Analysis_07MAY2019_new.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Data-sets\" data-toc-modified-id=\"Data-sets-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</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-1.1\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Synthetic data with unobservables</a></span></li><li><span><a href=\"#Data-without-unobservables\" data-toc-modified-id=\"Data-without-unobservables-1.2\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Data without unobservables</a></span></li></ul></li><li><span><a href=\"#Algorithms\" data-toc-modified-id=\"Algorithms-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Algorithms</a></span><ul class=\"toc-item\"><li><span><a href=\"#Contraction-algorithm\" data-toc-modified-id=\"Contraction-algorithm-2.1\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span>Contraction algorithm</a></span></li><li><span><a href=\"#Causal-approach---metrics\" data-toc-modified-id=\"Causal-approach---metrics-2.2\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Causal approach - metrics</a></span></li></ul></li><li><span><a href=\"#Performance-comparison\" data-toc-modified-id=\"Performance-comparison-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</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-3.1\"><span class=\"toc-item-num\">3.1&nbsp;&nbsp;</span>With unobservables in the data</a></span></li><li><span><a href=\"#Without-unobservables\" data-toc-modified-id=\"Without-unobservables-3.2\"><span class=\"toc-item-num\">3.2&nbsp;&nbsp;</span>Without unobservables</a></span></li></ul></li></ul></div>"
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    "<!-- ##  Causal model\n",
    "\n",
    "Our model is defined by the probabilistic expression \n",
    "\n",
    "\\begin{equation} \\label{model_disc}\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 $x$. In the model Z is a latent, unobserved variable, and can be excluded from the expression with do-calculus by showing that $X$ is admissible for adjustment. Model as a graph:\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)? **NO**\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.) -->\n",
    "\n",
    "Imports and settings."
   ]
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   "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",
    "from sklearn.model_selection import train_test_split\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",
    "\n",
    "def fxn():\n",
    "    warnings.warn(\"deprecated\", DeprecationWarning)\n",
    "\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.\n",
    "\n",
    "The generated data will have M\\*N rows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    '''Return value of sigmoid function (inverse of logit) at x.'''\n",
    "\n",
    "    return 1 / (1 + np.exp(-x))\n",
    "\n",
    "\n",
    "def generateDataWithUnobservables(nJudges_M=100,\n",
    "                                  nSubjects_N=500,\n",
    "                                  beta_X=1.0,\n",
    "                                  beta_Z=1.0,\n",
    "                                  beta_W=0.2):\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(range(0, nJudges_M), 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",
    "    df = df.assign(Z=npr.normal(size=nJudges_M * nSubjects_N))\n",
    "    df = df.assign(W=npr.normal(size=nJudges_M * nSubjects_N))\n",
    "\n",
    "    # Calculate P(Y=0|X, Z, W)\n",
    "    probabilities_Y = sigmoid(beta_X * df.X + beta_Z * df.Z + beta_W * df.W)\n",
    "\n",
    "    # Result is 0 if P(Y = 0| X = x; Z = z; W = w) >= 0.5 , 1 otherwise\n",
    "    df = df.assign(result_Y=np.where(probabilities_Y >= 0.5, 0, 1))\n",
    "\n",
    "    # For the conditional probabilities of T we add noise ~ N(0, 0.1)\n",
