measuring-bias-and-discrimination/measuring-bias-regression.ipynb

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      "name": "Measuring_Bias_Regression_3.ipynb",
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        "THYXrjvTCn8H"
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  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# **Measuring Bias in Regression Tasks**\n"
      ],
      "metadata": {
        "id": "pFKF6N69kCay"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In order to make sure that your algorithm treats everyone equally, it is important to measure the bias. Here, we will illustrate how to measure bias in a regression context. \n",
        "\n",
        "Suppose we have a dataset involving grades of students from a school, and a range of features that could be useful for prediction of their grades. If some of these features involve sex, the models trained from this dataset could show bias against a certain sex. We would like to avoid such discrimination, because it causes prejudice and might cause disadvantages to some people.\n",
        "\n",
        "In this notebook, we will:\n",
        "1. Install and import useful modules and load the data\n",
        "2. Code Bias Metrics for regression tasks\n",
        "3. Download student performance dataset\n",
        "4. Train a regression model to predict grades\n",
        "5. Check this model for bias\n",
        "\n",
        "We will implement a Light Gradient Boosting Machine with [scikit-learn](https://scikit-learn.org/stable/) in 4, and check it's bias in 5.\n",
        "\n"
      ],
      "metadata": {
        "id": "EwBbVkPqsbuR"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Base Modules**"
      ],
      "metadata": {
        "id": "4B2PuMweDIOS"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!pip install scikit-learn==0.21.3\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "%matplotlib inline"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ePoS2ium8_vF",
        "outputId": "d2ebb0dc-0c53-427a-be3e-f2cf00c56170"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Requirement already satisfied: scikit-learn==0.21.3 in /usr/local/lib/python3.7/dist-packages (0.21.3)\n",
            "Requirement already satisfied: joblib>=0.11 in /usr/local/lib/python3.7/dist-packages (from scikit-learn==0.21.3) (1.1.0)\n",
            "Requirement already satisfied: scipy>=0.17.0 in /usr/local/lib/python3.7/dist-packages (from scikit-learn==0.21.3) (1.4.1)\n",
            "Requirement already satisfied: numpy>=1.11.0 in /usr/local/lib/python3.7/dist-packages (from scikit-learn==0.21.3) (1.21.6)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Bias Metrics**"
      ],
      "metadata": {
        "id": "THYXrjvTCn8H"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "Below we display the code for a number of different metrics useful in quantifying bias in regression tasks."
      ],
      "metadata": {
        "id": "04Lw9bN1_nFm"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "absent-intermediate"
      },
      "outputs": [],
      "source": [
        "def DispImpactQ90(yobs, ypred, gmaj, gmin):    \n",
        "    ### Get quantile 90%\n",
        "    QX = np.quantile(ypred, .9)\n",
        "    \n",
        "    ### Disparate Impact (a.k.a. Adverse Impact Ratio)\n",
        "    SR_min = (gmin * (ypred > QX)).sum()/gmin.sum() # success rate minority\n",
        "    SR_maj = (gmaj * (ypred > QX)).sum()/gmaj.sum() # success rate majority\n",
        "    \n",
        "    return SR_min/SR_maj\n",
        "\n",
        "def DispImpactQ80(yobs, ypred, gmaj, gmin):   \n",
        "    ### Get quantile 80%\n",
        "    QX = np.quantile(ypred, .8)\n",
        "    \n",
        "    ### Disparate Impact (a.k.a. Adverse Impact Ratio)\n",
