{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Medical Expenditure Tutorial" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## This tutorial demonstrates classification model learning with bias mitigation as a part of a Care Management use case using Medical Expenditure data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The notebook demonstrates how the AIF 360 toolkit can be used to detect and reduce bias when learning classifiers using a variety of fairness metrics and algorithms . It also demonstrates how explanations can be generated for predictions made by models learnt with the toolkit using LIME.\n", "\n", "Classifiers are built using Logistic Regression as well as Random Forests.\n", "\n", "Bias detection is demonstrated using several metrics, including disparate impact, average odds difference, statistical parity difference, equal opportunity difference, and Theil index.\n", "\n", "Bias alleviation is explored via a variety of methods, including reweighing (pre-processing algorithm), prejudice remover (in-processing algorithm), and disparate impact remover (pre-processing technique).\n", "\n", "Data from the [Medical Expenditure Panel Survey](https://meps.ahrq.gov/mepsweb/) is used in this tutorial. See [Section 2](#data_used) below for more details.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Table of Contents" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[1. Use Case](#use_case)
\n", "[2. Data Used](#data_used)
\n", "[3. Learning model (from 2015 Panel 19 data)](#2015-data)
\n", "    [3.1. Load data & create splits for learning/validating/testing model](#2015-data-load)
\n", "    [3.2. Learning model from original data](#original-2015-data)
\n", "        [3.2.1. Metrics for original data](#original-2015-metrics)
\n", "        [3.2.2. Learning Logistic Regression (LR) classifier from original data](#lr_orig)
\n", "            [3.2.2.1. Training LR model from original data](#lr-train)
\n", "            [3.2.2.2. Validating LR model from original data](#lr-validate)
\n", "            [3.2.2.3. Testing LR model from original data](#lr-test)
\n", "        [3.2.3. Learning Random Forest (RF) classifier from original data](#rf_orig)
\n", "            [3.2.3.1. Training RF model from original data](#rf-train)
\n", "            [3.2.3.2. Validating RF model from original data](#rf-validate)
\n", "            [3.2.3.3. Testing RF model from original data](#rf-test)
\n", "    [3.3 Bias Mitigation using pre-processing technique - Reweighing](#reweighing-2015)
\n", "        [3.3.1. Transform data](#reweighing-2015-transform)
\n", "        [3.3.2. Metrics for transformed data](#reweighing-2015-metrics)
\n", "        [3.3.3. Learning Logistic Regression (LR) classifier from data transformed by reweighing](#lr_transf)
\n", "            [3.3.3.1. Training LR model after reweighing](#lr-rw-train)
\n", "            [3.3.3.2. Validating LR model after reweighing](#lr-rw-validate)
\n", "            [3.3.3.3. Testing LR model after reweighing](#lr-rw-test)
\n", "        [3.3.4. Learning Random Forest classifier (RF) from data transformed by reweighing](#rf_transf)
\n", "            [3.3.4.1. Training RF model after reweighing](#rf-rw-train)
\n", "            [3.3.4.2. Validating RF model after reweighing](#rf-rw-validate)
\n", "            [3.3.4.3. Testing RF model after reweighing](#rf-rw-test)
\n", "    [3.4. Bias Mitigation using in-processing technique - Prejudice Remover (PR)](#kamishima)
\n", "        [3.4.1. Training PR model](#ks-train)
\n", "        [3.4.2. Validating PR model](#ks-validate)
\n", "        [3.4.3. Testing PR model](#ks-test)
\n", "    [3.5. Bias Mitigation using pre-processing technique - Disparate Impact Remover (DIR)](#disparate-impact)
\n", "        [3.5.1. Training DIR model](#di-train)
\n", "        [3.5.2. Validating DIR model](#di-validate)
\n", "        [3.5.3. Testing DIR model](#di-test)
\n", "    [3.6. Summary of Model Learning Results](#summary-2015-learning)
\n", "[4. Deploying model](#deployment-2015-2015)
\n", "    [4.1. Testing learned model on 2015 Panel 20 deployment data](#deployment-2015)
\n", "    [4.2. Generating explanations for model predictions on 2015 Panel 20 deployment data using LIME](#lime)
\n", "    [4.3. Testing learned model on 2016 Panel 21 deployment data](#deployment-2016)
\n", "[5. Re-learning model (from 2016 Panel 21 data)](#learning-2016)
\n", "[6. Re-deploying Model](#deployment-2016-2016)
\n", "[7. Overall Summary](#final-summary)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Use Case" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to demonstrate how AIF 360 can be used to detect and mitigate bias in classfier models, we adopt the following use case:\n", "\n", "a) a data scientist develops a 'fair' healthcare utilization scoring model with respect to defined protected classes. Fairness may be dictated by legal or government regulations, such as a requirement that additional care decisions be not predicated on factors such as race of the patient.\n", "\n", "b) developer takes the model AND performance characteristics / specs of the model (e.g. accuracy, fairness tests, etc. basically the model factsheet) and deploys the model in an enterprise app that prioritizes cases for care management.\n", "\n", "c) the app is put into production and starts scoring people and making recommendations. \n", "\n", "d) explanations are generated for each recommendation\n", "\n", "e) both recommendations and associated explanations are given to nurses as a part of the care management process. The nurses can evaluate the recommendations for quality and correctness and provide feedback.\n", "\n", "f) nurse feedback as well as analysis of usage data with respect to specs of the model w.r.t accuracy and fairness is communicated to AI Ops specialist and LOB user periodically.\n", "\n", "g) when significant drift in model specs relative to the model factsheet is observed, the model is sent back for retraining." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Data used" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The specific data used is the [2015 Full Year Consolidated Data File](https://meps.ahrq.gov/mepsweb/data_stats/download_data_files_detail.jsp?cboPufNumber=HC-181) as well as the [2016 Full Year Consolidated Data File](https://meps.ahrq.gov/mepsweb/data_stats/download_data_files_detail.jsp?cboPufNumber=HC-192)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The 2015 file contains data from rounds 3,4,5 of panel 19 (2014) and rounds 1,2,3 of panel 20 (2015). The 2016 file contains data from rounds 3,4,5 of panel 20 (2015) and rounds 1,2,3 of panel 21 (2016).\n", "\n", "For this demonstration, three datasets were constructed: one from panel 19, round 5 (used for learning models), one from panel 20, round 3 (used for deployment/testing of model - steps); the other from panel 21, round 3 (used for re-training and deployment/testing of updated model)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For each dataset, the sensitive attribute is 'RACE' constructed as follows: 'Whites' (privileged class) defined by the features RACEV2X = 1 (White) and HISPANX = 2 (non Hispanic); 'Non-Whites' that included everyone else. \n", "\n", "Along with race as the sensitive feature, other features used for modeling include demographics (such as age, gender, active duty status), physical/mental health assessments, diagnosis codes (such as history of diagnosis of cancer, or diabetes), and limitations (such as cognitive or hearing or vision limitation).\n", "\n", "To measure utilization, a composite feature, 'UTILIZATION', was created to measure the total number of trips requiring some sort of medical care by summing up the following features: OBTOTV15(16), the number of office based visits; OPTOTV15(16), the number of outpatient visits; ERTOT15(16), the number of ER visits; IPNGTD15(16), the number of inpatient nights, and + HHTOTD16, the number of home health visits.\n", "\n", "The model classification task is to predict whether a person would have 'high' utilization (defined as UTILIZATION >= 10, roughly the average utilization for the considered population). High utilization respondents constituted around 17% of each dataset.\n", "\n", "To simulate the scenario, each dataset is split into 3 parts: a train, a validation, and a test/deployment part.\n", "\n", "We assume that the model is initially built and tuned using the 2015 Panel 19 train/test data. (Use case steps a-b.)