    "    probabilities_T = sigmoid(beta_X * df.X + beta_Z * df.Z)\n",
    "    probabilities_T += npr.normal(0, np.sqrt(0.1), nJudges_M * nSubjects_N)\n",
    "\n",
    "    df = df.assign(probabilities_T=probabilities_T)\n",
    "\n",
    "    # Sort by judges then probabilities in decreasing order\n",
    "    # Most dangerous for each judge are at the top.\n",
    "    df.sort_values(by=[\"judgeID_J\", \"probabilities_T\"],\n",
    "                   ascending=False,\n",
    "                   inplace=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",
    "    # Halve the data set to test and train\n",
    "    train, test = train_test_split(df, test_size=0.5)\n",
    "\n",
    "    train_labeled = train.copy()\n",
    "    test_labeled = test.copy()\n",
    "\n",
    "    # Set results as NA if decision is negative.\n",
    "    train_labeled.loc[train_labeled.decision_T == 0, 'result_Y'] = np.nan\n",
    "    test_labeled.loc[test_labeled.decision_T == 0, 'result_Y'] = np.nan\n",
    "\n",
    "    return train_labeled, train, test_labeled, test, df"
   ]
  },
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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",
    "* $\\beta_X$ = `beta_X`, coefficient for $X$\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 $p_y = P(Y=0)$\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 $Y \\sim \\text{Bernoulli}(\\frac{1}{1+exp\\{-\\beta_X \\cdot X\\}})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generateDataWithoutUnobservables(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(range(0, nJudges_M), 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 feature X from standard Gaussian distribution, N(0, 1).\n",
    "    df = df.assign(X=npr.normal(size=nJudges_M * nSubjects_N))\n",
    "\n",
    "    # Calculate P(Y=1|X=x) = 1 / (1 + exp(-beta_X * x)) = sigmoid(beta_X * x)\n",
    "    df = df.assign(probabilities_Y=sigmoid(beta_X * df.X))\n",
    "\n",
    "    # Draw Y ~ Bernoulli(sigmoid(beta_X * x)) = Bin(1, p)\n",
    "    df = df.assign(\n",
    "        result_Y=npr.binomial(n=1, p=df.probabilities_Y, size=nJudges_M * nSubjects_N))\n",
    "\n",
    "    # Invert the probabilities. P(Y=0 | X) = 1 - P(Y=1 | X)\n",
    "    df.probabilities_Y = 1 - df.probabilities_Y\n",
    "\n",
    "    # Sort by judges then probabilities in decreasing order\n",
    "    # I.e. the most dangerous for each judge are first.\n",
    "    df = df.sort_values(by=[\"judgeID_J\", \"probabilities_Y\"], 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",
    "    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",
    "    # Halve the data set to test and train\n",
    "    train, test = train_test_split(df, test_size=0.5)\n",
    "\n",
    "    train_labeled = train.copy()\n",
    "    test_labeled = test.copy()\n",
    "\n",
    "    # Set results as NA if decision is negative.\n",
    "    train_labeled.loc[train_labeled.decision_T == 0, 'result_Y'] = np.nan\n",
    "    test_labeled.loc[test_labeled.decision_T == 0, 'result_Y'] = np.nan\n",
    "\n",
    "    return train_labeled, train, test_labeled, test, df"
   ]
  },
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   "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",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def contraction(df, judgeIDJ_col, decisionT_col, resultY_col, modelProbS_col,\n",
    "                accRateR_col, r):\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 the estimated failure rate at acceptance rate r.\n",
    "    '''\n",
    "    # Get ID of the most lenient judge.\n",
    "    most_lenient_ID_q = df[judgeIDJ_col].loc[df[accRateR_col].idxmax()]\n",
    "\n",
    "    # Subset. \"D_q is the set of all observations judged by q.\"\n",