        "    SR_min = (gmin * (ypred > QX)).sum()/gmin.sum() # success rate minority\n",
        "    SR_maj = (gmaj * (ypred > QX)).sum()/gmaj.sum() # success rate majority\n",
        "    \n",
        "    return SR_min/SR_maj\n",
        "\n",
        "def DispImpactQ50(yobs, ypred, gmaj, gmin):  \n",
        "    ### Get quantile 50%\n",
        "    QX = np.quantile(ypred, .5)\n",
        "    \n",
        "    ### Disparate Impact (a.k.a. Adverse Impact Ratio)\n",
        "    SR_min = (gmin * (ypred > QX)).sum()/gmin.sum() # success rate minority\n",
        "    SR_maj = (gmaj * (ypred > QX)).sum()/gmaj.sum() # success rate majority\n",
        "    \n",
        "    return SR_min/SR_maj\n",
        "\n",
        "def NoAdvImpactLevel(yobs, ypred, gmaj, gmin):  \n",
        "    ##### find maximum score that not allow adverse impact\n",
        "    ### grid\n",
        "    q = np.linspace(1.0, 0.0, 100)\n",
        "    pred_value = []\n",
        "    sr_maj = []\n",
        "    sr_min = []\n",
        "    \n",
        "    ### try different values\n",
        "    for (i, v) in enumerate(q):\n",
        "        pred = np.quantile(ypred, v)\n",
        "        pass_members = (ypred > pred)\n",
        "        if ( sum(gmin * pass_members)/sum(gmin) ) / ( sum(gmaj * pass_members)/sum(gmaj) ) > 0.8:\n",
        "            if ( sum(gmin * pass_members)/sum(gmin) ) / ( sum(gmaj * pass_members)/sum(gmaj) ) < 1.2:\n",
        "                break\n",
        "            \n",
        "    return pred\n",
        "\n",
        "def AvgScoreSpread(yobs, ypred, gmaj, gmin):\n",
        "    ### get averages\n",
        "    avg_min = ypred[gmin==1].mean()\n",
        "    avg_maj = ypred[gmaj==1].mean()\n",
        "    \n",
        "    return avg_min - avg_maj\n",
        "\n",
        "def AvgScoreSpreadTop20(yobs, ypred, gmaj, gmin):    \n",
        "    ### Get top 20%\n",
        "    topX = np.argsort(ypred)[-int(ypred.shape[0]*0.2):]\n",
        "    ypred = ypred[topX]\n",
        "    gmin = gmin[topX]\n",
        "    gmaj = gmaj[topX]\n",
        "    \n",
        "    ### get averages\n",
        "    avg_min = ypred[gmin==1].mean()\n",
        "    avg_maj = ypred[gmaj==1].mean()\n",
        "    \n",
        "    return avg_min - avg_maj\n",
        "\n",
        "    \n",
        "def ZScoreSpread(yobs, ypred, gmaj, gmin):\n",
        "    ### get means and pooled std\n",
        "    avg_min = ypred[gmin==1].mean()  \n",
        "    avg_maj = ypred[gmaj==1].mean()\n",
        "    n_min = sum(gmin==1)\n",
        "    n_maj = sum(gmaj==1)\n",
        "    pool_sd = np.sqrt( (n_min-1) * (ypred[gmin==1].std() ** 2.0 + (n_maj-1) * ypred[gmaj==1].std() ** 2.0) / (n_maj + n_min - 2) )\n",
        "    \n",
        "    return (avg_min - avg_maj)/pool_sd\n",
        "\n",
        "def ZScoreSpreadTop20(yobs, ypred, gmaj, gmin):\n",
        "    ### Get top 20%\n",
        "    topX = np.argsort(ypred)[-int(ypred.shape[0]*0.2):]\n",
        "    ypred = ypred[topX]\n",
        "    gmin = gmin[topX]\n",
        "    gmaj = gmaj[topX]\n",
        "    \n",
        "    ### get means and pooled std\n",
        "    avg_min = ypred[gmin==1].mean()  \n",
        "    avg_maj = ypred[gmaj==1].mean()\n",
        "    n_min = sum(gmin==1)\n",
        "    n_maj = sum(gmaj==1)\n",
        "    pool_sd = np.sqrt( (n_min-1) * (ypred[gmin==1].std() ** 2.0 + (n_maj-1) * ypred[gmaj==1].std() ** 2.0) / (n_maj + n_min - 2) )\n",
        "    \n",
        "    return (avg_min - avg_maj)/pool_sd\n",
        "\n",
        "def AdvImpactAUC(yobs, ypred, gmaj, gmin):\n",
        "    ### thresholds\n",
        "    thresh = [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0]\n",
        "\n",
        "    ### pass rate per thresh\n",
        "    pass_min = []\n",
        "    pass_maj = []\n",
        "    for (i, t) in enumerate(thresh):\n",
