" margins=True))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Algorithms\n",
"\n",
"### Contraction algorithm\n",
"\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",
"metadata": {},
"outputs": [],
"source": [
"def contraction(df,\n",
" judgeIDJ_col,\n",
" decisionT_col,\n",
" resultY_col,\n",
" modelProbS_col,\n",
" accRateR_col,\n",
" '''\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",
" \n",
" Returns:\n",
" u = The estimated failure rate at acceptance rate r.\n",
" '''\n",
" # Get ID of the most lenient judge.\n",
" most_lenient_ID = df[judgeIDJ_col].loc[df[accRateR_col].idxmax()]\n",
" D_q = df[df[judgeIDJ_col] == most_lenient_ID].copy()\n",
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" # All observations of R_q have observed outcome labels\n",
" R_q = D_q[D_q[decisionT_col] == 1]\n",
"\n",
" # \"Observations deemed as high risk by B are at the top of this list\"\n",
" R_sort_q = R_q.sort_values(by=modelProbS_col, ascending=False)\n",
"\n",
" number_to_remove = int(\n",
" round((1.0 - r) * D_q.shape[0] - (D_q.shape[0] - R_q.shape[0])))\n",
"\n",
" # \"R_B is the list of observations assigned to t = 1 by B\"\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": [
"### Causal algorithm\n",
"\n"
]
},
{
"cell_type": "code",
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"metadata": {},
"outputs": [],
"source": [
"def f(x, model, class_value):\n",
" '''\n",
" Parameters:\n",
" x = individual features\n",
" model = a trained sklearn predictive model. Predicts probabilities for given x.\n",
" class_value = the result (class) to predict (usually 0 or 1).\n",
" \n",
" Returns:\n",
" The probabilities (as vector) of class value (class_value) given \n",
" individual features (x) and the trained, predictive model (model).\n",
" '''\n",
" if x.ndim == 1:\n",
" # if x is vector, transform to column matrix.\n",
" f_values = model.predict_proba(np.array(x).reshape(-1, 1))\n",
" else:\n",
" f_values = model.predict_proba(x)\n",
"\n",
" return f_values[:, model.classes_ == class_value].flatten()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Performance comparison\n",
"\n",
"Below we try to replicate the results obtained by Lakkaraju and compare their model's performance to the one of ours.\n",
"\n",
"### With unobservables in the data\n",
"\n",
"#### Predictive models\n",
"Lakkaraju says that they used logistic regression. We train the predictive models using only *observed observations*, i.e. observations for which labels are available. We then predict the probability of negative outcome for all observations in the test data and attach it to our data set."
"metadata": {},
"outputs": [],
"source": [
"# instantiate the model (using the default parameters)\n",
"logreg = LogisticRegression(solver='lbfgs')\n",
"\n",
"# fit, reshape X to be of shape (n_samples, n_features)\n",
"logreg = logreg.fit(\n",
" train_labeled.X[train_labeled.decision_T == 1].values.reshape(-1, 1),\n",
" train_labeled.result_Y[train_labeled.decision_T == 1])\n",
"\n",
"# predict probabilities and attach to data\n",
"label_probs_logreg = logreg.predict_proba(test.X.values.reshape(-1, 1))\n",
"\n",
"test = test.assign(B_prob_0_logreg=label_probs_logreg[:, 0])\n",
"test_labeled = test_labeled.assign(B_prob_0_logreg=label_probs_logreg[:, 0])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We train another logistic regression model for predicting the probability of positive decision with a given leniency r and individual features x. See part 2 of eq. 1."
]
},
"metadata": {},
"outputs": [],
"source": [
"# Instantiate the model (using the default parameters)\n",
"decision_model = LogisticRegression(solver='lbfgs')\n",
"\n",
"# fit, reshape X to be of shape (n_samples, n_features)\n",
"decision_model = decision_model.fit(train[['X', 'acceptanceRate_R']],\n",
" train.decision_T)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's plot the failure rates against the acceptance rates using the difference. For the causal model we plot $P(Y=0|do(R=r))$ against r."