    "    D_q = df[df[judgeIDJ_col] == most_lenient_ID_q].copy()\n",
    "\n",
    "    # All observations of R_q have observed outcome labels.\n",
    "    # \"R_q is the set of observations in D_q with observed outcome labels.\"\n",
    "    R_q = D_q[D_q[decisionT_col] == 1].copy()\n",
    "\n",
    "    # Sort observations in R_q in descending order of confidence scores S and\n",
    "    # assign to R_sort_q.\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 approach - metrics\n",
    "\n",
    "Generalized performance:\n",
    "\n",
    "$$\n",
    "\\mathbf{gp} = \\sum_{x\\in\\mathcal{X}}  f(x)\\delta(F(x) < r)P(X=x)\n",
    "$$\n",
    "\n",
    "and empirical performance:\n",
    "\n",
    "$$\n",
    "\\mathbf{ep} = \\dfrac{1}{n} \\sum_{(x, y) \\in \\mathcal{D}} \\delta(y=0) \\delta(F(x) < r)\n",
    "$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\n",
    "f(x) = P(Y=0|T=1, X=x)\n",
    "$$\n",
    "\n",
    "and\n",
    "\n",
    "$$\n",
    "F(x_0) = \\int P(x)~\\delta(P(Y=0|T=1, X=x) > P(Y=0|T=1, X=x_0)) ~ dx = \\int P(x)~\\delta(f(x) > f(x_0)) ~ dx.\n",
    "$$\n",
    "\n",
    "NB: in code the direction of inequality was changed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def getProbabilityForClass(x, model, class_value):\n",
    "    '''\n",
    "    Function (wrapper) for obtaining the probability of a class given x and a \n",
    "    predictive model.\n",
    "    \n",
    "    Parameters:\n",
    "    x = individual features, an array, shape (observations, features)\n",
    "    model = a trained sklearn model. Predicts probabilities for given x. Should\n",
    "    accept input of size (observations, features)\n",
    "    class_value = the resulting class to predict (usually 0 or 1).\n",
    "    \n",
    "    Returns:\n",
    "    The probabilities of given class label for each x.\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",
    "    # Get correct column of predicted class, remove extra dimensions and return.\n",
    "    return f_values[:, model.classes_ == class_value].flatten()\n",
    "\n",
    "\n",
    "def cdf(x_0, model, class_value):\n",
    "    '''\n",
    "    Cumulative distribution function as described above.\n",
    "    \n",
    "    '''\n",
    "    prediction = lambda x: getProbabilityForClass(\n",
    "        np.array([x]).reshape(-1, 1), model, class_value)\n",
    "\n",
    "    prediction_x_0 = prediction(x_0)\n",
    "\n",
    "    x_values = np.linspace(-10, 10, 40000)\n",
    "\n",
    "    x_preds = prediction(x_values)\n",
    "\n",
    "    y_values = scs.norm.pdf(x_values)\n",
    "\n",
    "    results = np.zeros(x_0.shape[0])\n",
    "\n",
    "    for i in range(x_0.shape[0]):\n",
    "        \n",
    "        y_copy = y_values.copy()\n",
    "        \n",
    "        y_copy[x_preds > prediction_x_0[i]] = 0\n",
    "        \n",
    "        results[i] = si.simps(y_copy, x=x_values)\n",
    "\n",
    "    return results"
   ]
  },
  {
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fitLogisticRegressionModel(x_train, y_train, x_test, class_value):\n",
    "    '''\n",
    "    Fit logistic regression model with given inputs. Checks their shape if \n",
    "    incompatible.\n",
    "    \n",
    "    Parameters:\n",
    "    \n",
    "    \n",
    "    Returns:\n",
    "    (1) Trained LogisticRegression model\n",
    "    (2) Probabilities for given test inputs for given class.\n",
    "    '''\n",
    "\n",
    "    # Instantiate the model (using the default parameters)\n",
    "    logreg = LogisticRegression(solver='lbfgs')\n",
    "\n",
    "    # Check shape and fit the model.\n",
    "    if x_train.ndim == 1:\n",
    "        logreg = logreg.fit(x_train.values.reshape(-1, 1), y_train)\n",
    "    else:\n",