        "        pass_value = np.quantile(ypred, t)\n",
        "        pass_min += [(gmin[ypred > pass_value]==1).sum() / (gmin==1).sum()]\n",
        "        pass_maj += [(gmaj[ypred > pass_value]==1).sum() / (gmaj==1).sum()]\n",
        "\n",
        "    ### AUC\n",
        "    return sum( (np.array(pass_min[1:])-np.array(pass_min[:-1]))*(np.array(pass_maj[1:])-np.array(pass_maj[0])) )\n",
        "\n",
        "def ConcVal(yobs, ypred):\n",
        "    return np.corrcoef(ypred, yobs)[1,0]\n",
        "\n",
        "def RMSE(yobs, ypred):\n",
        "    return np.sqrt( ((yobs - ypred) ** 2.0).mean() )\n",
        "\n",
        "def ConcValSpread(yobs, ypred, gmaj, gmin):\n",
        "    cv_min = np.corrcoef(ypred[gmin==1], yobs[gmin==1])[1,0]\n",
        "    cv_maj = np.corrcoef(ypred[gmaj==1], yobs[gmaj==1])[1,0]\n",
        "    return cv_min - cv_maj\n",
        "\n",
        "def RmseRatio(yobs, ypred, gmaj, gmin):\n",
        "    rmse_min = np.sqrt( ( (yobs[gmin==1] - ypred[gmin==1]) ** 2.0 ).mean() )\n",
        "    rmse_maj = np.sqrt( ( (yobs[gmaj==1] - ypred[gmaj==1]) ** 2.0).mean() )\n",
        "    return rmse_min / rmse_maj\n",
        "\n",
        "def ConcValSpreadTop20(yobs, ypred, gmaj, gmin):\n",
        "    ### Get top 20%\n",
        "    topX = np.argsort(ypred)[-int(ypred.shape[0]*0.2):]\n",
        "    ypred = ypred[topX]\n",
        "    yobs = yobs[topX]\n",
        "    gmin = gmin[topX]\n",
        "    gmaj = gmaj[topX]\n",
        "    \n",
        "    ### compute metric\n",
        "    cv_min = np.corrcoef(ypred[gmin==1], yobs[gmin==1])[1,0]\n",
        "    cv_maj = np.corrcoef(ypred[gmaj==1], yobs[gmaj==1])[1,0]\n",
        "    return cv_min - cv_maj\n",
        "\n",
        "\n",
        "def RmseRatioSpreadTop20(yobs, ypred, gmaj, gmin):\n",
        "    ### Get top 20%\n",
        "    topX = np.argsort(ypred)[-int(ypred.shape[0]*0.2):]\n",
        "    ypred = ypred[topX]\n",
        "    yobs = yobs[topX]\n",
        "    gmin = gmin[topX]\n",
        "    gmaj = gmaj[topX]\n",
        "    \n",
        "    ### compute metric\n",
        "    rmse_min = np.sqrt( ( (yobs[gmin==1] - ypred[gmin==1]) ** 2.0).mean() )\n",
        "    rmse_maj = np.sqrt( ( (yobs[gmaj==1] - ypred[gmaj==1]) ** 2.0).mean() )\n",
        "    return rmse_min / rmse_maj\n",
        "\n",
        "def AI_ROC(yobs, ypred, gmaj, gmin):\n",
        "    from matplotlib import pyplot as plt\n",
        "    ### thresholds\n",
        "    thresh = [1.0, 0.9, 0.8, 0.7, 0.6, 0.5, 0.4, 0.3, 0.2, 0.1, 0.0]\n",
        "\n",
        "    ### pass rate per thresh\n",
        "    pass_min = []\n",
        "    pass_maj = []\n",
        "    for (i, t) in enumerate(thresh):\n",
        "        pass_value = np.quantile(ypred, t)\n",
        "        pass_min += [(gmin[ypred > pass_value]==1).sum() / (gmin==1).sum()]\n",
        "        pass_maj += [(gmaj[ypred > pass_value]==1).sum() / (gmaj==1).sum()]\n",
        "\n",
        "    # charting\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.plot(np.array(pass_min) * 100.0, np.array(pass_maj) * 100.0)\n",
        "    ax.plot([0, 100], [0, 100], linestyle='--')\n",
        "    ax.set_xlabel(\"Minority Pass Rate %\")\n",
        "    ax.set_ylabel(\"Majority Pass Rate %\")\n",
        "    return plt.show()\n",
        "\n",
        "\n",
        "def AI_Curve(yobs, ypred, gmaj, gmin):\n",
        "    from matplotlib import pyplot as plt\n",
        "    # quantiles\n",
        "    q = np.linspace(0.0, 1.0, 200)\n",
        "    pred_value = []\n",
        "    other_form_maj = []\n",
        "    other_form_min = []\n",
        "    \n",
        "    # grid values\n",
        "    for (i, v) in enumerate(q):\n",
        "        pred = np.quantile(ypred, v)\n",
        "        pass_members = (ypred > pred)\n",