\n", "It is then put into practice and used to score people to identify potential candidates for care management (Use case steps c-e). Initial deployment is simulated to 2015 Panel 20 test/deployment data. To show change in performance and/or fairness over time, (use case steps f-g), the 2016 Panel 21 test/deployment data is used. Finally, if drift is observed, the 2016 train/validation data is used to learn a new model and evaluated again on the 2016 test/deployment data" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "C:\\ProgramData\\Anaconda3\\lib\\site-packages\\h5py\\__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n", " from ._conv import register_converters as _register_converters\n" ] } ], "source": [ "# Load all necessary packages\n", "import sys\n", "sys.path.append(\"../\")\n", "import numpy as np\n", "\n", "#Datasets\n", "from aif360.datasets.meps_dataset_panel19_fy2015 import MEPSDataset19\n", "from aif360.datasets.meps_dataset_panel20_fy2015 import MEPSDataset20\n", "from aif360.datasets.meps_dataset_panel21_fy2016 import MEPSDataset21\n", "\n", "#Fairness Metrics\n", "from aif360.metrics import BinaryLabelDatasetMetric\n", "from aif360.metrics import ClassificationMetric\n", "\n", "#Scalers\n", "from sklearn.preprocessing import StandardScaler\n", "from sklearn.preprocessing import MinMaxScaler\n", "\n", "from sklearn.metrics import accuracy_score\n", "\n", "#Classifiers\n", "from sklearn.ensemble import RandomForestClassifier\n", "from sklearn.linear_model import LogisticRegression\n", "\n", "#Bias Mitigation Techniques\n", "from aif360.algorithms.preprocessing.reweighing import Reweighing\n", "from aif360.algorithms.inprocessing.prejudice_remover import PrejudiceRemover\n", "from aif360.algorithms.preprocessing import DisparateImpactRemover\n", "\n", "\n", "from IPython.display import Markdown, display\n", "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "\n", "#LIME\n", "from aif360.datasets.lime_encoder import LimeEncoder\n", "import lime\n", "import lime.lime_tabular\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Learning model (from 2015 Panel 19 data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.1. Load data & create splits for learning/validating/testing model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Get the dataset and split into train, validate, and test\n", "seed = 1\n", "np.random.seed(seed)\n", "split_1 = 0.5\n", "split_2 = 0.8\n", "shuffle=True\n", "\n", "dataset_orig_panel19 = MEPSDataset19()\n", "dataset_orig_panel19_train, dataset_orig_panel19_validate, dataset_orig_panel19_test = \\\n", " dataset_orig_panel19.split([split_1,split_2], shuffle=shuffle)\n", "\n", "sens_attr = dataset_orig_panel19_train.protected_attribute_names[0]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Show 2015 dataset details**" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Training Dataset shape" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(7915, 138)\n" ] }, { "data": { "text/markdown": [ "#### Validation Dataset shape" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(4749, 138)\n" ] }, { "data": { "text/markdown": [ "#### Test Dataset shape" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(3166, 138)\n" ] }, { "data": { "text/markdown": [ "#### Favorable and unfavorable labels" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "1.0 0.0\n" ] }, { "data": { "text/markdown": [ "#### Protected attribute names" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "['RACE']\n" ] }, { "data": { "text/markdown": [ "#### Privileged and unprivileged protected attribute values" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[array([1.])] [array([0.])]\n" ] }, { "data": { "text/markdown": [ "#### Dataset feature names" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "['RACE', 'AGE', 'PCS42', 'K6SUM42', 'MCS42', 'REGION=1', 'REGION=2', 'REGION=3', 'REGION=4', 'SEX=1', 'SEX=2', 'MARRY=1', 'MARRY=2', 'MARRY=3', 'MARRY=4', 'MARRY=5', 'MARRY=6', 'MARRY=7', 'MARRY=8', 'MARRY=9', 'MARRY=10', 'FTSTU=-1', 'FTSTU=1', 'FTSTU=2', 'FTSTU=3', 'ACTDTY=1', 'ACTDTY=2', 'ACTDTY=3', 'ACTDTY=4', 'HONRDC=1', 'HONRDC=2', 'HONRDC=3', 'HONRDC=4', 'RTHLTH=-1', 'RTHLTH=1', 'RTHLTH=2', 'RTHLTH=3', 'RTHLTH=4', 'RTHLTH=5', 'MNHLTH=-1', 'MNHLTH=1', 'MNHLTH=2', 'MNHLTH=3', 'MNHLTH=4', 'MNHLTH=5', 'HIBPDX=-1', 'HIBPDX=1', 'HIBPDX=2', 'CHDDX=-1', 'CHDDX=1', 'CHDDX=2', 'ANGIDX=-1', 'ANGIDX=1', 'ANGIDX=2', 'MIDX=-1', 'MIDX=1', 'MIDX=2', 'OHRTDX=-1', 'OHRTDX=1', 'OHRTDX=2', 'STRKDX=-1', 'STRKDX=1', 'STRKDX=2', 'EMPHDX=-1', 'EMPHDX=1', 'EMPHDX=2', 'CHBRON=-1', 'CHBRON=1', 'CHBRON=2', 'CHOLDX=-1', 'CHOLDX=1', 'CHOLDX=2', 'CANCERDX=-1', 'CANCERDX=1', 'CANCERDX=2', 'DIABDX=-1', 'DIABDX=1', 'DIABDX=2', 'JTPAIN=-1', 'JTPAIN=1', 'JTPAIN=2', 'ARTHDX=-1', 'ARTHDX=1', 'ARTHDX=2', 'ARTHTYPE=-1', 'ARTHTYPE=1', 'ARTHTYPE=2', 'ARTHTYPE=3', 'ASTHDX=1', 'ASTHDX=2', 'ADHDADDX=-1', 'ADHDADDX=1', 'ADHDADDX=2', 'PREGNT=-1', 'PREGNT=1', 'PREGNT=2', 'WLKLIM=-1', 'WLKLIM=1', 'WLKLIM=2', 'ACTLIM=-1', 'ACTLIM=1', 'ACTLIM=2', 'SOCLIM=-1', 'SOCLIM=1', 'SOCLIM=2', 'COGLIM=-1', 'COGLIM=1', 'COGLIM=2', 'DFHEAR42=-1', 'DFHEAR42=1', 'DFHEAR42=2', 'DFSEE42=-1', 'DFSEE42=1', 'DFSEE42=2', 'ADSMOK42=-1', 'ADSMOK42=1', 'ADSMOK42=2', 'PHQ242=-1', 'PHQ242=0', 'PHQ242=1', 'PHQ242=2', 'PHQ242=3', 'PHQ242=4', 'PHQ242=5', 'PHQ242=6', 'EMPST=-1', 'EMPST=1', 'EMPST=2', 'EMPST=3', 'EMPST=4', 'POVCAT=1', 'POVCAT=2', 'POVCAT=3', 'POVCAT=4', 'POVCAT=5', 'INSCOV=1', 'INSCOV=2', 'INSCOV=3']\n" ] } ], "source": [ "# print out some labels, names, etc.\n", "display(Markdown(\"#### Training Dataset shape\"))\n", "print(dataset_orig_panel19_train.features.shape)\n", "display(Markdown(\"#### Validation Dataset shape\"))\n", "print(dataset_orig_panel19_validate.features.shape)\n", "display(Markdown(\"#### Test Dataset shape\"))\n", "print(dataset_orig_panel19_test.features.shape)\n", "display(Markdown(\"#### Favorable and unfavorable labels\"))\n", "print(dataset_orig_panel19_train.favorable_label, dataset_orig_panel19_train.unfavorable_label)\n", "display(Markdown(\"#### Protected attribute names\"))\n", "print(dataset_orig_panel19_train.protected_attribute_names)\n", "display(Markdown(\"#### Privileged and unprivileged protected attribute values\"))\n", "print(dataset_orig_panel19_train.privileged_protected_attributes, \n", " dataset_orig_panel19_train.unprivileged_protected_attributes)\n", "display(Markdown(\"#### Dataset feature names\"))\n", "print(dataset_orig_panel19_train.feature_names)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.2. Learning model from original data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2.1. Metrics for original data" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Original training dataset" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean outcomes between privileged and unprivileged groups = -0.136594\n" ] } ], "source": [ "# Metric for the original dataset\n", "sens_idx = dataset_orig_panel19_train.protected_attribute_names.index(sens_attr)\n", "privileged_groups = [{sens_attr:dataset_orig_panel19_train.privileged_protected_attributes[sens_idx][0]}]\n", "unprivileged_groups = [{sens_attr:dataset_orig_panel19_train.unprivileged_protected_attributes[sens_idx][0]}]\n", "metric_orig_panel19_train = BinaryLabelDatasetMetric(dataset_orig_panel19_train, \n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "display(Markdown(\"#### Original training dataset\"))\n", "print(\"Difference in mean outcomes between privileged and unprivileged groups = %f\" % \\\n", " metric_orig_panel19_train.mean_difference())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2.2. Learning Logistic Regression (LR) classifier from original data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2.2.1. Training LR model from original data" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Train model on given dataset\n", "\n", "dataset = dataset_orig_panel19_train # data to train on\n", "\n", "scale = StandardScaler().fit(dataset.features) # remember the scale\n", "\n", "model = LogisticRegression(random_state = 1) # model to learn\n", "\n", "X_train = scale.transform(dataset.features) #apply the scale\n", "y_train = dataset.labels.ravel()\n", "\n", "\n", "model.fit(X_train, y_train,\n", " sample_weight=dataset.instance_weights)\n", "y_train_pred = model.predict(X_train)\n", "\n", "#save model\n", "lr_orig_panel19 = model\n", "lr_scale_orig_panel19 = scale" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2.2.2. Validating LR model from original data" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████| 50/50 [00:00<00:00, 176.05it/s]\n" ] } ], "source": [ "#Validate model on given dataset and find threshold for best balanced accuracy\n", "import numpy as np\n", "from tqdm import tqdm\n", "thresh_arr = np.linspace(0.01, 0.5, 50)\n", "\n", "scale = lr_scale_orig_panel19\n", "\n", "model = lr_orig_panel19 #model to validate\n", "dataset = dataset_orig_panel19_validate #data to validate on\n", "\n", "X_validate = scale.transform(dataset.features) #apply the same scale as applied to the training data\n", "y_validate = dataset.labels.ravel()\n", "y_validate_pred_prob = model.predict_proba(X_validate)\n", "\n", "\n", "bal_acc_arr = []\n", "disp_imp_arr = []\n", "avg_odds_diff_arr = []\n", "stat_par_diff = []\n", "eq_opp_diff = []\n", "theil_ind = []\n", " \n", "for thresh in tqdm(thresh_arr):\n", " y_validate_pred = (y_validate_pred_prob[:,1] > thresh).astype(np.double)\n", "\n", " dataset_pred = dataset.copy()\n", " dataset_pred.labels = y_validate_pred\n", "\n", " classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", " bal_acc = 0.5*(classified_metric.true_positive_rate() + classified_metric.true_negative_rate())\n", " \n", " acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", " bal_acc_arr.append(bal_acc)\n", " avg_odds_diff_arr.append(classified_metric.average_odds_difference())\n", " disp_imp_arr.append(metric_pred.disparate_impact())\n", " stat_par_diff.append(classified_metric.statistical_parity_difference())\n", " eq_opp_diff.append(classified_metric.equal_opportunity_difference())\n", " theil_ind.append(classified_metric.theil_index())\n", "\n", " \n", "thresh_arr_best_ind = np.where(bal_acc_arr == np.max(bal_acc_arr))[0][0]\n", "thresh_arr_best = np.array(thresh_arr)[thresh_arr_best_ind]\n", "\n", "best_bal_acc = bal_acc_arr[thresh_arr_best_ind]\n", "disp_imp_at_best_bal_acc = np.abs(1.0-np.array(disp_imp_arr))[thresh_arr_best_ind]\n", "\n", "avg_odds_diff_at_best_bal_acc = avg_odds_diff_arr[thresh_arr_best_ind]\n", "\n", "stat_par_diff_at_best_bal_acc = stat_par_diff[thresh_arr_best_ind]\n", "eq_opp_diff_at_best_bal_acc = eq_opp_diff[thresh_arr_best_ind]\n", "theil_ind_at_best_bal_acc = theil_ind[thresh_arr_best_ind]" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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+zUIY0CKUqn7S1S/EpUgodWMSSiueJ7/dzcJdMSz9Rz9ahJXhYvg5ObBxowmh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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot balanced accuracy, abs(1-disparate impact)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, np.abs(1.0-np.array(disp_imp_arr)), color='r')\n", "ax2.set_ylabel('abs(1-disparate impact)', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], \n", " color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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Ga9Y497rC4U6du8Dfv97NukNpDI0J5bWxnQir72N2LFPIHF3nSDiTzd0fbeFsbgGzb+/G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Jr1oIhYBfysMOmTtcoVb4SqMW9PUrcFSK19hwI7MnKZunqbNwMHklpATwQuIfWXPIzUektEvBAR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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot average odds difference\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, avg_odds_diff_arr, color='r')\n", "ax2.set_ylabel('avg. odds diff.', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.1900\n", "Best balanced accuracy: 0.7627\n", "Corresponding abs(1-disparate impact) value: 0.6066\n", "Corresponding average odds difference value: -0.1831\n", "Corresponding statistical parity difference value: -0.2643\n", "Corresponding equal opportunity difference value: -0.1608\n", "Corresponding Theil index value: 0.0936\n" ] } ], "source": [ "lr_thresh_arr_orig_panel19_best = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % lr_thresh_arr_orig_panel19_best)\n", "lr_best_bal_acc_arr_orig_panel19 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_orig_panel19)\n", "lr_disp_imp_at_best_bal_acc_orig_panel19 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_orig_panel19)\n", "lr_avg_odds_diff_at_best_bal_acc_orig_panel19 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_orig_panel19)\n", "lr_stat_par_diff_at_best_bal_acc_orig_panel19 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_orig_panel19)\n", "lr_eq_opp_diff_at_best_bal_acc_orig_panel19 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_orig_panel19)\n", "lr_theil_ind_at_best_bal_acc_orig_panel19 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_orig_panel19)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2.2.3. Testing LR model from original data" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Evaluate performance of a given model with a given threshold on a given dataset\n", "\n", "scale = lr_scale_orig_panel19\n", "\n", "dataset = dataset_orig_panel19_test #apply model to this data\n", "model = lr_orig_panel19 #this is the model applied\n", " #lr_transf_panel19 is LR model learned from Panel panel19 (panel1914)\n", " #transformed data\n", "thresh_arr = lr_thresh_arr_orig_panel19_best # lr_thresh_arr_transf_panel19_best wass threshold for LR\n", " # model with highest balanced accuracy\n", "\n", "\n", "X_data = scale.transform(dataset.features)\n", "y_data = dataset.labels.ravel()\n", "y_data_pred_prob = model.predict_proba(X_data) \n", "\n", " \n", "y_pred = (y_data_pred_prob[:,1] > thresh_arr).astype(np.double)\n", "\n", "dataset_pred = dataset.copy()\n", "dataset_pred.labels = y_pred\n", "\n", "classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", "TPR = classified_metric.true_positive_rate()\n", "TNR = classified_metric.true_negative_rate()\n", "bal_acc = 0.5*(TPR+TNR)\n", " \n", "acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", "\n", "#get results\n", "best_bal_acc = bal_acc\n", "disp_imp_at_best_bal_acc = np.abs(1.0-metric_pred.disparate_impact())\n", "\n", "avg_odds_diff_at_best_bal_acc = classified_metric.average_odds_difference()\n", "\n", "stat_par_diff_at_best_bal_acc = classified_metric.statistical_parity_difference()\n", "eq_opp_diff_at_best_bal_acc = classified_metric.equal_opportunity_difference()\n", "theil_ind_at_best_bal_acc = classified_metric.theil_index()" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.1900\n", "Best balanced accuracy: 0.7759\n", "Corresponding abs(1-disparate impact) value: 0.5738\n", "Corresponding average odds difference value: -0.2057\n", "Corresponding statistical parity difference value: -0.2612\n", "Corresponding equal opportunity difference value: -0.2228\n", "Corresponding Theil index value: 0.0921\n" ] } ], "source": [ "lr_thresh_arr_orig_panel19_best_test = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % lr_thresh_arr_orig_panel19_best_test)\n", "lr_best_bal_acc_arr_orig_panel19_best_test = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_orig_panel19_best_test)\n", "lr_disp_imp_at_best_bal_acc_orig_panel19_best_test = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_orig_panel19_best_test)\n", "lr_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test)\n", "\n", "lr_stat_par_diff_at_best_bal_acc_orig_panel19_best_test = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_orig_panel19_best_test)\n", "lr_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test)\n", "lr_theil_ind_at_best_bal_acc_orig_panel19_best_test = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_orig_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For all the fairness metrics displayed above, the value should be close to '0' for fairness.\n", "\n", "abs(1-disparate impact) is typically desired to be < 0.2 for classifier predictions to be fair.\n", "\n", "However, for a logistic regression classifier trained with original training data, at the best classification rate, this is quite high. This implies unfairness.\n", "\n", "Similarly, average odds difference = 0.5((FPR_unpriv-FPR_priv)+(TPR_unpriv-TPR_priv)) must be close to zero for the classifier to be fair.\n", "\n", "For a logistic regression classifier trained with original training data, at the best classification rate, this is still high. This still implies unfairness." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2.3. Learning Random Forest (RF) classifier from original data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2.3.1. Training RF model from original data" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Train model on given dataset\n", "\n", "dataset = dataset_orig_panel19_train # data to train on\n", "\n", "scale = StandardScaler().fit(dataset.features) # remember the scale\n", "\n", "nestimators = 500\n", "minsamplesleaf = 25\n", "\n", "model = RandomForestClassifier(n_estimators = nestimators, min_samples_leaf = minsamplesleaf)\n", "\n", "X_train = scale.transform(dataset.features) #apply the scale\n", "y_train = dataset.labels.ravel()\n", "\n", "\n", "model.fit(X_train, y_train,\n", " sample_weight=dataset.instance_weights)\n", "y_train_pred = model.predict(X_train)\n", "\n", "#save model\n", "rf_orig_panel19 = model\n", "rf_scale_orig_panel19 = scale" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2.3.2. Validating RF model from original data" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████| 50/50 [00:00<00:00, 176.05it/s]\n" ] } ], "source": [ "#validate model on given dataset and find threshold for best balanced accuracy\n", "import numpy as np\n", "from tqdm import tqdm\n", "thresh_arr = np.linspace(0.01, 0.5, 50)\n", "\n", "scale = rf_scale_orig_panel19\n", "\n", "model = rf_orig_panel19 #model to validate\n", "dataset = dataset_orig_panel19_validate #data to validate on\n", "\n", "X_validate = scale.transform(dataset.features) #apply the same scale as applied to the training data\n", "y_validate = dataset.labels.ravel()\n", "y_validate_pred_prob = model.predict_proba(X_validate)\n", "\n", "\n", "bal_acc_arr = []\n", "disp_imp_arr = []\n", "avg_odds_diff_arr = [] \n", "stat_par_diff = []\n", "eq_opp_diff = []\n", "theil_ind = []\n", " \n", "for thresh in tqdm(thresh_arr):\n", " y_validate_pred = (y_validate_pred_prob[:,1] > thresh).astype(np.double)\n", "\n", " dataset_pred = dataset.copy()\n", " dataset_pred.labels = y_validate_pred\n", "\n", " classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", " bal_acc = 0.5*(classified_metric.true_positive_rate() + classified_metric.true_negative_rate())\n", " \n", " acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", " bal_acc_arr.append(bal_acc)\n", " avg_odds_diff_arr.append(classified_metric.average_odds_difference())\n", " disp_imp_arr.append(metric_pred.disparate_impact())\n", " stat_par_diff.append(classified_metric.statistical_parity_difference())\n", " eq_opp_diff.append(classified_metric.equal_opportunity_difference())\n", " theil_ind.append(classified_metric.theil_index())\n", " \n", "thresh_arr_best_ind = np.where(bal_acc_arr == np.max(bal_acc_arr))[0][0]\n", "thresh_arr_best = np.array(thresh_arr)[thresh_arr_best_ind]\n", "\n", "best_bal_acc = bal_acc_arr[thresh_arr_best_ind]\n", "disp_imp_at_best_bal_acc = np.abs(1.0-np.array(disp_imp_arr))[thresh_arr_best_ind]\n", "\n", "avg_odds_diff_at_best_bal_acc = avg_odds_diff_arr[thresh_arr_best_ind]\n", "\n", "stat_par_diff_at_best_bal_acc = stat_par_diff[thresh_arr_best_ind]\n", "eq_opp_diff_at_best_bal_acc = eq_opp_diff[thresh_arr_best_ind]\n", "theil_ind_at_best_bal_acc = theil_ind[thresh_arr_best_ind]" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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DHTj+WIgKTkKpG5NQKhxtd3wqd83YSEigD9892J0aVfzMLqlo+/bpELpwIfz9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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot balanced accuracy, abs(1-disparate impact)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, np.abs(1.0-np.array(disp_imp_arr)), color='r')\n", "ax2.set_ylabel('abs(1-disparate impact)', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], \n", " color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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Ry8i5W8mzaOaM7EBIoHRYcGbffPON2SEIF+fhoXj5tlb4enkw89d4svMsPDew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\ntnB7AiGBPvRuVsvsUIQQwvH+8x8jyR0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vDlu3Qnrk/fhpRzP54Zf9VrZgQqpr16507drV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\n7XUoxuTpvffe8zoEk5cVK+DwYeiZ+wM3Y4zJh0h5oC/wZ+BywP9Rsn/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XDP40s4Yez/8NqylYw7axDXnTGQ7bfulHVo1hrHHw9PPw0HHRTLGUaMgNWrW/bcqVNhp53ihSus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\nhGrise7Es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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot average odds difference\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, avg_odds_diff_arr, color='r')\n", "ax2.set_ylabel('avg. odds diff.', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2200\n", "Best balanced accuracy: 0.7735\n", "Corresponding abs(1-disparate impact) value: 0.4850\n", "Corresponding average odds difference value: -0.1213\n", "Corresponding statistical parity difference value: -0.1984\n", "Corresponding equal opportunity difference value: -0.1128\n", "Corresponding Theil index value: 0.0895\n" ] } ], "source": [ "rf_thresh_arr_orig_panel19_best = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % rf_thresh_arr_orig_panel19_best)\n", "rf_best_bal_acc_arr_orig_panel19 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % rf_best_bal_acc_arr_orig_panel19)\n", "rf_disp_imp_at_best_bal_acc_orig_panel19 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % rf_disp_imp_at_best_bal_acc_orig_panel19)\n", "rf_avg_odds_diff_at_best_bal_acc_orig_panel19 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % rf_avg_odds_diff_at_best_bal_acc_orig_panel19)\n", "\n", "rf_stat_par_diff_at_best_bal_acc_orig_panel19 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % rf_stat_par_diff_at_best_bal_acc_orig_panel19)\n", "rf_eq_opp_diff_at_best_bal_acc_orig_panel19 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % rf_eq_opp_diff_at_best_bal_acc_orig_panel19)\n", "rf_theil_ind_at_best_bal_acc_orig_panel19 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % rf_theil_ind_at_best_bal_acc_orig_panel19)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.2.3.3. Testing RF model from original data" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Evaluate performance of a given model with a given threshold on a given dataset\n", "\n", "scale = rf_scale_orig_panel19\n", "\n", "dataset = dataset_orig_panel19_test #apply model to this data\n", "model = rf_orig_panel19 #this is the model applied\n", " #lr_transf_panel19 is LR model learned from Panel panel19 (panel1914)\n", " #transformed data\n", "thresh_arr = rf_thresh_arr_orig_panel19_best # lr_thresh_arr_transf_panel19_best wass threshold for LR\n", " # model with highest balanced accuracy\n", "\n", "\n", "X_data = scale.transform(dataset.features)\n", "y_data = dataset.labels.ravel()\n", "y_data_pred_prob = model.predict_proba(X_data) \n", "\n", " \n", "y_pred = (y_data_pred_prob[:,1] > thresh_arr).astype(np.double)\n", "\n", "dataset_pred = dataset.copy()\n", "dataset_pred.labels = y_pred\n", "\n", "classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", "TPR = classified_metric.true_positive_rate()\n", "TNR = classified_metric.true_negative_rate()\n", "bal_acc = 0.5*(TPR+TNR)\n", " \n", "acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", "\n", "#get results\n", "best_bal_acc = bal_acc\n", "disp_imp_at_best_bal_acc = np.abs(1.0-metric_pred.disparate_impact())\n", "\n", "avg_odds_diff_at_best_bal_acc = classified_metric.average_odds_difference()\n", "\n", "stat_par_diff_at_best_bal_acc = classified_metric.statistical_parity_difference()\n", "eq_opp_diff_at_best_bal_acc = classified_metric.equal_opportunity_difference()\n", "theil_ind_at_best_bal_acc = classified_metric.theil_index()" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2200\n", "Best balanced accuracy: 0.7682\n", "Corresponding abs(1-disparate impact) value: 0.5021\n", "Corresponding average odds difference value: -0.1409\n", "Corresponding statistical parity difference value: -0.2182\n", "Corresponding equal opportunity difference value: -0.1222\n", "Corresponding Theil index value: 0.0933\n" ] } ], "source": [ "rf_thresh_arr_orig_panel19_best_test = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % rf_thresh_arr_orig_panel19_best_test)\n", "rf_best_bal_acc_arr_orig_panel19_best_test = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % rf_best_bal_acc_arr_orig_panel19_best_test)\n", "rf_disp_imp_at_best_bal_acc_orig_panel19_best_test = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % rf_disp_imp_at_best_bal_acc_orig_panel19_best_test)\n", "rf_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % rf_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test)\n", "\n", "rf_stat_par_diff_at_best_bal_acc_orig_panel19_best_test = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % rf_stat_par_diff_at_best_bal_acc_orig_panel19_best_test)\n", "rf_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % rf_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test)\n", "rf_theil_ind_at_best_bal_acc_orig_panel19_best_test = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % rf_theil_ind_at_best_bal_acc_orig_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As in the case of the logistic regression classifier learnt from the original data, the fairness metrics for the random forest classifier have values that are quite far from 0.\n", "\n", "For example, abs(1-disparate impact) has a value of over 0.5 as opposed to the typical desired value of < 0.2.\n", "\n", "This indicates that the random forest classifier learnt from the original data is also unfair." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.3. Bias Mitigation using pre-processing technique - Reweighing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.1. Transform data" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "RW = Reweighing(unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "RW.fit(dataset_orig_panel19_train)\n", "dataset_transf_panel19_train = RW.transform(dataset_orig_panel19_train)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.2. Metrics for transformed data" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Transformed training dataset" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean outcomes between privileged and unprivileged groups = 0.000000\n" ] } ], "source": [ "metric_transf_panel19_train = BinaryLabelDatasetMetric(dataset_transf_panel19_train, \n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "display(Markdown(\"#### Transformed training dataset\"))\n", "print(\"Difference in mean outcomes between privileged and unprivileged groups = %f\" % \\\n", " metric_transf_panel19_train.mean_difference())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.3. Learning Logistic Regression (LR) classifier from data transformed by reweighing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.3.1. Training LR model after reweighing" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Train model on given dataset\n", "\n", "dataset = dataset_transf_panel19_train # data to train on\n", "\n", "scale = StandardScaler().fit(dataset.features) # remember the scale\n", "\n", "model = LogisticRegression(random_state = 1) # model to learn\n", "\n", "X_train = scale.transform(dataset.features) #apply the scale\n", "\n", "y_train = dataset.labels.ravel()\n", "\n", "\n", "model.fit(X_train, y_train,\n", " sample_weight=dataset.instance_weights)\n", "y_train_pred = model.predict(X_train)\n", "\n", "#save model\n", "lr_transf_panel19 = model\n", "lr_scale_transf_panel19 = scale" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.3.2. Validating LR model after reweighing" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████| 50/50 [00:00<00:00, 175.43it/s]\n" ] } ], "source": [ "#validate model on given dataset and find threshold for best balanced accuracy\n", "import numpy as np\n", "from tqdm import tqdm\n", "thresh_arr = np.linspace(0.01, 0.5, 50)\n", "\n", "scale = lr_scale_transf_panel19\n", "\n", "model = lr_transf_panel19 #model to validate\n", "dataset = dataset_orig_panel19_validate #data to validate on\n", "\n", "X_validate = scale.transform(dataset.features) #apply the same scale as applied to the training data\n", "y_validate = dataset.labels.ravel()\n", "y_validate_pred_prob = model.predict_proba(X_validate)\n", "\n", "\n", "bal_acc_arr = []\n", "disp_imp_arr = []\n", "avg_odds_diff_arr = []\n", "stat_par_diff = []\n", "eq_opp_diff = []\n", "theil_ind = []\n", " \n", "for thresh in tqdm(thresh_arr):\n", " y_validate_pred = (y_validate_pred_prob[:,1] > thresh).astype(np.double)\n", "\n", " dataset_pred = dataset.copy()\n", " dataset_pred.labels = y_validate_pred\n", "\n", " classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", " bal_acc = 0.5*(classified_metric.true_positive_rate() + classified_metric.true_negative_rate())\n", " \n", " acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", " bal_acc_arr.append(bal_acc)\n", " avg_odds_diff_arr.append(classified_metric.average_odds_difference())\n", " disp_imp_arr.append(metric_pred.disparate_impact())\n", " stat_par_diff.append(classified_metric.statistical_parity_difference())\n", " eq_opp_diff.append(classified_metric.equal_opportunity_difference())\n", " theil_ind.append(classified_metric.theil_index())\n", "\n", " \n", "thresh_arr_best_ind = np.where(bal_acc_arr == np.max(bal_acc_arr))[0][0]\n", "thresh_arr_best = np.array(thresh_arr)[thresh_arr_best_ind]\n", "\n", "best_bal_acc = bal_acc_arr[thresh_arr_best_ind]\n", "disp_imp_at_best_bal_acc = np.abs(1.0-np.array(disp_imp_arr))[thresh_arr_best_ind]\n", "\n", "avg_odds_diff_at_best_bal_acc = avg_odds_diff_arr[thresh_arr_best_ind]\n", "\n", "stat_par_diff_at_best_bal_acc = stat_par_diff[thresh_arr_best_ind]\n", "eq_opp_diff_at_best_bal_acc = eq_opp_diff[thresh_arr_best_ind]\n", "theil_ind_at_best_bal_acc = theil_ind[thresh_arr_best_ind]" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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wleAqAEhLt/Hm7/uYtf4o3RtW4NMBzfHzlnaXopgZN86MphVSd6XktHR+2R5J\nXHIanu5ueLgrPN3Ms4e7G55u6vJxpRQLd0TyS2gkJb09GNO5NsPbB+HrJf8fFiqtYdYsePZZuHgR\nnnkGxo+HzMWPkZHwxRdm263oaBNsn3gCBg0CP5fNU4VGgqsEVwmugtikVB7/fgcrD5xlZIdavHBb\nQ1lU4kRmzZoFwLBhwyyto8hbutRsBj9mjAkeRdT+qEtM/OMAy/edIbCkN090q8OAG2vg5SG7eRSq\n6GgTXmfNgqAg89X/8uVmOkB6OvTubQJr166y1VUhkuAqwVWCq4uLOJ/Ag7O2cvhsHG/cFcL9rWtY\nXZLII5njaoeTJ6FpU6hSxawmd4LtibYdO8d7yw6wOfwc1cv58HSPevRuWlX+UlnYVq0yf9nZv1+m\nAxQBElwluEpwdWF7T17iga83k5yWzpRBLehY9zpX0gpRlKWlwS23wKZNZnuiBg2srshuWmtWHTzL\n+8sOsPfUJRpUKsUzt9SnW8MKsjVdYUpJMfuxtmol0wEsJsFVgqsEVxelteaeqRs4fi6B70e1pk6F\nUlaXJITjJSRA//5mr9ZvvjHbHTkhm03z+65TfPjnAY7GJNCyZlme79WAG4PKWV2aEIVKgqsEVwmu\nLmrd4WgGTd/EG31CGNKmptXliHz46quvABglvdD/7dw5uOMOMzVgyhTzda+TS0238dPWE3y6/BBn\nYpPp3rACz/VsQL2K8hdP4RokuEpwleDqou77cgPHYxJY9VwXvD0KsF+3KHDdu3cHYPny5RZXUoSc\nOAG33gpHjsB335lmA8VIYko6X68LZ+rKI8SnpNGvRTWe6lGPKmWK/txdIfJDgqsEVwmuLmjDkRgG\nfrWR13s3Ymi7IKvLEcKx9uyBnj3h0iVYuNAxbTyLqPPxKUxecZjZG46BguHtgni4i+wBK4ovCa4S\nXCW4uqCB0zZy5Gwcq5/rSglPGW0Vxcj69WZ6gLc3LFtmdhJwARHnE/jofwf5ZUckpbw9eKRrHYa1\nC5L/v0Wx4+rBVTbFEy5nc/g5NoTFMKZzbflDrZiYMmUKU6ZMsboM6/32G3TvDoGBJsC6SGgFqFbW\nl4/ua8aSJzrSsmZZ3l26ny4frOTHLceJS06zujwhhIPIiKuMuLqcITM2se9ULGue64qPlwTX4qBX\nr14ALF261OJKLDRzJowaBc2bw5IlUN61t3bbGBbDu0v3E3riAkpBrQA/GlX1J6RKaUKq+tOoSmmZ\nTiCckquPuEpwleDqUrYdO0+/L9bz0m0NGdWp4Hq0C1FotIZ334UXXzR7tc6fDyVLWl1VkaC1Zv2R\nGLYdO8/uyIvsOXmJyAuJl19zVPmWAAAgAElEQVSvWsaHkKqlCaniT0hVf1oGlaV0CU8LKxYidxJc\nJbhKcHUhQ7/ezO7Ii6wZ11X6nwvnZ7PBU0/BpElw//1m1NVLRhFzcj4+hT0nL7H75MXLYTY82vwZ\nUM7Pi7f6hNCrcWWLqxTi2iS4SnCV4OoiQk9coM/kdTzfqwFjOte2uhzhQJ9++ikAY8eOtbiSQjZu\nHLz/vgmvEyeCmyxbuB6xSansirjIO0v3syvyIn2aVeH13iH4+8roqyh6JLhKcJXg6iJGzNrCjuPn\nWTvuZvy8ZbS1OOnduzcAixYtsriSQrR9O9x4IwwfDl99BdL+NN9S021MXnGYz/8+TEBJL96/pymd\n67n2XGFR9EhwleAqwdUF7Iq4yJ2fr+XZW+vzaNc6VpcjRP6kpUGbNhAZCfv2QZkyVldUrOyKuMjT\nP4Vy6Ewcg1rX4MXbGspfdkWR4erBVb5XEi5h0t+H8Pfx5IG20tpVFAOffQbbtsGnn0poLQCNq/nz\n2+MdGNWxFt9tPk6vT9ew5eg5q8sSQiDBVbiAPScv8r+9p3mwQy1KyYrhYmnixIlMnDjR6jIKx7Fj\nMH483H473Huv1dUUWyU83Xnp9hv4YVQbNJr7vtzA20v2kZSabnVpQrg0Ca6i2Pvsr8OUKuEhrV2L\nsQ0bNrBhwwaryyh4WsOjj5rnyZNlXmshaB0cwLKxnRh4Uw2mrQ6j9+dr2R150eqyhHBZMsdV5rgW\na/ujLtHzkzU80a0uT/eoZ3U5QuTPvHlw333w0UdmJwFRqFYeOMO4+TuJiUvh3X5NuKdlNatLEi7I\n1ee4SnCV4FqsPfrtdlYdPMu6cTfL1jbCPlrDjh1mI/8aNaB//6Ixj/TCBWjYEKpUgU2bwEMWC1nh\nQkIKj363nXWHY3iqez2e6FYHJSPfohC5enCVqQKi2Dp4OpYlu08xrF2QhNZi7t133+Xdd9/N30Ui\nIuC996BxY2jZ0nSjGjMGKlWCgQPhjz8g3cL5jc8/D2fOmK2vJLRapoyvFzOH3US/FtX4ePlBnv15\nJ6npNqvLEsJlSHAVxdbnfx/Gx9OdBzvUsroUUcBCQ0MJDQ3N+xvj4mD2bOje3YyuPv88+PvD1Klw\n9ixs3QqjRsGff0LPnuacF16A/fsd/yFysnYtfPklPPkktGhRuPcW/+Hl4cbEe5swtltdft4WwfCZ\nW7iUlGp1WUK4BJkqIFMFiqXDZ+Lo8fEqHupUm+d7NbC6HFGUpKfDX3/BnDmwYAEkJEBwMAwZAoMH\nQ51s9vlNTobFi2HWLFi61FyjTRsYNqzgpxIkJ0Pz5hAfD3v2QMmSBXcvkWfztp7ghQW7qFOhJDOH\n30hlfx+rSxLFnL1TBZRSjwDPApWBPcCTWus11zi3M/AOUB/wBY4B07XWE686rx/wBlAbOAK8pLX+\nJR8fJ89kxFUUS5NXHKaEhzujOspoq8hiwQIzanrrrSaIDhliRjMPH4bXXss+tAJ4e0O/fvDbb2ZK\nwcSJEBt7ZSrBqFHm54Lw/vumycAXX0hoLYLubVWdWcNvIuJ8In0mr2PPSdlxQFhPKdUf+BR4G2gO\nrAeWKqVqXOMtccAkoBNwA/Am8HpG+M28ZlvgR+BboFnG8zylVOuC+hzZkRFXGXEtdiIvJNLp/RUM\nbxfEy3fcYHU5ohC88cYbAIwfPz77E5KT4bnnYNIkM3/1hRfMPqglSlz/TbU2TQBmzIBp00zonTcP\nmjS5/mte7cABc70+feDHHx13XeFw+6MumSkDialMGdxSWsWKAmPPiKtSahOwU2s9KsuxQ8DPWusX\n7LzPAiBZaz0w4+cfgXJa6x5ZzlkOnM08J5uLeAP3AD2B1kCljFdOA1uAP4Ef0TrRnppARlxFMTRz\nbTgAI2Ruq8s4cOAABw4cyP7F8HDo2NGE1rFjYf16M3qan9AKZg/VVq3MSOjff8OlS9C6Ncycmb/r\nZtIaHnoIfHxMhyxRpDWoVJpfHmlPjQA/Rszawo9bjltdknBRSikvoCUmFGb1J9DOzms0zzh3VZbD\nbbO55h/ZXlMpP5R6HTgJzAbuB+oAJTMetYH+wAzgJEq9gVJ2faXk8iOu1atX13PmzLG6DOEgNq3Z\nfyqWUiU8qV5O5pq5usC1a6n/3nsordk/bhzRHTsW2L08z53jhjffpOyOHZzq2ZNDY8diy0c4rrRk\nCQ0++IADTz/NqTvvdGCloiDZtOb4uURik1KpUKoEFUt7W12SKGa6du2aAuzKcmia1npa5g9KqSpA\nJNBZa706y/FXgEFa6/rXurZSKgIoD3gAr2utJ2R5LQUYqbWeneXYA8BXWmvvqy50CqgAZO4VFw3s\nzHhWQADQBAjMeF0Dp9G6Sm6f3+X3VDl37hxdunSxugzhIF+tDuP9nfv47bF2NK7mb3U5wiopKTBu\nHHzyiRkV/fFHQoKDC/6+d90Fr79O5TffpHJEhJk60OA6FgeeOQN9+0KHDtT/4APqu8mXY84kNd3G\n+F938+H6EwQFeHFrSCV6NqpEs+plZM9X4QhpWutWdpx39cikyubY1TpiRkTbAO8ppcK11llH9+y9\nZkXgODAL+AGts9+KRakGwABgOGBXRw+XD66i+EhNtzFzXTita5WT0OpiXnnlFQAmTJgAR4+alf6b\nN8Pjj8MHH5jFVYXB3R0mTID27c0OBa1amX1XB2Y//es/YmNh9Wr4+GOzVde0aSCh1el4urvxTt/G\ntA4uxy87TjJjTThfrgqjsn8Jbm1UiZ4hlbgxqBzubhJiRYGIBtK5Mp80UwXM3NJr0lqHZ/xyl1Kq\nIvAakBlco/JwzQeBOWidlmOlJtC+hlJvAkNyPDeDBFdRbCzdHcXJi0lMuCvE6lJEITtx4oT5xcKF\nZosqm82Mdt5zjzUF3Xqr6b41YADcf/+VMHr11IHUVBOwly83j40bIS3NnPfBB6ZTlnBKSinubl6N\nu5tX42JCKn/tP83S3VF8v/k4s9YfJcDPix43VKRnSCXa1Q7Ey0P+giIcQ2udopTaBvQA5mV5qQcw\nPw+XcgOy/q1/Q8Y1PrjqmuuzKSJvk/1NwLXrPS4/x1V2FSgetNbcNXkdcclpLH+qM24ykuFaUlJM\n84CPPzYb9P/0E9SubXVVJpi+9JIJoZl1JSaafWSXL4eVK83IqlJmt4Pu3c2jffv8Lx4TRVJ8chqr\nDp5l6e4o/t53mviUdEqV8KBzvfJ0rBtI+zqBVCvra3WZogizc1eB/piR0keAdcAYzChoI631MaXU\nbACt9QMZ5z8OhAOZq1w7AR8DU7TWz2ec0w5YDYwHfgHuBiYAHbTWm3Io5m9Ao3W3bF4zX5dlmUub\nGwmuElyLhU1hMfSftpG37g5hUOuaVpcjCtLFi7Bz578fu3aZDfoffRQ+/LDwpgbYa9EiGDoULly4\ncqxOnStBtWtXKFfOuvqEJZJS01l3OJqlu6NYdfAsZ2OTAQgK8KVdnUA61AmkbXAAZf28LK5UFCV5\nbEDwHKYBwW7gqczFWkqplQBa6y4ZPz8JjAKCgDRMc4HpwFSttS3LNe/B7PEazJUGBAtyKcSGCa7u\n13jNhtZ2zwCQ4CrBtVgY+c1Wth8/z/rnb6aE53//3xBO6uRJWLfOhNN//jHPx45deb1sWWjalBdi\nY6F2bd4pynudhofDlClmsVa3bhAUZHVFogjRWnPoTBxrD0Wz7nA0m8LPEZechlIQUsWfdnUC6FAn\nkBuDysnvcS7O3uBaZFwruCpVBjiX7Ws5XU6CqwRXZxd2No5uH63i8Zvr8nSPelaXIxwlMtLM8YyN\nNYue6tc3m/E3bWqemzSBqlVBKUaPHg3AtGnTcrmoEM4hNd3GzogLrD0Uw7rD0ew4cZ7UdI2Ppzuj\nOwXzUOdgfL1kmYorcorgqtRQYGjGT10wOw+suuqsmkAt4BxaB2InS4JrHvvnzuLKh8/qX//iMvrs\nfgQ0wmx4+77WemputUhwdX4v/bKLedsiWDfuZsqXKmJfEYvr98gjMH26mQt6000y51O4tPjkNDYf\nPcfPWyP4fdcpKpUuwfO9GtC7aRWZ0+9inCS4vgq8igmsmf+BZreVFsDvaG33ZtWFvozxOvrnjsUE\n3KyPMOCnLNesBSzJuFZz4B3gM6VUvwL6GKKIOBefws/bIri7WVUJrcVJeLgJraNGQadOElqFy/Pz\n9qBr/QpMHtSCeWPaUr6UN0/+GErfL9az/fh5q8sT4loy93nNDLBZHzHA78DjebpgYY+45rd/rlKq\nPbAWaK+1Xp9x7D2gr9a6bpbzpmNWz7XN6Xoy4urcPvvrEB/+7yD/e6oTdSuWsroc4SgjRsD338OR\nI1Al10YqPPPMMwBMnDixoCsTokiw2TTzt0fw/h8HOBubTJ9mVRjXqwGV/aVjYHHnFCOuWeW0OOs6\nFOqIqyP652JWve3JDK0ZrtU/t5VSyvN6ahVFX1JqOt9sOEaX+uUltBYnBw7AN9+YqQJ2hFaAxMRE\nEhMTC7gwIYoONzfFva2qs+KZLjzatTZLdkfRdeJKPll+kMSUdKvLEyKr4cAIR12ssKcKBALu/LfL\nwmn+243hP5RS/sC9wFdXvVTpGtf04Eof3KzXGa2U2qqU2pqWlnNTB1F0LQo9SXRcMqM6FkIrT1F4\nXnsNfHxMy1Y7TZ48mcmTJxdcTUIUUSW9PXj21gb89XRnujWoyCfLD3HzhytZGBpJus21F1+LImM1\nEI5S/+6oolRDlOqEme5pN6uWJF5P/1yAwZjgOyeb16416fc/19VaTwOmgZkqYMd9RRGjtWb62jAa\nVi5Nu9oBVpcjHGXnTvjhB3jxRahQwepqhHAa1cv5MnlQC4aGn2PC4j2M/SGU//vpHyr5l6BqGR+q\nlfWlalkfqpXxoVpZH6qW9aGyv4907BKFYTJwK2bUdV+W462AWcAy4HZ7L1bYwfW6++dmGAXM11qf\nu+r4tfrnpmEm/4piZtXBsxw8HcdH9zVFKVlRW2y8+ir4+0PGnFV7PfnkkwB88sknBVGVEE7jplrl\nWPRoB5btiWJ35EUiLyQSeT6RdYejOR2bRNZlLUpBhVLeNKlWhrHd6hJS1d+6wkVx1iLjeelVx5dh\nBhlbkAeFGlzz0z9XKdUaaAo8mc3LG4A+Vx3rAWzVWqdef8WiqJq+JpyKpb25o4l9cyCFE9i6FX79\nFd54wzQWEEJcFzc3xW2NK3Nb48r/Op6SZiPqYhIRFxKIPJ9IRMbjr/2nueOztdzeuDJP31KP2uVL\nWlS5KKYyf0NPuup4SsZzntoGWrGrQJ7652Z533RM79z6+qqiM7bD2o2Z+/ol0B6YAgzUWucYiGVX\nAeez9+Qlbpu0hnE9G/BwlyLQj144Rs+eJryGh0MpWWwnRGG5lJTK9NVhTF8bTnKajXtaVGNs97pU\nKSM7FBRFTrirQBRQHhiN1jOyHB+BaSt7Bq1zXeeUqdDnuGqtf1RKBQAvc6V/7m1a68w+jv/Zz1Up\nVQoYAEy4OrRmXDNcKXUb8DHwMKYBwRO5hVbhnKavDcPXy537b7rW1r/C6axZA3/8AR98IKFViEJW\nuoQnT99SnwfaBTF5xWG+3XicX0IjGdKmJo90qU1ASdkjW+TLRqA3MAWl2gF7gYbAEMw6pI15uZi0\nfJURV6dy+lISHd77m0Gta/Ja70ZWlyMcQWvo0gUOHjT7tvr65vkSjz76KIDsLCCEA0ScT+DT5YeY\nvz0CH093RnYMZmTHWpQqIbtLFgVOOOLaFVie3SuADeiG1le3g70maXQsnMo364+SbtOMaJ+n3TNE\nUfbXX7B6NXz22XWFVgAfH/lKUwhHqVbWlw/ubcpDnYP58M+DfPrXIWZvOMroTrVpUKkUpX088ffx\noLSPJ6VLeFLC0yH7yoviSusVKPUk8AHgleWVFODZvIRWsHPEVSlaa82mPBXqJGTE1XnEJ6fR7t2/\naVc7gC8Gt7S6HOEIWkPbtnDqlBlx9ZavJIUoanZGXOCDPw6w5lB0tq97e7hlhFlPSpfwwN/HkzbB\nAQy4qQb+PjJK62hON+KaSamqQE+gImYnqWVoHZnny9gZXG1cWfw0V2uKTWNkCa7OId2mGTN3G3/t\nO82CR9rTrHoZq0sSjvDbb9C7N0yfDg8+aHU1QogcnDiXQHRcMhcTU7mUlGaeMx9JqVxMNI+YuBT2\nR8Xi5+XOfTdWZ0T7WlQvd33fpoj/ctrg6iB5Ca6ZJyYDvwDTtWZFAdZWKCS4Fn1aa15dtIfZG44x\n4a5GPNA2yOqShCPYbNCiBcTHw9694Hn9IzOjR48GYNq0aY6qTgiRD3tOXmTGmnAW/XMSm9b0DKnE\nyI7BtKghW93ll1MGV6XKYZpI1Qeuntul0drukQt757h+DNwDVAdKYFb4D1CKMGAGMEtrouy9qRB5\nMW11GLM3HOOhTsESWouT+fPhn39g7tx8hVaAgADpniZEUdKoij8f9W/Gcz0b8M2Go3y78RhLdkXR\nokYZRnUM5pZGlXB3k+YxLkGp2pjtT8tn9ypmYNTu4JqnXQWUogMwEOiH6UxFxg3TgYXAW1oTavcF\niwAZcS3aFoZGMvaHUO5sWoVP+zfDTX6jKx7S0yEkBNzcTJtXd1ncIURxFp+cxrytJ5ixLpwT5xKp\nXs6HEe1rcV+r6vh5yzrxvHC6EVel5gCDcjhDo7Xdfwhc13ZYSlEdmA10xgTXzMScBtynNQvzfFGL\nSHAtujaGxfDAjM00q1GGOQ/ehLeHhJtiY84ceOABM+rat6/V1QghCkm6TfPnnii+WhPG9uMX8PVy\n5+YGFbitcWW61C+Pr5eE2Nw4YXA9DlQF3gZewuTFu4AXMV2znkDrP+2+XB5HXHtgOl3dCbhjAivA\nDqA0UBvYqzUhdl/UYhJci6ZDp2Pp98V6KpQuwfwx7fD3lZWpxUZqKjRoAP7+sG2baZieT8OHDwdg\n5syZ+b6WEKJwbDt2nvnbI/hjdxQx8SmU8HSja/0K9GpcmZsbVKCkjMRmywmDazJmamoAcI7MEVal\nagLhwCdo/bS9l7PrvwqleBYYDQRnHsJsGrsQ+Fhr1iiFHxAJ1LP35kJk5/SlJIbN3IK3pzuzht8o\nobW4mTQJwsJg8WKHhFaA6tWrO+Q6QojC07JmWVrWLMuE3o3YcvQ8S3adYtmeKJbujsLLw43O9cpz\nW+NKdGtYkdI5ND9ITbcRn5xGXMajnK8X5Ut5oxz0+4vItxRM3ryEWeDvhVLVgNiM1wcBdgfXvO4q\noDJu/DUwSWuOXnXefqCu1jjNd7oy4lq0xCWncd/UDRyNieenh9oSUtXf6pKEI+3ZAy1bwq23wq+/\nOiy4CiGKh3SbZtux8yzdfYqlu6KIupSEp7uiTXAAXu5uxCanXQ6p8clpxCalkZxm+891Avy8aFi5\nNA0rl8p4Lk2dCiXxdHez4FM5lhOOuIYDNTD7t27ADILuwYTYlsAltLZ7j8u8BNcw4DNghtbEXeO8\nKoCn1hyztwCrSXAtOlLTbYyYtYX1R2KYMbQVXepXyP1NwnmkpECbNhARAbt3QwX59yuEuDabTRMa\ncYGlu06x5lA07m6Kkt4e5lHCAz9vD0p5m+fM477e7pyNTWbfqUvsOxXLgdOxpGQEW093Rd0KpS4H\n2gaVShMU6EsVfx+nWvjrhMF1MdAL6IQZXR3DlS1WAZai9R12X87O4HoXsEhr8r6Sq4iT4Fo0aK15\n7uedzNsWwXv9GtP/xhpWlyQc7eWX4a23zEjrXXc59NKDBw8GYO7cuQ69rhDCuaWl2wiLjmffqUvs\nzQiz+05d4mxs8uVzvDzcqFnOl6BAP2oF+hEU4EdQoC+1Av2oWKpEkQu1ThhcbwZuBP4ETgJ/Aw0z\nXt0H3InWYfZezt6ZzyuB6kqRoDWXe74pRSDgC1zUmov23lSIq3361yHmbYvgiZvrSGgtjjZsgHfe\ngWHDHB5aAerXr+/wawohnJ+Huxv1KpaiXsVS3NWs6uXj0XHJHDwdy9HoBI7GxBMeHc/R6HhWHTx7\neYQWoISnG7UCS/LsrfW4uUFFKz6C89P6b0xYNZQKAZpgdqLaj9bpebmcvSOu84E+wFNaMynL8ceA\nT4FftOaevNy4qJARV+st3nmSx77bQb8W1Zh4bxOZUF/cxMdDs2ZmN4GdO6F0aasrEkKIbNlsmlOX\nkjgafSXMrj50lkNn4hjXswEPdQq2/M8opxtxzaRUAGa6QCAQDaxG65g8X8bO4BoBVAZqaE1kluNV\ngAggUmucclmvBFfr9f9yA9FxySwd2wkvD+efOC+u8sgjMHUqrFgBnTtbXY0QQuRJYko6z/78D4t3\nnqJv86q83bcxJTytW4PulMFVqdeAcYBXlqMpwLto/XpeLmVvSshs03XhquMXr3pdiDyJT05j+/Hz\ndL+hooTW4mjZMvjiC3j66QINrQMGDGDAgAEFdn0hhOvy8XLns4HN+b8e9ViwI5L+0zZy5lKS1WU5\nD6WeBV4BvDG7U2U+vIFXUOr/8nI5e5NC5l5bt1x1PPPnbHcZECI3m8JjSE3XdKorf/cpdmJiYMQI\naNQI3nyzQG/VrFkzmjVrVqD3EEK4LqUUj3ery9TBLTl0OpY7P1/Lzoirx/LENTya8ZwIfAe8m/Gc\niAmwj+flYvYuztoOdAe+VopGmFVgDTEbxmpgW15uKkSm1QejKeHpRsuaZa0uRTiS1maKQHQ0/P47\nlChRoLd7/vnnC/T6QggB0DOkEjUD2jHym63cO3UDH9zblN5Nq1hdVlFXkcw2r1ovv3xUqR7AH0Ce\n9ka0d8R1asZzaeB14KeM58wNY7/Iy02FyLTm0Fla1wqwdL6QKAA//AA//QSvvQbNm1tdjRBCOEzD\nyqVZ+Fh7mlYrwxPf7+CDP/ZjsxW73UIdaV/G88arjm/IeN6dl4vZFVy1ZgHwEf+em5C5rO5Drfk1\nLzcVAiDyQiJHzsbTsW6g1aUIR4qIMKOtbdvCc88Vyi379etHv379CuVeQggRWNKbuSNbM+DG6kxe\ncYSH5m4jLjnN6rKKqpcxI66PXHX8ESAVeDEvF7N3qgBa84xS/Aj0xgz7nsY0JdiSlxsKkWntobMA\ndJT5rcWHzWbmtaakwOzZ4GH3bzH50rZt20K5jxBCZPLycOOdvo2pX6kUbyzeS78p65k+tBXVy/la\nXVpR8yxmMf87KPUYcAKolvE4C7yIUpnhVaN1t5wuZtd2WMWZbIdlnUe/286W8HNserGb5fviCQf5\n/HN4/HGzk8CYMVZXI4QQhWLNobM8+u126lYsxc9j2hbon2lOtx2WUjawq/OqwgTXHOcO2j0cohQe\nwG1AfcDn6te1ZoK91xIi3aZZdziabg0qSmgtLg4cMFMDevWChx6yuhohhCg0HeuWZ+FjHbBpLX+m\nZc9h/1DsCq5KUQHT9jWnvooSXIXd9py8yIWEVDrVk/mtxcKePaaVq48PzJgBhfwbd+/evQFYtGhR\nod5XCCEy1Qp0nkHQQqW1Qzdpt/dirwMN+O/irKyLtISw25pD0QC0ryPB1ektXAht2kBcHCxeDJUr\nF3oJ3bp1o1u3HKdFCSGES1FKPaKUCldKJSmltimlOuZwbl+l1J9KqbNKqVil1CalVO+rzhmmlNLZ\nPAp2v8Or2DtV4BbM/IRZwPCMX4/FbBqrMZvJCmG31QfP0qhKaQJLeltdirheNhu88YbZ8urGG+GX\nX6BqVUtKGTt2rCX3FUKIokgp1R/4FLNyf23G81Kl1A1a6+PZvKUz8DdmB4BzwCDgF6VUF631mizn\nJQC1s75Ra517GzGl3IDWQA1Mx6x/03p27p/KsDe4Zv5p9DwmuKI1nyvFCmAXZmWYEHaJy2jz+mCH\nYKtLEdcrNhYeeAB+/RWGDoWpUwu8yYAQQgi7PQ3M0lp/lfHz40qpnsDDwAtXn6y1vvpv/68rpW4H\n+gBr/n2qjspTJUo1BBYB1/pDXwN2B1d7pwqkZzzHYPbcQinKA8cyjo+294ZCbAozbV5l/1Yndfiw\n2aP1t9/gk09g5kzLQ2uvXr3o1auXpTUIIURRoJTyAloCf1710p9AuzxcqhRw/qpjPkqpY0qpCKXU\nYqWUPR1mpmBGaa813TRPU07tHXGNwYy6+gNRmBHWb4HM4WGn7ddZrlw5Vq5caXUZLuXMxSSebZJO\nyondrIywuhqRF2W3bOGGCRPAzY09773HhaZNYdUqq8uifn2zblT+XxZCuAAPpdTWLD9P01pPy/Jz\nIOCO2W8/q9NAd3tuoJR6FJP15mQ5fAAYAfyDCbVjgXVKqaZa60M5XK4lZlT1V2AZkGJPDdeszZ59\nXJXif8DNmPkJYzFzH7K+ca3WdM5PIVaRfVwLX7cPV1KtrC/fjLjJ6lKEvbSGDz+EceOgUSMzRSBY\npnoIIURhy20fV6VUFSAS6JR1fqpS6lVgoNa6QS7X74cJrAO01tfcqkUp5Q6EAiu01k/kcMFDmGkC\n/mgdl9O97WHvVIGvgGlACcwOA2e5MrwbDTyZ30KEa5A2r04oMRGGDIFnn4W+fWH9egmtQghRdEVj\npnhWuup4Bf47CvsvWULrAzmFVgCtdTqwFaibSz1vY/LisyiV7xXZdk0V0JqfgJ8yf1aKukBXIA1Y\npzUX8luIcA2ZbV471ZM2r05hzx6zCGvHDnjzTXjxxULfo9Ue3bubb7+WL19ucSVCCGEtrXWKUmob\n0AOYl+WlHsD8a71PKXUf8A0wVGv9c273UabTQhPM1IGcCpqJUndhdiwYh1JnMPnx8hloXTv7N/9X\nrsFVKbyBvRk/3q41+7XmErDQ3psIkWn1oWgqlvamboWSVpcicpKaCu+/DxMmQKlSsGgR3HGH1VVd\nU//+/a0uQQghipKPgDlKqc3AOmAMUAWYCqCUmg2gtX4g4+cBmJHWZ4DVSqnM0doUrfW5jHNeBTYC\nh4DSwBOY4PpwjpUo9QLQGzPF1IsrO1VBZpvXPMg1uGpNslIEYCbihuXl4kJkldnmtXtDafNapO3Y\nASNGQGgo9O8PkyZBhb0bXUMAACAASURBVApWV5WjUaNGWV2CEEIUGVrrH5VSAZhRzsrAbuA2rXXm\nblA1rnrLGEwm/CTjkWkV0CXj12Uw00YrAReBHZh5tJtzKefxjGd11fN1sXdXgeXA3UBTYEt+bihc\n1+5I0+ZV5rcWUcnJpqHAu+9C+fKwYAHcfbfVVQkhhLgOWuspmK2osnutS04/X+M9TwFPXUcpJTGj\nqn2BP7CnYUEO7F2c9Qmmk8L3StFfKeorRY2sj/wUIVzDmoz5rdLmtQjatAlatIC33oLBg83cVicK\nrV26dKFLly5WlyGEEOK/Mhd5bclvaAX7R1xXY9JyOeC7bF7XebiWcFFrDkVLm9eiJiEBXnkFPv7Y\ntGtdsgSccCP/YcOGWV2CEEKI7P0M3AIsRalPgaP8e3EWaL3a3ovlJWzKpERx3aTNaxG0ahWMHGk6\nYY0ZA++9B6VLW13VdZHgKoQQRdYCzABnAGZ71avlafDT3hO/sfeCQmQns81rJ5nfar2ICHj5Zfjm\nG7Mf699/Q9euVleVL6mpqQB4enpaXIkQQohsOGzw0959XIc76obCNa05FE0JTzdaBjltd2DnFxtr\ntrj68ENIT4fnnjPTBPyu2YDFafTo0QOQlq9CCFEEOXTwU+alikKx+tBZ2gQH4O3hbnUprictDb7+\n2oTU06dhwAB45x0ICrK6MocZOXKk1SUIIYTIjtYOHfy0K7gqxde5nKK15kEH1COKoYjzCYSdjef+\nm2TziUKlNSxbZlq17tkD7dvDwoXQurXVlTnc4MGDrS5BCCFEIbB3xHUY1+5skNn1QIKryNbaQ9GA\ntHktVP/8YwLr//4HderA/Plme6ti2vghISEBAF9fX4srEUIIgVJfY1q5Ppjx65yY8+wkuwqIArfm\nsLR5LTQnT8L48TBzJpQpA598Ag8/DF5eVldWoG677TZA5rgKIUQRMQywYQY1h5F7W1eHB9f/Z+/O\nw6Sqrr2PfxcztMwtgwoiXkFREUVFMEaMgEjEAU3AKEbjjMYRvWo0DnHK1fiqcURQgsSIokZJVBAV\njcyDoCgiEWQebBobaIamu/f7xz4lTVHdXdXTqeH3eZ5+Ttc5u3atvtfElV1rr31QjPd1BO4CjgaS\n9xBzCZWOea0hGzb4dlbPPOM3Xt14o+8c0DwzNsNdfXXZR2WLiEiNs1J+j1ZeUruHeLsKLI9x+zsz\npgM5wNX482xF9qBjXqtZTg488gg89RTs2AEXXeRXXDtmVr/cwYMHhx2CiIjsdlApv1daZbsK1MFn\nyv2rIBZJQ5FjXn+mY16rVm4uPPYYPPEE5OfDb37juwZ06hR2ZKHIy8sDoGnTpiFHIiIiOLc85u9V\noDJdBRoAJwL1gbyqDErSx6dLcjhi/ya01DGvVSMvz9etPvYYbN4Mv/413H03dOkSdmShOuusswDV\nuIqIpLvKdhWI1Cy8WyXRSFrZurOQecs3cdlJmfW1dbXYsgWefBIefRR+/NF3CLjnHujaNezIksJ1\n110XdggiIlIDKttVYCfwD+CGqglH0smM7zZSWKxjXivthx/gqKNg7VoYONAnrMccE3ZUSWXQoEFh\nhyAiIjWgol0FAHY6x7qqDEbSy2f/1TGvVWLMGJ+0Tp4Mp54adjRJKSfH9wrOztb/SBIRSWeV6Sog\nUqZPv9Uxr5XmHIwaBT17Kmktw3nnnQeoxlVEJN3FuzmrP3A88LlzTChx/0ygGzDLOd6vnhAlFX2z\nbjNLc/K55MQOYYeS2mbMgEWLYOTIsCNJajfffHPYIYiISDzMGuLc9oq+Pd5SgT8CPYDTo+5vBe4B\npoMSV9nt7flrqF3LGHBk27BDSW2jRkFWlu8eIKUaOHBg2CGIiEhpzA4BHgH64rtR1cHscaAJ8Bec\n+yreqeJNXA8NrtOj7s8KrofF+4GS/oqLHe/MX8NJh2SrDVZlbNkCr74KQ4ZA48ZhR5PU1q3z5fZt\n2rQJORIREdmD2YH4/LE5fqN/pEvVLuC3wFrgD/FOVyvOcY2Ca/Rh842jnoswd8UmVv+4nbO67Rd2\nKKnttdf84QKXxn2Ec8YaMmQIQ4YMCTsMERHZ2z1AC3yiWtI/8Ylsn0Qmi3fFdS3QHp8RX1vi/h3B\ndU0iHyrp7e35q2lQtxb9umj1q1JGjYLDDoMTTgg7kqR32223hR2CiIjE1g+/ynoa8HGJ+4uD64GJ\nTBZv4joZuBS42ox+wYd1Bg4OgpmcyIdK+tpVVMy/v1hL3y5tyKpf2ROFM9iiRTB9uj9wwGK1UJaS\n+vfXqdMiIklq3+A6Ler+juCaUM/MeEsFHsZvxAKfrA4IrgbkB89F+M+SH9i0bRdnHaUygUoZNQrq\n1IGhQ8OOJCWsXLmSlStXhh2GiIjsLTe4doi6H9lVuzGRyeJKXJ3jO/xS7zf4ZDXy8zXQzzmWJvKh\nZjbMzJaZ2Q4zm2tmJ5Uzvp6Z3Re8Z6eZrTCz60o8v9jMXIyfBonEJZX39vw1NGtUl5932rf8wRJb\nQQH87W9w1lnQqlXY0aSEoUOHMlRJvohIMops7H/lpztmzwEv4r+1/yyRyeL+Ltc5ZgCHm3Ew0BpY\nHyS0CTGzwcATwDB8sMOA98ysi3NuRSlv+wfQDrgCWBJ8fsOoMdvwq8AlYnY7kBqzraCQSV+t55xj\n9qdenXgX82UvEyZATo42ZSXgzjvvDDsEERGJ7c/AGcAx7O4ocDl+AbQI+EsikyVchBgkqwknrCXc\nBIx2zr0QvP69mfUHrgZujx5sZv3wO84Ods7lBLe/jxmaczqCNkQffL2e7buKVCZQWaNGwQEHQL9+\nYUeSMvr0SWhTqoiI1BTnZmB2AfAMvrtAxCbgGpybmch0cS2LmTHWjCIz/hh1/87g/tj45rF6QHdg\nUtSjSUCvUt52NjAbuMnMVpnZEjN70syiW3M1NLPlwZh/mdnR8cQkVeft+Wto27QBx3VoUf5giW3V\nKpg4ES6+GGrrqNx4LV26lKVLE6pYEhGRmuLca/hvzvsBFwbXdjj3aqJTxbviemJwfTnq/ljgvhLP\ny5MN1AbWR91fT+l9vDoCPwN2AucCzYC/AvsB5wVjFgO/Axbge8teD0w1s6Occ0uiJzSzK/BlB9Sr\nVy/O0KUsufkFfPrtD1z6s4OoVUu74Cts9GgoLoZLLgk7kpTyu9/9DoApU6aEG4iIiOzJzNeyOncp\n0V2ozC4CwLkx8U4Xb+IaObcz+qv4SAKaaMNOF/XaYtyLqBU8+41zLg/AzK4FJppZa+fceufcdEqc\n6mVm04D5wO+B66IndM6NAEYAZGVllfa5koB3v1xLYbHjTB06UHHFxb5M4NRToWPHsKNJKffee2/Y\nIYiISGwX4/O4WBs3RgPFQJUnrjuAukBP4KMS93uWeB6PHHwhbnSi24q9V2Ej1gKrI0lrYFFwbR/r\nfc65IjObAxwSZ1xSSe/MX8MhrfahS9smYYeSuj7+GL7/Hh58MOxIUs7JJ58cdggiIpIIs8ipqwl9\nTRtv4volvhxgtBl34BPHw4AH8Fn0l/FM4pwrMLO5QF/g9RKP+gJvlPK2qcCvzGwf51ykl2yn4Lo8\n1hvMzICu+NIBqWarNm1j1ve5DO/XCVOz/IobNQqaN4dzzgk7kpSzeLE/gKVz584hRyIiIpidBZwV\nde/FqFGRxcXNiUwdb+I6Gp+47g/8rWQY+MR1dAKf+RjwspnNwielV+HrVZ8DMLMxAM65i4LxrwB3\nAS+Z2T34GtcngPHOuQ3Be+4GZuBbZTXBlwd0xXcqkGo2YcFaAM48av+QI0lhmzbBm2/C5ZdDA7Uf\nTtSVV14JqMZVRCRJdGN3iQD4fPG3McY5fGln3OJKXJ1jlBn98Zujoo13jugsuoy53Dgzawncia+d\nXQgMcM5FVk/bR43famZ98BuyZuPbJ/wTKHk4eTN8zWobIA/4HPi5c25WvHFJxb09fzVHt29G+5aN\nyh8ssf3977Bzp3q3VtCDKq8QEUlGJfcwxfpK9ivghoQmdC7+vUlm/Bp/RFdrfG3pO87t8ZV/ysnK\nynL5+flhh5GyFq/bwmmPf8o9A7tw8YkHhR1OanIOjj7aH/E6Z07Y0YiISBIzs23Ouayw4yiTWVP8\noqIBS/HJa8ldxw7YiHMJJ2AJHUDgHK8Br+0ZG/sA5zq3RwmBZIi356+mdi3jl13VTaDC5s2DBQvg\nmWfCjiRlLVy4EIAjjjgi5EhERAS/od5vqje7D98OK+a+pERV6FxOM2qZMcCMV/AtskZVRTCSWpxz\nvD1/DSf+