    "        logreg = logreg.fit(x_train, y_train)\n",
    "\n",
    "    # Check shape and predict probabilities.\n",
    "    if x_test.ndim == 1:\n",
    "        label_probs_logreg = logreg.predict_proba(x_test.values.reshape(-1, 1))\n",
    "    else:\n",
    "        label_probs_logreg = logreg.predict_proba(x_test)\n",
    "\n",
    "    return logreg, label_probs_logreg[:, logreg.classes_ == class_value]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### With unobservables in the data\n",
    "\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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1| 0 1 2 3 4 2| 0 1 2 3 4 3| 0 1 2 3 4 4| 0 1 2 3 4 5| 0 1 2 3 4 6| 0 1 2 3 4 7| 0 1 2 3 4 8| 0 1 2 3 4 "
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.005544   0.0022     0.01027108 0.00470851 0.00425303]\n",
      " [0.02112    0.008248   0.02691527 0.02059184 0.01725623]\n",
      " [0.046616   0.018488   0.04842042 0.03653877 0.03691361]\n",
      " [0.082656   0.031824   0.08504799 0.06495903 0.06255394]\n",
      " [0.126216   0.04844    0.12745866 0.12681319 0.0954118 ]\n",
      " [0.181      0.06864    0.18465026 0.18324289 0.13430768]\n",
      " [0.244616   0.086416   0.24131455 0.25093638 0.17210743]\n",
      " [0.321824   0.10564    0.32405645 0.31731251 0.21823937]]\n"
     ]
    }
   ],
   "source": [
    "def bailIndicator(r, y_model, x_train, x_test):\n",
    "    '''\n",
    "    Indicator function for whether a judge will bail or jail a suspect.\n",
    "    \n",
    "    Algorithm:\n",
    "    ----------\n",
    "    \n",
    "    (1) Calculate recidivism probabilities from training set and assign to\n",
    "        predictions_train.\n",
    "    \n",
    "    (2) Calculate recidivism probabilities from test set and assign to\n",
    "        predictions_test.\n",
    "    \n",
    "    (3) Construct a cumulative distribution function of the probabilities in\n",
    "        in predictions_train.\n",
    "    \n",
    "    (4)\n",
    "    For pred in predictions_test:\n",
    "        \n",
    "        if pred belongs to a percentile (computed from step (3)) lower than r\n",
    "            return True\n",
    "        else\n",
    "            return False\n",
    "    \n",
    "    \n",
    "    Returns a boolean array indicating a bail decision.\n",
    "    '''\n",
    "\n",
    "    predictions_train = y_model.predict_proba(x_train)[:, 0]\n",
    "\n",
    "    predictions_test = y_model.predict_proba(x_test)[:, 0]\n",
    "\n",
    "    return [\n",
    "        scs.percentileofscore(predictions_train, pred, kind='weak') < r\n",
    "        for pred in predictions_test\n",
    "    ]\n",
    "\n",
    "\n",
    "failure_rates = np.zeros((8, 5))\n",
    "failure_sems = np.zeros((8, 5))\n",
    "\n",
    "nIter = 5\n",
    "\n",
    "for r in np.arange(1, 9):\n",
    "\n",
    "    print(r, end=\"| \")\n",
    "\n",
    "    f_rate_true = np.zeros(nIter)\n",
    "    f_rate_label = np.zeros(nIter)\n",
    "    f_rate_human = np.zeros(nIter)\n",
    "    f_rate_cont = np.zeros(nIter)\n",
    "    f_rate_caus = np.zeros(nIter)\n",
    "\n",
    "    for i in range(nIter):\n",
    "\n",
    "        print(i, end=\" \")\n",
    "\n",
    "        train_labeled, train, test_labeled, test, df = generateDataWithUnobservables(\n",
    "        )\n",
    "\n",
    "        logreg, predictions = fitLogisticRegressionModel(\n",
    "            train_labeled.dropna().X,\n",
    "            train_labeled.dropna().result_Y, test.X, 0)\n",
    "        test = test.assign(B_prob_0_logreg=predictions)\n",
    "\n",
    "        logreg, predictions_labeled = fitLogisticRegressionModel(\n",
    "            train_labeled.dropna().X,\n",
    "            train_labeled.dropna().result_Y, test_labeled.X, 0)\n",