        "        other_form_maj += [sum(gmaj * pass_members)/sum(gmaj)]\n",
        "        other_form_min += [sum(gmin * pass_members)/sum(gmin)]\n",
        "        pred_value += [pred]\n",
        "\n",
        "    # charting\n",
        "    fig, ax = plt.subplots()\n",
        "    ax.plot(pred_value, np.array(other_form_min)/np.array(other_form_maj))\n",
        "    ax.plot([np.quantile(ypred, 0.0), np.quantile(ypred, 1.0)], [0.8, 0.8], linestyle='--')\n",
        "    ax.set_xlabel(\"Score\")\n",
        "    ax.set_ylabel(\"Adverse Impact\")\n",
        "    return plt.show()\n",
        "\n",
        "\n",
        "def compute_model_metrics(ypred, yobs=None, gmaj=None, gmin=None):\n",
        "    \n",
        "    if yobs is None:\n",
        "        # metrics\n",
        "        perf_metrics = {}\n",
        "        # fairness metrics\n",
        "        fair_metrics = {\"Disparate Impact (Q 90%)\": DispImpactQ90,\n",
        "                        \"Disparate Impact (Q 80%)\": DispImpactQ80,\n",
        "                        \"Disparate Impact (Q 50%)\": DispImpactQ50,\n",
        "                        \"Avg Score Spread\": AvgScoreSpread,\n",
        "                        \"Avg Score Spread (top 20%)\": AvgScoreSpreadTop20,\n",
        "                        \"Z-score Spread\": ZScoreSpread,\n",
        "                        \"Z-score Spread (top 20%)\": ZScoreSpreadTop20,\n",
        "                        \"Adv Impact AUC\": AdvImpactAUC\n",
        "                       }\n",
        "        \n",
        "    else:\n",
        "        # metrics\n",
        "        from sklearn import metrics\n",
        "        perf_metrics = {\"Concurrent Validity\": ConcVal, \n",
        "                        \"RMSE\": RMSE, \n",
        "                       }\n",
        "        # fairness metrics\n",
        "        fair_metrics = {\"Disparate Impact (Q 90%)\": DispImpactQ90,\n",
        "                        \"Disparate Impact (Q 80%)\": DispImpactQ80,\n",
        "                        \"Disparate Impact (Q 50%)\": DispImpactQ50,\n",
        "                        \"Avg Score Spread\": AvgScoreSpread,\n",
        "                        \"Avg Score Spread (top 20%)\": AvgScoreSpreadTop20,\n",
        "                        \"Z-score Spread\": ZScoreSpread,\n",
        "                        \"Z-score Spread (top 20%)\": ZScoreSpreadTop20,\n",
        "                        \"Adv Impact AUC\": AdvImpactAUC,\n",
        "                        \"Concurrent Validity Spread\": ConcValSpread,\n",
        "                        \"RMSE Ratio\": RmseRatio,\n",
        "                        \"Concurrent Validity Spread (top 20%)\": ConcValSpreadTop20,\n",
        "                        \"RMSE Ratio (top 20%)\": RmseRatioSpreadTop20\n",
        "                       }\n",
        "        \n",
        "    # compute performance metrics\n",
        "    metrics = []\n",
        "    for pf in perf_metrics.keys():\n",
        "        metrics += [[pf, perf_metrics[pf](yobs, ypred)]]\n",
        "            \n",
        "    if (gmaj is not None) and (gmin is not None):\n",
        "        for ff in fair_metrics.keys():\n",
        "            metrics += [[ff, fair_metrics[ff](yobs, ypred, gmaj, gmin)]]\n",
        "    \n",
        "    return pd.DataFrame(metrics, columns=[\"Metric\", \"Value\"])\n"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Load Data**"
      ],
      "metadata": {
        "id": "Yg3uJ72vBfHX"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "If running in colab the dataset is obtained in the next cell with the !wget command. If running locally, download zip file from (https://archive.ics.uci.edu/ml/machine-learning-databases/00320/student.zip) and unpack the dataset in the same folder as notebook."
