Analysis_07MAY2019_new.ipynb

    "    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",
    "df = generateData()\n",
    "\n",
    "pd.crosstab(df.decision_T, df.result_Y, margins=True)\n",
    "\n",
    "display(df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(25000, 8)\n",
      "(25000, 8)\n",
      "(25000, 8)\n",
      "(25000, 8)\n"
     ]
    },
    {
     "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>decision_T</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>result_Y</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.0</th>\n",
       "      <td>3565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.0</th>\n",
       "      <td>8163</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "decision_T     1\n",
       "result_Y        \n",
       "0.0         3565\n",
       "1.0         8163"
      ]
     },
     "execution_count": 190,
     "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()"
   ]
  },
  {
   "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": 191,
   "metadata": {},
   "outputs": [],
   "source": [
    "def contraction(df,\n",
    "                judgeIDJ_col,\n",
    "                decisionT_col,\n",
    "                resultY_col,\n",
    "                modelProbS_col,\n",
    "                accRateR_col,\n",
    "                r,\n",
    "                binning=False):\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",
    "    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",
    "    # First sort by acceptance rate and judge ID.\n",
    "    sorted_df = df.sort_values(by=[accRateR_col, judgeIDJ_col],\n",
    "                               ascending=False)\n",
    "\n",
    "    # Get the ID of the most lenient judge\n",
    "    most_lenient_ID = sorted_df[judgeIDJ_col].values[0]\n",
    "\n",
    "    # Subset\n",
    "    D_q = sorted_df[sorted_df[judgeIDJ_col] == most_lenient_ID].copy()\n",
    "\n",
    "    # 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",
   "execution_count": 192,
   "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",
    "### Predictive models\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": 193,
   "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "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": [
    "### Visual comparison\n",
    "\n",
    "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."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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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",
    "    df_sorted = test.sort_values(by='B_prob_0_logreg', inplace=False, \n",
    "                                 ascending=True)\n",
    "\n",
    "    to_release = int(round(df_sorted.shape[0] * r / 10))\n",
    "\n",
    "    # Failure was coded as zero.\n",
    "    failure_rates[r - 1, 0] = np.mean(df_sorted.result_Y[0:to_release] == 0)\n",
    "    \n",
    "    #### Labeled outcomes only\n",
    "    # Sort by failure probabilities, subjects with the smallest risk are first. \n",
    "    df_sorted = test_labeled.sort_values(by='B_prob_0_logreg', inplace=False,\n",
    "                                         ascending=True)\n",
    "    \n",
    "    # Ensure that only labeled outcomes are available\n",
    "    df_sorted = df_sorted[df_sorted.decision_T == 1]\n",
    "    \n",
    "    to_release = int(round(df_sorted.shape[0] * r / 10))\n",
    "\n",
    "    failure_rates[r - 1, 1] = np.mean(df_sorted.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",
    "        'acceptanceRate_R', r / 10, False)\n",
    "\n",
    "    #### Causal effect\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='magenta')\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",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0 (0.017088007566874997, 7.490802276143562e-11)\n",
      "1.0 (0.33637396099663436, 6.582823022108186e-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))\n",
    "\n",
    "# Multiple runs -> error bars\n",
    "# result ->  coinflipping, in y\n",
    "# email, jure and himabindu\n",
    "# delta(F(x) < r) , kertymääfunktio jotenkin"
   ]
  },
  {
   "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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