    "        test_labeled = test_labeled.assign(B_prob_0_logreg=predictions_labeled)\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",
    "\n",
    "        to_release = int(round(test.shape[0] * r / 10))\n",
    "\n",
    "        # Calculate failure rate as the ratio of failures to those who were given a\n",
    "        # positive decision, i.e. those whose probability of negative outcome was\n",
    "        # low enough.\n",
    "        f_rate_true[i] = np.sum(\n",
    "            test.result_Y[0:to_release] == 0) / test.shape[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',\n",
    "                                 inplace=True,\n",
    "                                 ascending=True)\n",
    "\n",
    "        to_release = int(round(test_labeled.shape[0] * r / 10))\n",
    "\n",
    "        f_rate_label[i] = np.sum(\n",
    "            test_labeled.result_Y[0:to_release] == 0) / test_labeled.shape[0]\n",
    "\n",
    "        #### Human evaluation\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[\n",
    "            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",
    "        f_rate_human[i] = np.sum(\n",
    "            released.result_Y == 0) / correct_leniency_list.shape[0]\n",
    "\n",
    "        #### Contraction, logistic regression\n",
    "        f_rate_cont[i] = contraction(test_labeled, 'judgeID_J', 'decision_T',\n",
    "                                     'result_Y', 'B_prob_0_logreg',\n",
    "                                     'acceptanceRate_R', r / 10)\n",
    "\n",
    "        #### Causal model - empirical performance\n",
    "        #\n",
    "        f_rate_caus[i] = np.sum(\n",
    "            (test_labeled.dropna().result_Y == 0)\n",
    "            & bailIndicator(r * 10, logreg, train.X.values.reshape(-1, 1),\n",
    "                    test_labeled.dropna().X.values.reshape(-1, 1))\n",
    "        ) / test_labeled.dropna().result_Y.shape[0]\n",
    "\n",
    "        #print(\"diff: \", f_rate_caus[i] - (np.sum((test_labeled.dropna().result_Y == 0) & (cdf(test_labeled.dropna().X, logreg, 0) < (r /10))) / test_labeled.dropna().result_Y.shape[0]))\n",
    "\n",
    "    failure_rates[r - 1, 0] = np.mean(f_rate_true)\n",
    "    failure_rates[r - 1, 1] = np.mean(f_rate_label)\n",
    "    failure_rates[r - 1, 2] = np.mean(f_rate_human)\n",
    "    failure_rates[r - 1, 3] = np.mean(f_rate_cont)\n",
    "    failure_rates[r - 1, 4] = np.mean(f_rate_caus)\n",
    "\n",
    "    failure_sems[r - 1, 0] = scs.sem(f_rate_true)\n",
    "    failure_sems[r - 1, 1] = scs.sem(f_rate_label)\n",
    "    failure_sems[r - 1, 2] = scs.sem(f_rate_human)\n",
    "    failure_sems[r - 1, 3] = scs.sem(f_rate_cont)\n",
    "    failure_sems[r - 1, 4] = scs.sem(f_rate_caus)\n",
    "\n",
    "x_ax = np.arange(0.1, 0.9, 0.1)\n",
    "\n",
    "plt.figure(figsize=(14, 8))\n",
    "plt.errorbar(x_ax,\n",
    "             failure_rates[:, 0],\n",
    "             label='True Evaluation',\n",
    "             c='green',\n",
    "             yerr=failure_sems[:, 0])\n",
    "plt.errorbar(x_ax,\n",
    "             failure_rates[:, 1],\n",
    "             label='Labeled outcomes',\n",
    "             c='magenta',\n",
    "             yerr=failure_sems[:, 1])\n",
    "plt.errorbar(x_ax,\n",
    "             failure_rates[:, 2],\n",
    "             label='Human evaluation',\n",
    "             c='red',\n",
    "             yerr=failure_sems[:, 2])\n",
    "plt.errorbar(x_ax,\n",
    "             failure_rates[:, 3],\n",
    "             label='Contraction, log.',\n",
    "             c='blue',\n",
    "             yerr=failure_sems[:, 3])\n",
    "plt.errorbar(x_ax,\n",
    "             failure_rates[:, 4],\n",