      ],
      "metadata": {
        "id": "8xw1h9cfBaMR"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "!wget https://archive.ics.uci.edu/ml/machine-learning-databases/00320/student.zip\n",
        "!unzip student.zip"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xK7ZIBHH8jEw",
        "outputId": "b86e6cf1-87e6-457b-93ee-e7df2cd6f1ba"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "--2022-04-26 18:21:39--  https://archive.ics.uci.edu/ml/machine-learning-databases/00320/student.zip\n",
            "Resolving archive.ics.uci.edu (archive.ics.uci.edu)... 128.195.10.252\n",
            "Connecting to archive.ics.uci.edu (archive.ics.uci.edu)|128.195.10.252|:443... connected.\n",
            "HTTP request sent, awaiting response... 200 OK\n",
            "Length: 20478 (20K) [application/x-httpd-php]\n",
            "Saving to: ‘student.zip.1’\n",
            "\n",
            "student.zip.1       100%[===================>]  20.00K  --.-KB/s    in 0.05s   \n",
            "\n",
            "2022-04-26 18:21:39 (404 KB/s) - ‘student.zip.1’ saved [20478/20478]\n",
            "\n",
            "Archive:  student.zip\n",
            "replace student-mat.csv? [y]es, [n]o, [A]ll, [N]one, [r]ename: A\n",
            "  inflating: student-mat.csv         \n",
            "  inflating: student-por.csv         \n",
            "  inflating: student-merge.R         \n",
            "  inflating: student.txt             \n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# read dataset with pandas\n",
        "data = pd.read_csv('student-mat.csv',delimiter=';')\n",
        "data"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "s0Mm5lzL8u3d",
        "outputId": "a85aa8c8-f630-4255-cece-0ed2bbfdd10c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    school sex  age address famsize Pstatus  Medu  Fedu      Mjob      Fjob  \\\n",
              "0       GP   F   18       U     GT3       A     4     4   at_home   teacher   \n",
              "1       GP   F   17       U     GT3       T     1     1   at_home     other   \n",
              "2       GP   F   15       U     LE3       T     1     1   at_home     other   \n",
              "3       GP   F   15       U     GT3       T     4     2    health  services   \n",
              "4       GP   F   16       U     GT3       T     3     3     other     other   \n",
              "..     ...  ..  ...     ...     ...     ...   ...   ...       ...       ...   \n",
              "390     MS   M   20       U     LE3       A     2     2  services  services   \n",
              "391     MS   M   17       U     LE3       T     3     1  services  services   \n",
              "392     MS   M   21       R     GT3       T     1     1     other     other   \n",
              "393     MS   M   18       R     LE3       T     3     2  services     other   \n",
              "394     MS   M   19       U     LE3       T     1     1     other   at_home   \n",
              "\n",
              "     ... famrel freetime  goout  Dalc  Walc health absences  G1  G2  G3  \n",
              "0    ...      4        3      4     1     1      3        6   5   6   6  \n",
              "1    ...      5        3      3     1     1      3        4   5   5   6  \n",
              "2    ...      4        3      2     2     3      3       10   7   8  10  \n",
              "3    ...      3        2      2     1     1      5        2  15  14  15  \n",
              "4    ...      4        3      2     1     2      5        4   6  10  10  \n",
              "..   ...    ...      ...    ...   ...   ...    ...      ...  ..  ..  ..  \n",
              "390  ...      5        5      4     4     5      4       11   9   9   9  \n",
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              "\n",
              "[395 rows x 33 columns]"
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              "\n",
              "  <div id=\"df-d5216f9b-d30d-485f-b5a6-30b2873ba08c\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <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></th>\n",
              "      <th>school</th>\n",
              "      <th>sex</th>\n",
              "      <th>age</th>\n",
              "      <th>address</th>\n",
              "      <th>famsize</th>\n",
              "      <th>Pstatus</th>\n",
              "      <th>Medu</th>\n",
              "      <th>Fedu</th>\n",
              "      <th>Mjob</th>\n",
              "      <th>Fjob</th>\n",
              "      <th>...</th>\n",
              "      <th>famrel</th>\n",
              "      <th>freetime</th>\n",
              "      <th>goout</th>\n",
              "      <th>Dalc</th>\n",
              "      <th>Walc</th>\n",
              "      <th>health</th>\n",
              "      <th>absences</th>\n",
              "      <th>G1</th>\n",
              "      <th>G2</th>\n",
              "      <th>G3</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>GP</td>\n",
              "      <td>F</td>\n",
              "      <td>18</td>\n",
              "      <td>U</td>\n",
              "      <td>GT3</td>\n",
              "      <td>A</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>at_home</td>\n",
              "      <td>teacher</td>\n",
              "      <td>...</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>6</td>\n",
              "      <td>5</td>\n",
              "      <td>6</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>GP</td>\n",
              "      <td>F</td>\n",
              "      <td>17</td>\n",
              "      <td>U</td>\n",
              "      <td>GT3</td>\n",
              "      <td>T</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>at_home</td>\n",
              "      <td>other</td>\n",
              "      <td>...</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>GP</td>\n",
              "      <td>F</td>\n",
              "      <td>15</td>\n",
              "      <td>U</td>\n",
              "      <td>LE3</td>\n",
              "      <td>T</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>at_home</td>\n",
              "      <td>other</td>\n",