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\n",
"text/plain": [
"<Figure size 1008x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"failure_rates = np.zeros((8, 5))\n",
"\n",
"for r in np.arange(1, 9):\n",
" \n",
" #### True evaluation\n",
" # Sort by failure probabilities, subjects with the smallest risk are first. \n",
" test.sort_values(by='B_prob_0_logreg', inplace=True, ascending=True)\n",
" to_release = int(round(test.shape[0] * r / 10))\n",
" # Calculate failure rate as the ratio of failures to successes among those \n",
" # who were given a positive decision, i.e. those whose probability of negative\n",
" # outcome was low enough.\n",
" failure_rates[r - 1, 0] = np.mean(test.result_Y[0:to_release] == 0)\n",
" \n",
" #### Labeled outcomes only\n",
" # Sort by failure probabilities, subjects with the smallest risk are first. \n",
" test_labeled.sort_values(by='B_prob_0_logreg', inplace=True, ascending=True)\n",
" \n",
" to_release = int(round(test_labeled.shape[0] * r / 10))\n",
" failure_rates[r - 1, 1] = np.mean(test_labeled.result_Y[0:to_release] == 0)\n",
" \n",
" #### Human error rate\n",
" # Get judges with correct leniency as list\n",
" correct_leniency_list = test_labeled.judgeID_J[\n",
" test_labeled['acceptanceRate_R'].round(1) == r / 10].values\n",
"\n",
" # Released are the people they judged and released, T = 1\n",
" released = test_labeled[test_labeled.judgeID_J.isin(correct_leniency_list)\n",
" & (test_labeled.decision_T == 1)]\n",
"\n",
" # Get their failure rate, aka ratio of reoffenders to number of people judged in total\n",
" failure_rates[r - 1, 2] = np.sum(\n",
" released.result_Y == 0) / correct_leniency_list.shape[0]\n",
" \n",
" #### Contraction, logistic regression\n",
" failure_rates[r - 1, 3] = contraction(\n",
" test_labeled, 'judgeID_J', 'decision_T', 'result_Y', 'B_prob_0_logreg',\n",
" #### Causal effect - \"vanilla\" (wrong) model\n",
" # Integral of P(Y=0 | T=1, X=x)*P(T=1 | R=r, X=x)*P(X=x) from negative to\n",
" # positive infinity.\n",
" failure_rates[r - 1, 4] = si.quad(lambda x: f(np.array([x]), logreg, 0) * \n",
" f(np.array([[x, r/10]]), decision_model, 1) * \n",
" scs.norm.pdf(x), -np.inf, np.inf)[0]\n",
"\n",
"# Error bars TBA\n",
"\n",
"plt.figure(figsize=(14, 8))\n",
"plt.plot(np.arange(0.1, 0.9, .1), failure_rates[:, 0], label='True Evaluation', c='green')\n",
"plt.plot(np.arange(0.1, 0.9, .1), failure_rates[:, 1], label='Labeled outcomes', c='black')\n",
"plt.plot(np.arange(0.1, 0.9, .1), failure_rates[:, 2], label='Human evaluation', c='red')\n",
"plt.plot(np.arange(0.1, 0.9, .1), failure_rates[:, 3], label='Contraction, log.', c='blue')\n",
"plt.plot(np.arange(0.1, 0.9, .1), failure_rates[:, 4], label='Causal effect', c='magenta')\n",
"\n",
"plt.title('Failure rate vs. Acceptance rate')\n",
"plt.xlabel('Acceptance rate')\n",
"plt.ylabel('Failure rate')\n",
"plt.legend()\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.0 (0.018287661925724383, 8.00221559955285e-11)\n",
"1.0 (0.3419746629567682, 6.491768654045975e-09)\n"
]
}
],
"source": [
"# Below are estimates for P(Y=0 | do(R=0)) and P(Y=0 | do(R=1))\n",
"r = 0.0\n",
"print(r, si.quad(lambda x: f(np.array([[x, r]]), decision_model, 1) * \\\n",
" f(np.array([x]), logreg, 0) * scs.norm.pdf(x), -np.inf, np.inf))\n",
"\n",
"r = 1.0\n",
"print(r, si.quad(lambda x: f(np.array([[x, r]]), decision_model, 1) * \\\n",
" f(np.array([x]), logreg, 0) * scs.norm.pdf(x), -np.inf, np.inf))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"So it can be concluded that:\n",
"\n",
"\\begin{equation*}\n",
"P(Y=0 | \\text{do}(R=0)) \\approx 0.018 \\\\\n",
"P(Y=0 | \\text{do}(R=1)) \\approx 0.340 \\\\\n",
"\\end{equation*}"
]
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{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Without unobservables\n",
"\n",
"\n",
"#### Predictive model\n"
]
},
{
"cell_type": "code",
"execution_count": 203,
"metadata": {},
"outputs": [],
"source": [
"# instantiate the model (using the default parameters)\n",
"logreg = LogisticRegression(solver='lbfgs')\n",
"\n",
"# fit, reshape X to be of shape (n_samples, n_features)\n",
"logreg = logreg.fit(\n",
" s_train.X[s_train.decision_T == 1].values.reshape(-1, 1),\n",
" s_train.result_Y[s_train.decision_T == 1])\n",
"\n",
"## predict probabilities and attach to data\n",
"#label_probs_logreg = logreg.predict_proba(s_test.X.values.reshape(-1, 1))\n",
"#\n",
"#test = test.assign(B_prob_0_logreg=label_probs_logreg[:, 0])\n",
"#test_labeled = test_labeled.assign(B_prob_0_logreg=label_probs_logreg[:, 0])"
]
},
{
"cell_type": "code",
"execution_count": 215,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.072 0.14 0.2 0.25 0.3 0.344 0.378 0.412]\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},