    "             label='Causal model, ep',\n",
    "             c='black',\n",
    "             yerr=failure_sems[:, 4])\n",
    "\n",
    "plt.title('Failure rate vs. Acceptance rate with unobservables')\n",
    "plt.xlabel('Acceptance rate')\n",
    "plt.ylabel('Failure rate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "print(failure_rates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Without unobservables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "| iteration: 1 ,0 1 2 3 4 | iteration: 2 ,0 1 2 3 4 | iteration: 3 ,0 1 2 3 4 | iteration: 4 ,0 1 2 3 4 | iteration: 5 ,0 1 2 3 4 | iteration: 6 ,0 1 2 3 4 | iteration: 7 ,0 1 2 3 4 | iteration: 8 ,0 1 2 3 4 "
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.015672   0.015672   0.02077658 0.0168399  0.03213019]\n",
      " [0.04256    0.04256    0.04143341 0.04854146 0.07905376]\n",
      " [0.075808   0.075808   0.07616197 0.06881769 0.13324914]\n",
      " [0.11696    0.11696    0.11272757 0.12694184 0.1941261 ]\n",
      " [0.163664   0.163664   0.16585906 0.16208214 0.2442222 ]\n",
      " [0.215816   0.215816   0.214522   0.22351695 0.28915824]\n",
      " [0.27644    0.27644    0.28466479 0.28419799 0.32621678]\n",
      " [0.341944   0.341944   0.34848206 0.34073762 0.34775226]]\n"
     ]
    }
   ],
   "source": [
    "f_rates = np.zeros((8, 5))\n",
    "f_sems = np.zeros((8, 5))\n",
    "\n",
    "nIter = 5\n",
    "\n",
    "for r in np.arange(1, 9):\n",
    "\n",
    "    print(\"| iteration:\", r, \",\", end=\"\")\n",
    "\n",
    "    s_f_rate_true = np.zeros(nIter)\n",
    "    s_f_rate_gs = np.zeros(nIter)\n",
    "    s_f_rate_human = np.zeros(nIter)\n",
    "    s_f_rate_cont = np.zeros(nIter)\n",
    "    s_f_rate_caus = np.zeros(nIter)\n",
    "\n",
    "    for i in range(nIter):\n",
    "\n",
    "        print(i, end=\" \")\n",
    "\n",
    "        s_train_labeled, s_train, s_test_labeled, s_test, s_df = generateDataWithoutUnobservables(\n",
    "        )\n",
    "\n",
    "        s_logreg, predictions = fitLogisticRegressionModel(\n",
    "            s_train_labeled.dropna().X,\n",
    "            s_train_labeled.dropna().result_Y, s_test.X, 0)\n",
    "        s_test = s_test.assign(B_prob_0_logreg=predictions)\n",
    "\n",
    "        s_logreg, predictions_labeled = fitLogisticRegressionModel(\n",
    "            s_train_labeled.dropna().X,\n",
    "            s_train_labeled.dropna().result_Y, s_test_labeled.X, 0)\n",
    "        s_test_labeled = s_test_labeled.assign(\n",
    "            B_prob_0_logreg=predictions_labeled)\n",
    "\n",
    "        s_f_rate_cont[i] = contraction(s_test_labeled, 'judgeID_J',\n",
    "                                       'decision_T', 'result_Y',\n",
    "                                       'B_prob_0_logreg', 'acceptanceRate_R',\n",
    "                                       r / 10)\n",
    "\n",
    "#         s_f_rate_caus[i] = np.sum(\n",
    "#             (s_test_labeled.dropna().result_Y == 0)\n",
    "#             & (cdf(s_test_labeled.dropna().X, s_logreg, 0) < r /\n",
    "#                10)) / s_test_labeled.dropna().result_Y.shape[0]\n",
    "        \n",
    "        s_f_rate_caus[i] = np.sum(\n",
    "            (s_test_labeled.dropna().result_Y == 0)\n",
    "            & bailIndicator(r*10, s_logreg, s_train.X.values.reshape(-1,1), s_test_labeled.dropna().X.values.reshape(-1,1))) / s_test_labeled.dropna().result_Y.shape[0]\n",
    "\n",
    "#         s_f_rate_caus[i] = si.quad(\n",
    "#             lambda x: getProbabilityForClass(np.array([x]), s_logreg, 0) * (\n",
    "#                 r / 10) * scs.norm.pdf(x), -np.inf, np.inf)[0]\n",
    "\n",
    "        #### True evaluation\n",
    "        # Sort by estimated failure probabilities, subjects with the smallest risk are first.\n",