              "      <td>...</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>10</td>\n",
              "      <td>7</td>\n",
              "      <td>8</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>GP</td>\n",
              "      <td>F</td>\n",
              "      <td>15</td>\n",
              "      <td>U</td>\n",
              "      <td>GT3</td>\n",
              "      <td>T</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>health</td>\n",
              "      <td>services</td>\n",
              "      <td>...</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>15</td>\n",
              "      <td>14</td>\n",
              "      <td>15</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>GP</td>\n",
              "      <td>F</td>\n",
              "      <td>16</td>\n",
              "      <td>U</td>\n",
              "      <td>GT3</td>\n",
              "      <td>T</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>other</td>\n",
              "      <td>other</td>\n",
              "      <td>...</td>\n",
              "      <td>4</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "      <td>2</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>6</td>\n",
              "      <td>10</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>...</th>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "      <td>...</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>390</th>\n",
              "      <td>MS</td>\n",
              "      <td>M</td>\n",
              "      <td>20</td>\n",
              "      <td>U</td>\n",
              "      <td>LE3</td>\n",
              "      <td>A</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>services</td>\n",
              "      <td>services</td>\n",
              "      <td>...</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>4</td>\n",
              "      <td>11</td>\n",
              "      <td>9</td>\n",
              "      <td>9</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>391</th>\n",
              "      <td>MS</td>\n",
              "      <td>M</td>\n",
              "      <td>17</td>\n",
              "      <td>U</td>\n",
              "      <td>LE3</td>\n",
              "      <td>T</td>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>services</td>\n",
              "      <td>services</td>\n",
              "      <td>...</td>\n",
              "      <td>2</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>14</td>\n",
              "      <td>16</td>\n",
              "      <td>16</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>392</th>\n",
              "      <td>MS</td>\n",
              "      <td>M</td>\n",
              "      <td>21</td>\n",
              "      <td>R</td>\n",
              "      <td>GT3</td>\n",
              "      <td>T</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>other</td>\n",
              "      <td>other</td>\n",
              "      <td>...</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>10</td>\n",
              "      <td>8</td>\n",
              "      <td>7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>393</th>\n",
              "      <td>MS</td>\n",
              "      <td>M</td>\n",
              "      <td>18</td>\n",
              "      <td>R</td>\n",
              "      <td>LE3</td>\n",
              "      <td>T</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>services</td>\n",
              "      <td>other</td>\n",
              "      <td>...</td>\n",
              "      <td>4</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>4</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>11</td>\n",
              "      <td>12</td>\n",
              "      <td>10</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>394</th>\n",
              "      <td>MS</td>\n",
              "      <td>M</td>\n",
              "      <td>19</td>\n",
              "      <td>U</td>\n",
              "      <td>LE3</td>\n",
              "      <td>T</td>\n",
              "      <td>1</td>\n",
              "      <td>1</td>\n",
              "      <td>other</td>\n",
              "      <td>at_home</td>\n",
              "      <td>...</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>5</td>\n",
              "      <td>8</td>\n",
              "      <td>9</td>\n",
              "      <td>9</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>395 rows × 33 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-d5216f9b-d30d-485f-b5a6-30b2873ba08c')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "        \n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
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              "\n",
              "    .colab-df-convert:hover {\n",
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              "    [theme=dark] .colab-df-convert {\n",
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              "\n",
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              "        buttonEl.style.display =\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# check data column types\n",
        "data.dtypes"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "r-i4nd4COe2Q",
        "outputId": "081b6492-ea4d-4bc8-b2cd-375175cb34d9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "school        object\n",
              "sex           object\n",
              "age            int64\n",
              "address       object\n",
              "famsize       object\n",
              "Pstatus       object\n",
              "Medu           int64\n",
              "Fedu           int64\n",
              "Mjob          object\n",
              "Fjob          object\n",
              "reason        object\n",
              "guardian      object\n",
              "traveltime     int64\n",
              "studytime      int64\n",
              "failures       int64\n",
              "schoolsup     object\n",
              "famsup        object\n",
              "paid          object\n",
              "activities    object\n",
              "nursery       object\n",
              "higher        object\n",
              "internet      object\n",
              "romantic      object\n",
              "famrel         int64\n",
              "freetime       int64\n",
              "goout          int64\n",
              "Dalc           int64\n",
              "Walc           int64\n",
              "health         int64\n",
              "absences       int64\n",
              "G1             int64\n",
              "G2             int64\n",
              "G3             int64\n",
              "dtype: object"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Preprocess Data and Train Model**"
      ],
      "metadata": {
        "id": "rkJiVjicB8B8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "In the following section we will\n",
        "1. Drop the grades from years 1 and 2 because of high correlation with year 3\n",
        "2. Separate categorical and numerical columns\n",
        "3. Create a simple preprocessing Pipeline with scikit-learn\n",
        "4. Train a LGBM model with scikit-learn\n"
      ],
      "metadata": {
        "id": "Tp0EAmH7GOBH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# drop grades from first and second year because high correlation with third\n",
        "\n",
        "data.drop(columns = ['G1','G2'],inplace=True)"
      ],
      "metadata": {
        "id": "TQhqCl6DNa0C"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# separate categorical and numerical data\n",
        "\n",
        "categorical = []\n",
        "numerical = []\n",
        "\n",
        "for col in data.columns:\n",
        "  if col == 'G3':\n",
        "    pass\n",
        "  elif col == 'sex':\n",
        "    pass\n",
        "  elif data[col].dtype == object:\n",
        "    categorical.append(col)\n",
        "  else:\n",
        "    numerical.append(col)\n",
        "\n",
        "print (categorical)\n",
        "print (numerical)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Jmyybzg1O8MX",
        "outputId": "3700f7e8-a4b8-4272-bfea-81484aacea32"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "['school', 'address', 'famsize', 'Pstatus', 'Mjob', 'Fjob', 'reason', 'guardian', 'schoolsup', 'famsup', 'paid', 'activities', 'nursery', 'higher', 'internet', 'romantic']\n",
            "['age', 'Medu', 'Fedu', 'traveltime', 'studytime', 'failures', 'famrel', 'freetime', 'goout', 'Dalc', 'Walc', 'health', 'absences']\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Below we create a simple pipeline that will one hot encode categorical columns, and standard scale numerical ones."
      ],
      "metadata": {
        "id": "xVpMopGECEG0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# create a pipeline\n",
        "\n",
        "from sklearn.pipeline import Pipeline\n",
        "from sklearn.preprocessing import OneHotEncoder\n",
        "from sklearn.preprocessing import StandardScaler\n",
        "from sklearn.compose import ColumnTransformer\n",
        "\n",
        "\n",
        "categorical_transformer = Pipeline(steps=[('onehot', OneHotEncoder(handle_unknown='ignore'))])\n",
        "numeric_transformer = Pipeline(steps=[('scaler', StandardScaler())])\n",
        "\n",
        "preprocessor = ColumnTransformer(\n",
        "    transformers=[\n",
        "        ('num', numeric_transformer, numerical),\n",
        "        ('cat', categorical_transformer, categorical)\n",
        "    ])"
      ],
      "metadata": {
        "id": "xlAc8UflPpva"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "Below we train test split our data with a 70/30 ratio to prepare for training. We also remove the 'sex' attribute because we do not want to use protected attributes in training."
      ],
      "metadata": {
        "id": "bvruIZUbCgoP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# train test split 70/30\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "\n",
        "df_train, df_test = train_test_split(data, test_size=0.3,random_state=42)\n",
        "\n",
        "df_train_X = df_train.drop(columns=['G3','sex'])\n",
        "df_test_X = df_test.drop(columns=['G3','sex'])\n",
        "df_train_y = df_train['G3']\n",
        "df_test_y = df_test['G3']"
      ],
      "metadata": {
        "id": "KbVFtWjTNrL3"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We train a LGBM regression model. It performed best of 5 regression models tested."
      ],
      "metadata": {
        "id": "OG903PqHC0Vk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# fit and predict.\n",
        "\n",
        "from lightgbm import LGBMRegressor\n",
        "\n",
        "lgbmr = Pipeline([\n",
        "     ('preprocessor', preprocessor),\n",
        "     ('reg', LGBMRegressor())])\n",
        "\n",
        "lgbmr.fit(df_train_X,df_train_y)\n",
        "y_pred = lgbmr.predict(df_test_X)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HK-vu73BR_rd",
        "outputId": "739cad4a-efa6-4ae6-a5b8-f9fdef8142ac"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/sklearn/preprocessing/_encoders.py:110: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
            "  X_int = np.zeros((n_samples, n_features), dtype=np.int)\n",
            "/usr/local/lib/python3.7/dist-packages/sklearn/preprocessing/_encoders.py:111: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
            "  X_mask = np.ones((n_samples, n_features), dtype=np.bool)\n",
            "/usr/local/lib/python3.7/dist-packages/sklearn/preprocessing/_encoders.py:110: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
            "  X_int = np.zeros((n_samples, n_features), dtype=np.int)\n",
            "/usr/local/lib/python3.7/dist-packages/sklearn/preprocessing/_encoders.py:111: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
            "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
            "  X_mask = np.ones((n_samples, n_features), dtype=np.bool)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## **Display Performance and Bias Metrics**"
      ],
      "metadata": {
        "id": "3gunvpy8B8J8"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We must define vectors containing the sex of the individuals to check for bias."