    "        s_sorted = s_test.sort_values(by='B_prob_0_logreg',\n",
    "                                      inplace=False,\n",
    "                                      ascending=True)\n",
    "\n",
    "        to_release = int(round(s_sorted.shape[0] * r / 10))\n",
    "\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",
    "        s_f_rate_true[i] = np.sum(\n",
    "            s_sorted.result_Y[0:to_release] == 0) / s_sorted.shape[0]\n",
    "\n",
    "        #### \"Golden standard\"\n",
    "        # Sort by actual failure probabilities, subjects with the smallest risk are first.\n",
    "        s_sorted = s_test.sort_values(by='probabilities_Y',\n",
    "                                      inplace=False,\n",
    "                                      ascending=True)\n",
    "\n",
    "        to_release = int(round(s_sorted.shape[0] * r / 10))\n",
    "\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",
    "        s_f_rate_gs[i] = np.sum(\n",
    "            s_sorted.result_Y[0:to_release] == 0) / s_sorted.shape[0]\n",
    "\n",
    "        #### Human error rate\n",
    "        # Get judges with correct leniency as list\n",
    "        correct_leniency_list = s_test_labeled.judgeID_J[\n",
    "            s_test_labeled['acceptanceRate_R'].round(1) == r / 10].values\n",
    "\n",
    "        # Released are the people they judged and released, T = 1\n",
    "        released = s_test_labeled[\n",
    "            s_test_labeled.judgeID_J.isin(correct_leniency_list)\n",
    "            & (s_test_labeled.decision_T == 1)]\n",
    "\n",
    "        # Get their failure rate, aka ratio of reoffenders to number of people judged in total\n",
    "        s_f_rate_human[i] = np.sum(\n",
    "            released.result_Y == 0) / correct_leniency_list.shape[0]\n",
    "\n",
    "    f_rates[r - 1, 0] = np.mean(s_f_rate_true)\n",
    "    f_rates[r - 1, 1] = np.mean(s_f_rate_gs)\n",
    "    f_rates[r - 1, 2] = np.mean(s_f_rate_human)\n",
    "    f_rates[r - 1, 3] = np.mean(s_f_rate_cont)\n",
    "    f_rates[r - 1, 4] = np.mean(s_f_rate_caus)\n",
    "\n",
    "    f_sems[r - 1, 0] = scs.sem(s_f_rate_true)\n",
    "    f_sems[r - 1, 1] = scs.sem(s_f_rate_gs)\n",
    "    f_sems[r - 1, 2] = scs.sem(s_f_rate_human)\n",
    "    f_sems[r - 1, 3] = scs.sem(s_f_rate_cont)\n",
    "    f_sems[r - 1, 4] = scs.sem(s_f_rate_caus)\n",
    "\n",
    "x_ax = np.arange(0.1, 0.9, 0.1)\n",
    "\n",
    "plt.figure(figsize=(14, 8))\n",
    "plt.errorbar(x_ax,\n",
    "             f_rates[:, 0],\n",
    "             label='True Evaluation',\n",
    "             c='green',\n",
    "             yerr=f_sems[:, 0])\n",
    "plt.errorbar(x_ax,\n",
    "             f_rates[:, 1],\n",
    "             label='\"Golden standard\"',\n",
    "             c='magenta',\n",
    "             yerr=f_sems[:, 1])\n",
    "plt.errorbar(x_ax,\n",
    "             f_rates[:, 2],\n",
    "             label='Human evaluation',\n",
    "             c='red',\n",
    "             yerr=f_sems[:, 2])\n",
    "plt.errorbar(x_ax,\n",
    "             f_rates[:, 3],\n",
    "             label='Contraction, log.',\n",
    "             c='blue',\n",
    "             yerr=f_sems[:, 3])\n",
    "plt.errorbar(x_ax,\n",
    "             f_rates[:, 4],\n",
    "             label='Causal model, ep',\n",
    "             c='black',\n",
    "             yerr=f_sems[:, 4])\n",
    "\n",
    "plt.title('Failure rate vs. Acceptance rate without unobservables')\n",
    "plt.xlabel('Acceptance rate')\n",
    "plt.ylabel('Failure rate')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()\n",
    "\n",
    "print(f_rates)"
   ]
  }
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