      ],
      "metadata": {
        "id": "qs8DCZmYHhdH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# define minority and majority vectors\n",
        "gmaj = df_test['sex']=='M'\n",
        "gmin = df_test['sex']=='F'\n",
        "gmaj = gmaj.to_numpy()\n",
        "gmin = gmin.to_numpy()\n",
        "yobs = df_test_y.to_numpy()"
      ],
      "metadata": {
        "id": "R1HAA0QPSUfB"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "We can now compute a range of accuracy and fairness metrics, displayed in the dataframe below. The first two are accuracy metrics, the remaining 11 are fairness metrics."
      ],
      "metadata": {
        "id": "5aikYt0EFJSB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "compute_model_metrics(ypred=y_pred, yobs=yobs, gmaj=gmaj, gmin=gmin)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 488
        },
        "id": "OSvWYho_1YpX",
        "outputId": "ff3c7823-750f-4544-8959-bea971c07be7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                                  Metric     Value\n",
              "0                    Concurrent Validity  0.537991\n",
              "1                                   RMSE  3.973615\n",
              "2               Disparate Impact (Q 90%)  0.751232\n",
              "3               Disparate Impact (Q 80%)  0.525862\n",
              "4               Disparate Impact (Q 50%)  0.949944\n",
              "5                       Avg Score Spread -0.706965\n",
              "6             Avg Score Spread (top 20%)  0.240590\n",
              "7                         Z-score Spread -0.050052\n",
              "8               Z-score Spread (top 20%)  0.115542\n",
              "9                         Adv Impact AUC  0.579141\n",
              "10            Concurrent Validity Spread  0.141491\n",
              "11                            RMSE Ratio  1.064280\n",
              "12  Concurrent Validity Spread (top 20%)  0.600145\n",
              "13                  RMSE Ratio (top 20%)  1.052818"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-95cf91e4-4186-45cd-9518-9a51c165e8b1\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Metric</th>\n",
              "      <th>Value</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>Concurrent Validity</td>\n",
              "      <td>0.537991</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>RMSE</td>\n",
              "      <td>3.973615</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>Disparate Impact (Q 90%)</td>\n",
              "      <td>0.751232</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Disparate Impact (Q 80%)</td>\n",
              "      <td>0.525862</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Disparate Impact (Q 50%)</td>\n",
              "      <td>0.949944</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>Avg Score Spread</td>\n",
              "      <td>-0.706965</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>6</th>\n",
              "      <td>Avg Score Spread (top 20%)</td>\n",
              "      <td>0.240590</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>7</th>\n",
              "      <td>Z-score Spread</td>\n",
              "      <td>-0.050052</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>8</th>\n",
              "      <td>Z-score Spread (top 20%)</td>\n",
              "      <td>0.115542</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9</th>\n",
              "      <td>Adv Impact AUC</td>\n",
              "      <td>0.579141</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>10</th>\n",
              "      <td>Concurrent Validity Spread</td>\n",
              "      <td>0.141491</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>11</th>\n",
              "      <td>RMSE Ratio</td>\n",
              "      <td>1.064280</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>12</th>\n",
              "      <td>Concurrent Validity Spread (top 20%)</td>\n",
              "      <td>0.600145</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>13</th>\n",
              "      <td>RMSE Ratio (top 20%)</td>\n",
              "      <td>1.052818</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
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              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
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              "    .colab-df-convert:hover {\n",
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              "      fill: #174EA6;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
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              "\n",
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              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## ***Final Remarks***"
      ],
      "metadata": {
        "id": "jb9BtnJgguIT"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "We observe through some metrics that there is a strong negative bias towards students of female sex. For instance we look at the Disparate Impact Q 80% of 0.52 (a value of 1 would be fair). This means male students are about 2 times more likely to be predicted in the top 20% of grades. We would like to avoid such prediction bias, as it might be detrimental to female students in admissions or other scenarios."
      ],
      "metadata": {
        "id": "4wiJEkSagyAg"
      }
    }
  ]
}