Tzb7Nq4fdjipa9QoX9d6/vlhR5Kyrr32Wq699tqwwxARSRpmNszMlpnZDjOba2YnlTF2\nkJlNMrMfzGyLmc00szNjjDvXzL42s53BtfzdxM7dg3NV1rMwoRVXM47Dn3gwBH+YAJTdg1XS2LwV\nm1j943Zu6tup/MES2/bt8MorcN550KxZ2NGkrEceeSTsEEREkoaZDcZvZB8GfBZc3zOzLs65FTHe\ncjK+3emdQC5wAfCWmfV2zv0nmLMnMA64G3gTGAS8bmYnuvKObTUbCtwIdAaidyA7nIs7Hy23xtWM\ng4I/4EJ2ty4oWWC7Hfinc1wQ74cmE9W4Vtwf317IuNkrmXNnHxo3qBt2OKlp7FgYOtT3cO3dO+xo\nREQkycVT42pmM4EvnHOXl7i3BN+R6fY4P2cW8B/n3M3B63FAC+dc3xJjJgM/OOdK/8rQ7NfAq/hF\nzlgbtBzOxX3GeakZrhlXAkPZfcgAMT7QAa2dYyuSUXYVFfOvL9bSp0trJa2VMXIkHHwwqIF+pcyf\n77updOvWLeRIRETCZWb1gO7Ao1GPJgG9EpiqMb6TU0RPfIenkiYC5dVpXRNctwON8LljLtAS+DH4\niVtZS7PPsmd2XIA/Y/YN4DtgCkCqJ60tWrRQ78cK2LKzkEs6buPAFqb/+1VQw9Wr6fHJJyy97DJW\nfPJJ2OGktBtu8N1UHn/88ZAjERGpdnWC00EjRgRH2UdkA7XZ+2TR9UCfeD7AzK4BDgBeLnG7TSlz\nRp+GGq0rPp/sA0wDwLl9MbsLn/QOjCemiHhqChzwInCLcz4rNuPwRD4kmeXm5tJbX9Em7MZx8/lw\nSRGzB59C/Tpxr/BLSXfcAbVq0fHee+m4n7oyVMbo0aMBrbiKSEYodM4dG8e46FrQuPYkmdm5wCPA\nELd3J4CKzBkpa5j301iz2sBfgHuBJ4FTy4srIt5i2N8BA814C7/imhPvB0j62V5QxMSv1nHmUfsp\naa2oXbvgxRfhjDNASWulKWEVEflJDlDE3iuhrdh7xXQPQdL6MnCRc+6dqMfrKjIn/kjX5vgkdwu+\nBOF0Iu2yoEc5799DWe2w/gysDD7IguCuwNczfJbIh0h6+WDRerYVFHFmNyVcFTZhAqxfD1dcEXYk\naWH27NnMnj077DBERELnnCsA5gJ9ox71JfJVfQzmN1GNBS52zo2PMWR6onMG1gTXVsCi4Pe3CUpO\n8fWucSs1cXWO252jA9Ab36f1R3YnsZHiWsxYacZDiXyopLZ35q+mTZMG9DioZdihpK4RI+CAA6B/\n/7AjSQu33HILt9xyS9hhiIgki8eAi83sMjM7zMyeAPYDngMwszFmNiYy2MyGAH8HbgM+NbM2wU+L\nEnM+AfzCzG43s0PN7HbgFKC8zQWf43PHHsAYdueSkT1UCR1gFfeRr2bUwxfQDgX6A/VKPHbOkZLf\nGasdVmI25Rdw3AOTueTEDvzhl13CDic1LVvmOwncfbf/kUrTyVkikiniPfLVzIYBtwJtgYXAjc65\nT4NnUwCcc71LvI7V3uaTyJhg3HnA/fjjW78D/uCce7OcQLKAfYAtOLcNs9uAwUAh8BbwZ5wrKu/v\n+Wm6eBPXPWOgOf4Qggvx7RGUuGaItz5fxY3jFvD2NSdyVDs1zK+QO++Ehx6C77+Hdu3CjkZERFJI\nvIlrUjCrj09SASbh3LrKTpnQyVkRzrEJ3y7rWTM6QmoePiCJm7k0lyYN6nDE/k3DDiU1RTZlDRig\npLUKTZvmS6x69UqkRaGIiFQr53ZiNhJfmtq6KqasUOJaknMsBf5UBbFICpi5LJfjOrSgdq1Yh19I\nuf79b1i7Vpuyqtgdd9wBoJ7CIiLJZyn+5NXiqpis0omrZI4Nm3ewLCef84/XSmGFjRgB++8Pp58e\ndiRp5fnnnw87BBERie0vwPPAzcCdlZ1MiavEbcYy37FC3QQqaPlyeP99uOsuqKP/6FWlzp07hx2C\niIjE1gvYCNyO2SBgAf741wiHc5fGO5n+7Slxm7l0I/vUr8Ph+zUJO5TUNGqUv14a938+JU6fBEfm\nnnxyrE2xIiISot+y+3StzsFPNCWuUvVmLsul+4HNqVO7rHMrJKbCQp+4nn46tG8fdjRp5+6grZhq\nXEVEklJZG2MSam+lxFXikrN1J//dsJVBx+wfdiip6d13Yc0aeOaZsCNJSy+++GLYIYiISGwHVeVk\npSauZvw8kYmc49PKhyPJapbqWytnxAho2xZ++cuwI0lLHTt2DDsEERGJxbnlVTldWSuuU4h/+daV\nM5ekuJlLN9Kwbm26HqD+rQlbsQLeew/uuEObsqrJ5MmTAejTp0/IkYiISExmzfBtsRru9Sw40Sse\n5f1bVM06Bdhd31pX9a2Je/FFcE6bsqrR/fffDyhxFRFJOmZ1geeAi/AHEURLaPGzrIF/i3rdD2gD\nTAVWAQcAJ+JbHPwr3g+U1LMpv4Bv1m3h5r5tww4l9UQ2ZZ12GnToEHY0aevll18OOwQREYltOHBJ\nVU1WauLq3O4PMeMCfKY82DnGl7j/a+Af+GRW0tTs74P61o6qb03Y++/DqlXw5JNhR5LW2un4XBGR\nZDUEv6q6AOgW/P4WMAC/EPpZIpPF+71v5KSD96Puv4svJ7glkQ+V1DJzWS7169TiqHaqb03YiBHQ\npg2ccUbYkaS1999/n/ffj/6vJxERSQIHB9fzfrrj3HnAr/AdByYkMlm8iWuH4Dos6v41wfXARD5U\nUsvMZRs5un0z6tepHXYoqWXVKvj3v+F3v4O6dcOOJq09/PDDPPzww2GHISIie4v8C3A5UASAWUNg\nMlAbuDeRyeIthv0WOAJ4yIybgbVAWyAbv+T7bSIfKqlj845dfL1mM9f+4pCwQ0k9L74IxcVw2WVh\nR5L2Xn311bBDEBGR2DYB++K7CeTic8e7gK3B8/9JZLJ4E9c/4OsRagcfmB3cN6AYuCORD5XUMef7\nXIodnHBQi7BDSS1FRTByJPTrBwdVae9liaFNmzZhhyAiIrEtxSeu+wPzgNOA/w2eOWBZIpPFVSrg\nHP8C+gMzgw+x4DoD6Occ/07kQyV1zFyaS93axtHtm4cdSmqZOBFWroQrrgg7kowwYcIEJkxIqExK\nRERqxgf4b+YPBR7FL3gau1uu3pfIZOZcQkfEYkYjoDmwyTm2JfTmJJSVleXy8/PDDiNpnfX0VOrW\nMsZf3SvsUFLL2WfDjBk+eVV9a7Xr3bs3AFOmTAk1DhGR6mZm25xzWWHHUWFmJ+I3ahUC/8S5hDpT\nJXSMjxl18LWuLZ3jvUTeK6ln685CFq7O46qTdZxmQlavhn/9C265RUlrDRk/fnz5g0REJBnMSjRZ\nLSnuY5DM+BWwGphO0LrAjA/NWGpGv4oGIMlr7vJNFBU7ehyk/q0JeeklX+OqTVk1Jjs7m+zs7PIH\niohIzTPrgtl4zPKAHZjlYfY6Zl0SnSquxNWMk/AHDWSzZ13Cv/Gtss6L/U5JZTOXbqR2LaP7gapv\njduWLfDMM9CnDxx8cPnjpUq8+eabvPnmm2GHISIi0cyOx++ROgdojM8hGwODgJmYHZfIdPGWCtyO\nT3K/wRfXRkwOrj0T+VBJDTOX5XLk/k3Jqp9QRUlmu/deWLcO3n477EgyypPByWSDBg0KORIREYny\nGBCpyd0FbARa4vu7ZgXPT4p3snhLBU7AdxEYGHV/aXDdP94PlNSwvaCIL1b9SI+OaoMVt4UL4fHH\n4fLL4biE/gekVNLbb7/N2/ofCyIiyag7Pod8EmiGc/sBzYCnSjyPW7yJayRTXhF1v2HUVdLEvBWb\n2FXkOEH1rfFxDq65Bpo2hQcfDDuajNO0aVOaNtWRxCIiSWhTcL0L57YDBNc7g/sbE5ks3sR1dXCN\nLgkYHlxXJfKhkvxmLsullsGxHVTfGpdXXoFPP4WHH4aWSvZr2rhx4xg3blzYYYiIyN7GBNdDo+53\nDq4vJjJZvMWLE4ErgX9GbpjxDXAIfvl3YiIfKslv5tKNHL5fUxo3UDuncuXlwfDhcPzxcOmlYUeT\nkZ599lkABg8eHHIkIiIS5Tv8quoEzF7Af3vfHrgMvzC6HLOLfhrt3JhYk0TEdQCBGfsD8/HFtCXf\nYEEw3Zz7aVU2pegAgr3t2FVE13sncdEJB3LnGQl3qsg8N94ITzwBs2bBsceGHU1G2rbNn4XSqFGj\nkCMREaleKXcAgVkxe+aOZXE4V+aiarxHvq4GTgQmsfuoruLg9UmpmrRKbAtW/khBYTE9Ouor73J9\n8QX89a9w5ZVKWkPUqFEjJa0iIsnLEvgpU9x9jpzjW6C/GQ2AFkCuc+xIOHRJejOX5WIGx6m+tWyR\nDVnNmsEDD4QdTUYbO3YsABdeeGHIkYiISJRLqnKyuBJXM5oCTYFtzpEDrAnuZwONgDznyKvKwCQ8\nM5dtpHPrxjRrVC/sUJLb2LHw2WcwciS0UNuwMI0cORJQ4ioiknSc+1tVThdvV4EXgWXAb6LuDwnu\nj6rKoCQ8BYXFzF2+iRNUJlC2H3/0G7JOOAEuqdL/MSkV8MEHH/DBBx+EHYaIiJTHrBZmgzG7BbNu\nib493sS1R3B9I+r+m/h6hB5IWvhy9Y/s2FVMj4O0glimu++GnBx4+mmoFe9/jKS61K1bl7p11QFD\nRCTpmD2E2QbM7g7uvA68AjwMzMbs1ESmi/ffuPsG1x+j7udFPZcUN2NpLgDHK3Et3YIF8NRTcPXV\ncMwxYUcjwOjRoxk9enTYYYiIyN5647tSfYrZ/sA57N6IVRu4LZHJ4k1ctwTXflH3I6+3JvKhkrxm\nLsvlkFb70HKf+mGHkpyKi2HYMH/IwJ/+FHY0ElDiKiKStA4Orl8BkfPQx7J709bRiUwWb1eBeUAf\n4EUzDgcWAYcBN+F7c81N5EMlORUWFTP3+1zOOWb/sENJXmPGwLRp8NJL0FxdF5LFlClTwg5BRERi\ni5zHnYs/PcsBE/CHWr0ENElksngT1+fwiWsT4N4S9y0I4NlEPlSS08I1m8kvKKLHQdqYFdOmTXDr\nrdCrF1x0UfnjRUREJBdohS8RiHxT/y3QOPh9cyKTxXsAwZvAY8RuEvsX53YfBSupa+bSjQD06Kj6\n1pjuugs2btSGrCT0wgsv8MILL4QdhohI0jCzYWa2zMx2mNlcMzupjLFtzewVM/vGzIrMbHSMMReb\nmYvx06CcUBYE11eBk/Hlp18BHYP7KxL5uxI5gGC4GeOAM4HWwHrgHeeYncgHSvKauSyXjtlZtGpc\n3j+DGaagAB5+GJ591h840C3h7h1SzcaNGwfA5ZdfHnIkIiLhM7PBwBPAMOCz4PqemXVxzsVKFOsD\nOfid/leUMfU2dtesAuCcK+8wqoeBk4CGwev/w7lCzM4IXk8r5/17MOfiPT42PWVlZbn8/Pywwwhd\nUbGj232TOKNrWx4a1DXscJLHjBlw2WXw1VcwZAiMGAGNG5f/PhERkWpgZtucc1nljJkJfOGcu7zE\nvSXAeOfc7eW8919AjnPu4qj7FwNPOef2qUDQ7fAbs5bh3OfBvcPwJ7Euxbm18U4V94qrGY2BAcCB\nwF5Lcs5xX7xzSfJZtHYzW3YUqr41YutW+MMf4K9/hf33hwkT4Iwzyn+fiIhIiMysHtAdeDTq0SSg\nVyWnb2hmy/FtrOYDd7lIIloW51YCK6PuLapIAPEe+Xoc8C4+My5NSiauLVq00I5kIGdrATcfWUhW\n7rdMmbIk7HBC1WLWLDo99hj1N2xgzVlnsfTyyylq1Aj0z0nS+uc/fZn92WefHXIkIiLVro6ZzSnx\neoRzbkSJ19n4xHJ91PvW4zfaV9Ri4Hf4mtXGwPXAVDM7yjm3Z+Jg5ncwOzfmp9/L4tyYeIOIq1TA\njKlAzzI/0lE73g9NJioV8C4dPZslG7by6a2nhB1KeHJy4IYb4O9/h8MOgxdegBNPDDsqicPpp58O\nwHvvvRdyJCIi1au8UgEz2w9YDfzcOfefEvfvBs53zh1azvwxSwVijIusun7snLsu6mExUIxzdYLf\ny0o2Hc7FXQEQ78CuwYd+gj/2Nb+cICSF7NhVxNTvchh8bLuwQwmHc/CPf8D110NeHvzxj3DHHVBf\nhzCkCiWsIiI/yQGKgDZR91ux9ypshTnnioKV30NKGWKl/F4p8SauPwKNgEHO7XXsq6S4qf/NYceu\nYk49rHXYodS8devg0kvh3XehRw8YORKOOCLsqERERCrEOVdgZnOBvsDrJR71xS8+VgkzM/zC5oIY\njy8p5fdKizdxHYM/S/YIfFsFSSOTF20gq17tzOzfesUV8PHH8PjjcO21UDslK14y3hNPPAHA9ddf\nH3IkIiJJ4THgZTObBUwFrgL2wx8ohZmNAXDO/VR/amaRXo9NgOLgdYFz7uvg+d3ADGBJMOY6fOJ6\n9V6f7tzfYv5eBeJNXL8H8oC3zRiFL9DdVXKAc8RdWCvJwznHR9+s5+ed9qV+nQxL2mbP9t0C7r/f\nlwlIyvrwww8BJa4iIgDOuXFm1hK4E2gLLAQGOOeWB0Pax3hbdHeAgcByoEPwuhkwAl+CkBeM/7lz\nblbVRl+2eDdnlVtY61z8rbWSSaZvzvpyVR4Dn/qMR391FOd1PyDscGrWgAEwcyZ8/716s4qISEqI\np49r6MyWJjDa4dzB5Q/zEjm3Mvq411jHv8Y3UQLHkAXj65nZfcF7dprZCjO7LmrMuWb2dfD8azM7\nJ5GYMtXkResxfwuxcAAAIABJREFUg1M67xt2KDVr+nR47z249VYlrSIiIlWrA77vf+SnQ4x7Je/H\nLd5V0iorrK3AMWQA/wDa4Y8hW4I/cjZydBhm1hMYB9wNvAkMAl43sxOdczOrKvZ09OE36zmmfXNa\n7pNhO+jvuQeys/0RrpLyHn3U99kePnx4yJGIiEgg1qJmpbsLxJW4OkdVFtbeBIx2zr0QvP69mfXH\nF/fudQyZmfXDN8w92DmXE9z+PmrYDfg+Yg8Erx8ws1OC++dXYexpZV3eDhau3swtp3UOO5Sa9dln\nMGkSPPII7JP4yXWSfKZPnx52CCIiEuHc7m/0zQ4GPg1+/gCsAg4AHgR+Afw8kakTKRWotBLHkE2K\nelTWMWRnA7OBm8xslZktMbMnzaxkxtEzxpwTy5hT8KutAH0yrQ3W3XdD69YwbFjYkUgVeeONN3jj\njSrr8iIiIlXnSfyGrqtxbinOFeDcUnyng2zg8UQmiztxNWOoGfPMyDejKOqnMM5pyjqGLLpRbkRH\n4GfAUcC5wLVAf2B0iTFtEpnTzK4wszlmNqewMN7Q08+HizZwQPOGdGqdQauOn3wCH30E//u/0KhR\n2NGIiIiku5ODa8eo+/8TXH+WyGRxlQqY8Wvgb/jOAlVx+kF0hwKLcS+iVvDsN865PB+PXQtMNLPW\nzrlIwhr3nMGZviPAdxVIPPzUt72giKn/zeH849vjewhnAOf8qVht2sBVV4UdjVShhx9+GIDbbrst\n5EhERCTKVvy+pPcwe5ndpQJDSzyPW7ybsyI7WLbjT9ByQC7QEn+qVrynaVXkGLK1wOpI0hpYFFzb\nB+9bl+CcGW/qf3PYWVjMqYe1CjuUmvPxx/Dpp/Dkk9CwYfnjJWXMnz8/7BBERCS2l4Gb8d+631ji\nfmSBMaFzAOItFegaTN4ncsM59sXv4t+Fb1JbLudcARA5hqykvsC0Ut42Fdgvqqa1U3CNNNKdnuCc\nGe/Db9azT/069DioZdih1AznfG3r/vvD5ZeHHY1UsVdffZVXX3017DBERGRvd+CT01htVMcEz+MW\n74prpNHtPIKv382oDfwFuBdfeHtqnHMlegzZK8BdwEtmdg/+5IYngPHOuQ3BmCeAT83sduAt4Bzg\nFBKsm8gUxcWODxdt4OedsqlXp0b354Vn8mTfTeDpp6FBg7CjERERyQzO7QIuxuwhfG7WEv8N/Mc4\n922i08WbuG4GmuMz5C1AY+B0/JFfAD3i/cBEjyFzzm01sz7AX/HdBTYB/wRuKzFmmpkNAe7HJ9Lf\nAYPVwzW2hWvy2LBlJ6cemiHdBCK1re3awaWXhh2NVIM//elPANx1110hRyIiIjE5txhYXNlp4k1c\n1+AT11b4+tLjgbdLPM9N5EOdc88Az5TyrHeMe4uBfuXMOR4Yn0gcmWryog3UMjjl0Aypb504EWbM\ngOeeg/oZdtBChli8uNL/XSgiIjXBHweb0DGvJcWbuH4OHIFfWR3D3iusVXlAgVSzDxf507JaZNUL\nO5TqF1ltPfBAuKTKDoCTJDN27NiwQxARkfh0oPROUuWKN3EdBtwKbHGObWY0BQYDhfia0j9XNACp\nWWvztvPVms38b/9Dww6lZvz73zB7NowcCfUyIFEXERFJY/Ee+ZoP5Jd4/TDwcHUFJdXnw0V+P1uf\nTGiDFekk0LEjXHRR+eMlZf3xj38E4L777gs5EhERqU6lJq5me26SKo9zrKh8OFLdPly0nnYtGvI/\nrTLgtKx33oF58+Cll6Bu3bCjkWq0cuXKsEMQEZEaYM7FLjMwo5j4axCcc3GXHSSVrKwsl5+fX/7A\nNLCtoJBu933Ab45vzz1nHh52ONWruBiOOQby82HRIqiTkv94ioiI7MHMtjnnssofmZ7K+7d5hpwF\nmhk+W5JDQWExfQ7LgDZYb70FCxbAmDFKWkVERNJEWf9GV6eANPPhog00rl+H4w9qEXYo1e+hh6Bz\nZzj//LAjkRpw++23A/DQQw+FHImIiMTF9/T/ASjGubhXmEod6BzqHZRGiosdHy3ewM877Zv+p2Vt\n3Ahz58IDD2i1NUNs3Lgx7BBERKRiEvp2X/9WzxBfrs7jhy07OTUTugnMmOGvvXqFG4fUmBEjRoQd\ngoiIRJgNi2NUhep0405czegMXAl0BhpGPXbOcWpFApCa8eGi9f60rM4ZkLhOnw61a8Nxx4UdiYiI\nSCZ6ikocMlCWuBJXM7oDU4BGsR5TTcFJ1Zm8aAPdD2xO80w4LWvaNDjqKMjK2E2XGWf48OEAPPro\noyFHIiIiJVT5Jv94V1zvoIJLuhK+NT9u5+u1m7nt9Aw4LauwEGbNgosvDjsSqUHbt28POwQREdmt\nAKgLPAesL2VMI+CWRCeON3HthV9VHQY8G/x+FHA/cCj++FdJUh9+k0GnZX35pe/dqvrWjPL000+H\nHYKIiOw2HzgO+BjnXo85wncVSDhxjXd7ecvg+vfIDedYCFwBdAJuTPSDpeZ8uGg9B7ZsxMH7ZsBp\nWdOn+2vPnuHGISIikrlm4ssEelT1xPGuuG4H9gF2BL83CDZrbQ2en1nVgUnV2FZQyLTvNnJhjwMx\ny4DzJKZPhzZtoEOHsCORGnTDDTcA8Pjjj4cciYiIAH8CXgR+LGNMLnBQohPHm7huwCeuLYDv8eUB\nHwOFwfPiRD9YasZ/gtOyMqINFviNWT17QiYk6SIiIsnIuRwgp5wxDlie6NTxJq5fAh2BrsC/gMOA\nyLmhDpiU6AdLzfhw0Xoa16/DcR0y4LSs9eth6VK4+uqwI5EappVWEZHMEG+N673Ab/CrrffjE9XI\nktaHwPVVHplUWnGx46NvfuDnnTPgtCxQfauIiEgyMLsbs2YJjG+G2d3xDI1rxdU5FgALStzqb0Yz\noNC5n+pcJckszcknZ+tOTvqf7LBDqRnTp0PdutC9e9iRSA275pprAHUXEBFJEncDN2E2HhgHTMW5\n/D1GmGUBJwJDgHPxJan3ljdxZY58rQfklztKQjNv+SYAju3QPORIasi0aXDMMdCgQdiRSA1r2DD6\nMD8REQnR10AX4OLgpxiz7/F1rw7YF+jA7m/+DfgqnonLTFzNOAafCTcA/ukcH5lxGfAQfqPWDjOe\ndY7hCf05UiPmLt9E04Z16ZidAW2wCgpgzhzVt2YonZglIpJUugKXAsOBQ4DawMH4/VKw54la3wGP\nACPjmbjUxNWMn+HrVyNjrjHjEeBWfLZsQEPgRjP+6xzPxfvXSM2Yt2ITx7RvRq1aGbDDfv582LFD\n9a0iIiJhc64YeAF4AbPewGn4Awna4PPHdcBsYCLOfZzI1GWtuN6CP64r+h7Bh+YA2cHvQ0GJazLJ\n27aLJRu2cla3/cIOpWZoY1ZGu+KKKwAYMWJEyJGIiMgenJsCTKmq6craan4sfmV1Iv6o1/fwSaoD\nzneOVsAFwdguVRWQVI15K3196zEHZlB9a7t2cMABYUciIWjZsiUtW7Ysf6CIiKQ08/1fYzwwduJX\nZJs7x2YzmgKb8IlrA+fYZUY9/Glaxc5VaqNXaLKyslx+fvrtMfvLpMU8M+U7vri7H1n1U/L/NYlp\n3x569YJXXw07EhERkWpjZtucc1lhxxE3s+Pxi6GLcO5jzPoCTwLtgfeBi/bqOFCGslZc6wI4x+bg\nmhd54By7gmtBJKxE/gapfnOXb+Kwto0zI2ldtQpWrlSZgIiISMDMhpnZMjPbYWZzzeykMsa2NbNX\nzOwbMysys9GljDvXzL42s53B9Zw4QrkV+CvQCbO6wN+BTvh9UmfjW2fFrdysxow/xnNPkkdhUTHz\nV/7Ir7pnyNfmqm/NeJdccgkAL730UsiRiIiEz8wGA0/gSz0/C67vmVkX59yKGG+pj9+79DBwRSlz\n9sT3ZL0beBMYBLxuZic652aWEc7RwfUjoDt+f9RaYE3w+ix8chuXeJbjSmbCLsY9STLfrNvCtoKi\nzKpvbdAAunULOxIJSbt27cIOQUQkmdwEjHbOvRC8/r2Z9QeuBm6PHuyc+x64DsDMzitlzhuAj51z\nDwSvHzCzU4L755cRS+vguhI4Ofj9YeA1fAJ7YDx/UER5iatKAFLQvBV+Y1b3TElcp0+HY4+FevXC\njkRCct9994UdgohIUjCzeviVzOgG15OAXpWYuif+K/+SJgLXlvO+yKJnI+CI4PVX+H1TAEWJBFFW\n4lrusVvpoEWLFkyZMiXsMKqUbdrObd2K+e+CWfw37GCqWa2CAn42dy6rzjuPpWn2/0cREZEY6pjZ\nnBKvRzjnSvYCzMY3/F8f9b71QJ9KfG6bUuZsU877VuMPIZjA7i5UXwGRfp05iQRRauLqXGYkrrm5\nufTu3TvsMKrUz/78EV0PaMVVvbuHHUr1mzoVCgtpP3gw7dPs/48SvwsvvBCAsWPHhhyJiEi1K3TO\nHRvHuOi2URbjXqIqMudbwP8CJwTjZ+Hcesx+HTz/IpEAMmDLeWZZv3kHqzZt5+JeHcIOpWZoY5YA\nnTt3DjsEEZFkkYP/+j16JbQVe6+YJmJdBee8F2gCnAQsw9ffgm+H9SGQUB9LJa5pZt7yDKtvnTYN\nOnaE1q3LHytp66677go7BBGRpOCcKzCzuUBf4PUSj/oCb1Ri6unBHI9EzTmtnIB2ANfEuP8oe9fh\nlkuJa5qZu3wT9erU4vD9moYdSvVzzq+49qlMyY6IiEjaeQx42cxmAVOBq/A1pc8BmNkYAOfcRZE3\nmFmkNU8ToDh4XeCc+zq4/wTwqZndjv/6/xzgFOBncUVkdiS+xjYbvyo8Gee+TPQPU+KaZuau2MRR\nBzSlXp2yzpZIE99/D+vWqUxAGDJkCACv6uQ0ERGcc+PMrCVwJ9AWWAgMcM4tD4a0j/G2z6NeDwSW\nAx2COaeZ2RDgfvzX/98Bg8vp4QpmdYCRwNAYz8YAl+Fc3J0FlLimkR27ili4Oo/f/eygsEOpGZH6\n1l6V6e4h6aCbeviKiOzBOfcM8Ewpz3rHuFduC1Tn3HhgfIKh3A9cVMqzi/C1s3v1li2NEtc08tWa\nPHYVObq3z6D61qwsOOKIsCORkN12221hhyAiIrFdhO888AN+5XUFfsX3MvzmrotR4pqZ5gYbszLm\nxKzp06FHD6ijf4xFRESSVGTTzS9xbu5Pd83eBmbia2rjlgGFkJlj7vJNdGjZiOx96ocdSvXLz4cF\nC1TfKgCce+65nHvuuWGHISIie4sclrAk6v7i4DorkcmUuKYJ5xxzl/+YOauts2dDUZHqWwWAnj17\n0lP/I0ZEJBndCGwF7sesAUBw/ROwmd19XeOi71jTxMrc7eRs3ckxmVTfCnDCCeHGIUlh+PDhYYcg\nIiIRZkuj7+B7uV6B2UagJVAXyMdv9jo43qmVuKaJuStygQw6eGD6dOjcGVq0CDsSERER2VMH/Ias\nSKeCyO/18O25Ivf2AbISmViJa5qYu3wT+9SvQ6fWjcMOpfpFDh4488ywI5EkcWbwz8I777wTciQi\nIoLvHOCqY2Ilrmli7vIfObp9M2rXKrcNW+pbsgQ2btTGLPnJqaeeGnYIIiIS4VyH6ppaiWsa2LJj\nF4vXbabfLw4JO5SaEalv1cYsCVx//fVhhyAiIjVAiWsaWLAyj2KXYfWtTZvCYYeFHYmIiIiUxx/7\nOgDoDDTc67lz98U7lRLXNDB3+SbMoFv7ZmGHUjOmTfPdBGqpm5t4p59+OgDvvfdeyJGIiMgezFoB\nU/BJa2mUuGaSuSs20bl1Y5o0qBt2KNUvLw+++grOOy/sSCSJDBw4MOwQREQktnuBQ8t4ntAmLiWu\nKa642PH58k0M7LZf2KHUjFmzfFcB1bdKCcOGDQs7BBERia0fPjkdDVwS/H498Pvg94cTmUzftaa4\nJRu2smVnId0z6eABM+jRI+xIREREpHz7B9fbfrrj3FPAIKATcEAikylxTXFzl28CMmxj1hFHQJMm\nYUciSaRPnz706dMn7DBERGRvRcF1I7ALALN9geXB/SsSmUylAilu3opNtMyqx4EtG4UdSvUrLoYZ\nM2Dw4LAjkSQzWP9MiIgkq434VdemwDr8CuvfgR3B84RW3pS4prh5yzdxzIHNMcuAgwfmz/ebs1Tf\nKlEuv/zysEMQEZHYFuMT14OBT4ELgMipMQ6Yl8hkKhVIYbn5BSzNyc+MMgHn4Oabff/WoPWRiIiI\nJL0XgBFAA3yHgR8AC35ygBsSmUwrrilsXibVt44eDVOmwPPPQ6tWYUcjSaZ3794ATJkyJdQ4REQk\ninOvAa/99NrsEOAUoBCYinM/JjKdEtcUNnfFJurWNo7cv2nYoVSvH36A4cPhxBPhssvCjkaS0MUX\nXxx2CCIiEg/nNgNvV/TtSlxT2Nzlmzh8v6Y0qFs77FCq1003wZYtMGKETsuSmJS4iohkBmUBKWpX\nUTELVv6Y/mUCH3wAY8fCbbdBly5hRyNJateuXezatSvsMEREpJppxTVFfb1mMzsLi9M7cd22Da66\nCjp1gjvuCDsaSWJ9+/YFVOMqIpLuQklczWwYcAvQFvgKuME5959SxvYGPo7x6DDn3DfBmIuBl2KM\naeic2xHjfsrLiIMH/vQnWLoUPvoIGjQIOxpJYpep9llEJCPUeOJqZoOBJ4BhwGfB9T0z6+KcW1HG\nWw8Hcku8/iHq+TZ8j7CfpGvSCn5j1v7NGtK6SZomdF98AY88ApdcAqecEnY0kuQuvPDCsEMQEZEa\nEMaK603AaOfcC8Hr35tZf+Bq4PYy3rfBOZdTxnPnnFtXVUEmu3nLN3FchxZhh1E9iorgiiugeXOf\nvIqUY9u2bQA0apQBJ8iJiGSwGt2cZWb1gO7ApKhHk4DyjkOaY2ZrzexDM4u1BNfQzJab2Soz+5eZ\nHV0VMSejNT9uZ23ejvQtE3juOZg5E/7f/4OWLcOORlLAgAEDGDBgQNhhiIhINavpFddsoDawPur+\neqBPKe9Zi1+NnQ3UA4YCH5pZb+fcp8GYxcDvgAVAY+B6YKqZHeWcWxI9oZldAVwBUK9evUr9QWGY\nsXQjAMe0T8PEdfVquP126NsXLrgg7GgkRVx99dVhhyAiIjXAnHM192Fm+wGrgZ+X3IxlZncD5zvn\nDo1znneBQufcmaU8rw3MBz52zl1X1lxZWVkuPz8/3j8hKVwwcgYrcrfxyfBTqFXLwg6nag0aBO+9\nBwsXwsEHlz9eREQkg5jZNudcVthxhKWm+7jmAEVAm6j7rdh7FbYsM4FDSnvonCsC5pQ1JlWtzN3G\n1P9u5Ffd26Vf0vr22/DWW3DPPUpaJSF5eXnk5eWFHYaIiFSzGk1cnXMFwFygb9SjvsC0BKbqhi8h\niMnMDOha1phU9frcVZjBud0PCDuUqrV5M1xzDXTt6k/KEknAWWedxVlnnRV2GCIiUs3C6CrwGPCy\nmc0CpgJXAfsBzwGY2RgA59xFwesbgO/x/V7rARcCZwPnRiYMSg1mAEuAJsB1+MQ1rQrfiood4+es\n5KRD9mX/Zg3DDqdq3XknrFkDb7wBdeuGHY2kmOuuK7MiSERE0kSNJ67OuXFm1hK4E38AwUJggHNu\neTCkfdRb6gGPAvsD2/EJ7C+dc++WGNMMGIEvQcgDPsfX0c6qtj8kBJ/9N4c1eTv4wy/T7OjTWbPg\nqaf8imuPHmFHIylo0KBBYYcgIiI1oEY3ZyWjVNqcdc0r85j23xxm3HEq9evUDjucqtO3r9+MtXgx\nNGkSdjSSgnJyfIvn7OzskCMREalemb45K5QjXyVxm/IL+OCr9VxwQvv0SloXLoTJk+Ghh5S0SoWd\nd955AEyZMiXcQEREpFopcU0Rb32+moKiYgYf1y7sUKrWE09Aw4Zw+eVhRyIp7Oabbw47BBERqQE1\n3Q5LKsA5x2tzVtL1gKYc2iaNViVzcmDsWBg6VCdkSaUMHDiQgQMHhh2GiEjSMLNhZrbMzHaY2Vwz\nO6mc8ScH43aY2VIzuyrq+T1m5qJ+1lXvX7E3Ja4p4MvVeXyzbgu/PjbNVltHjIAdO+D668OORFLc\nunXrWLeuxv/7U0QkKZnZYOAJ4EHgaHzL0ffMLHoDfGT8QcC7wbijgYeAv5rZuVFDF+M31kd+jqyW\nP6AMKhVIAeNmr6R+nVqc2W2/sEOpOgUF8PTT0K8fdEmzLglS44YMGQKoxlVEJHATMNo590Lw+vdm\n1h/fJvT2GOOvAtY4534fvF5kZj2A4cAbJcYVOudCXSVQ4prkthcU8c78NQw4si1NGqRRf9Px433f\n1pEjw45E0sBtt90WdggiIknBzOoB3fGtREuaBPQq5W09g+clTQR+a2Z1nXO7gnsdzWw1UIA/xfQO\n59zSqok8PhmfuLZo0SKpV2l+3L6LKzrtoGOzjUkdZ0Kc45j77qNOu3bMql8f0uXvktA0aNAA0Iqr\niGSEOmY2p8TrEc65ESVeZwO1gfVR71sP9CllzjbA5Bjj6wTzrcUnqhcD3wCt8P34p5nZ4c65jRX4\nOyok4xPX3NxcevfuHXYYpRoyYjpr8+ow5Te98SfZpoFp03zP1qefpvcvfhF2NJIGVq5cCUC7dmlW\nBy4isrdC59yxcYyLbtRvMe6VN/6n+8659/Z4aDYDWAr8Fn8qao3I+MQ1mS3fmM+MpbkM79cpfZJW\n8C2wmjWDiy4KOxJJE0OHDgW04ioiAuQARfhV1JJasfcqbMS6UsYXAjFXU51zW83sK+CQioeaOCWu\nSez1OauoZXBe9zRaRVqxAt54A266CfbZJ+xoJE3ceeedYYcgIpIUnHMFZjYX6Au8XuJRX/bcaFXS\ndODsqHt9gTkl6lv3YGYNgEOBjysXcWKUuCapomLH+LmrOLnTvrRp2iDscKrO00/767XXhhuHpJU+\nfUor2xIRyUiPAS+b2SxgKr5rwH7AcwBmNgbAORf56vM54Fozexx4HjgRX896fmRCM3sUmACswK/G\n3gVkAX+r/j9nNyWuSerTb39g3eYd3D0wjVpF5ef73q3nnAPtY7aSE6mQpUv9ptaOHTuGHImISPic\nc+PMrCV+A1VbYCEwwDm3PBjSPmr8MjMbAPw/fMusNcB1zrmSK7QHAP/Ab9b6AZgBnFBizhphzpVV\np5v+srKyXH5+fthh7OXqsXOZtSyX6befSr06aXJOxHPPwdVXw2efwYknhh2NpJHIBkvVuIpIujOz\nbc65rLDjCItWXJPQxq07mbxoPb/t2SF9ktbiYr8p69hjoVdpbeREKubee+8NOwQREakBSlyT0Fuf\nr2ZXkePXx6XRpqxJk+Cbb2DsWEinDgmSFE4++eSwQxARkRqQJst56cM5x7jZK+nWrhmdWjcOO5yq\n8/jj0LYt/OpXYUciaWjx4sUsXrw47DBERKSaKXFNMvNX/siSDVsZnE6rrYsWwcSJMGwY1KsXdjSS\nhq688kquvPLKsMMQEZFqplKBJPPanJU0rFubM7q2DTuUqvPkk1C/PiixkGry4IMPhh2CiIjUACWu\nSWRbQSETFqxlwJFtadygbtjhVI3cXPjb3+DCC2HffcOORtJUL234ExHJCCoVSCLvfrmOrTsLk7tM\noKgIJk+G9aWdGhflhRdg+3a4/vrqjUsy2sKFC1m4cGHYYYiISDXTimsSeW3OSg7KzuK4Ds3DDqV0\n//d/cMcd/vcuXeCUU/zPySdDdvaeY3ftgqeegl/8Ao48suZjlYxxbXASm/q4ioikNyWuSWJZTj6z\nluVya//OWLK2i1q5Eu6/H047zSerH38Mo0fvPsa1a9c9E9mJE2HVKnjmmVDDlvT3yCOPhB2CiIjU\nAJ2clSQnZ/3f+9/w3CffMf32U2ndpEHY4cQ2eDC8847vEtChg7+3axfMnu2T2I8/hqlTYccO36s1\nKwtat4Zvv4VaqkoRERGpLJ2cJaErLCrmjXmr6N25VfImrR9+CK+9BvfeuztpBahb15+E1asX/OEP\nsHMnzJy5O4m96iolrVLt5s+fD0C3bt1CjkRERKqTVlyTYMX14282cMno2Tx3YXf6H9Em1Fhi2rUL\njjrKr6R+9RU0bBh2RCJ76N27N6AaVxFJf1pxldCNm72Slln1+MWhrcIOJba//tWXB7zzjpJWSUqP\nP/542CGIiEgNUOIaso1bdzJ50Xou7tWBenWS8Cv1tWvhnntgwAA444ywoxGJSSUCIiKZIQkzpczy\n1uerKSx2/OrYJO3deuutvm718cf9hiuRJDR79mxmz54ddhgiIlLNtOIaIuccr81ZyVHtmtG5TeOw\nw9nbf/4DY8f6vq2HHBJ2NCKluuWWWwDVuIqIpDslriFasCqPb9dv5cFzkrA5f2EhXHsttGu3+8AB\nkST11FNPhR2CiIjUACWuIXptzkoa1K3FGUe1DTuUvT3/PHzxBbz+uu/HKpLEjjjiiLBDEBGRGqAa\n15BsLyhiwvw1DDiiLU0a1A07nD398APceSeceiqce27Y0YiUa9q0aUybNi3sMEREpJppxTUk73+1\nli07C5NzU9btt8PWrb4NljZkSQq4IyhnUY2riEh6U+IaknGzV3Jgy0ac0LGFv+EcXH89LF0KTz21\n5+lUNWnWLBg1CoYPh8MOCycGkQQ9//zzYYcgIiI1QKUCIVi+MZ8ZS3P5VfcDsMiK5gsv+BXOiRPh\nyCNh5EifzNak4mK45hpo2xb++Mea/WyRSujcuTOdO3cOOwwREalmSlxDMH7uKszg3O4H+Buffw7X\nXQennQbffgvHHQeXXw6//CWsWVNzgY0aBXPmwKOPQuMkbM8lUopPPvmETz75JOwwRESkmpmr6VW9\nJJOVleXy8/Nr7POKih0/+/NHdGrdmL/97njIy4Pu3WHHDpg/H7Kz/crnM8/45v8NGvjSgfPPr956\n09xc6NQJunSBTz5RbauklN69ewOqcRWR9Gdm25xzGdvuRzWuNew/S35gbd4O7jqjiy8FuPRSWL7c\nJ4vZ2X5QrVq+h+ppp8FvfwsXXABvvgnPPgv77lv5IIqL/Wd++eXun1mzYNMmnyQraZUU8+KLL4Yd\ngoiI1AD59IhHAAAUOUlEQVQlrjXs9TmraN6oLqce1srXtL7xhv9qvlevvQcfcog/veovf4G77oJP\nP4URI+Dss+P7MOd8a6uvv94zSV240HcNiOjQwdfVPvAAdO1aJX+nSE3q2LFj2CGIiEgNUKlADZYK\n5OYX0OPByVx4woHc3WornHQSDBgAb71V/irnwoVw0UW+HnboUHjySX8wwOrVfvV0xQp/Lfn7ihWw\nffvuOVq08AlqyZ8jjlA9q6S8yZMnA9CnT5+QIxERqV6ZXiqgxLUGE9eXpi7j3glf8/7Qwzl0wMm+\nJGDePGjePL4JCgr8qugDD0C9erBzp//av6TWraF9ezjwQH9t3x4OPdQnqW3bqgxA0pJqXEUkUyhx\nVeJaI4mrc47Tn/gP9QzemfwITJoEU6fCsccmPtmcOfDSS74mNpKgHnggHHAANGxY9cGLJLmVK1cC\n0K5dEh7oISJShTI9cVWNaw1ZuHoz36zbwhtbP4N//ctvgqpI0gr+fRV9r0gaUsIqIpIZlLjWkNfm\nrKTXmq855pVH4Ne/hmHDwg5JJG28//77APTv3z/kSEREpDqpVKAGSgV27Cqi/x3j+eeo39Msu5n/\nqr9Jk2r9TJFMohpXEckUmV4qoMS1BhLXt+euoMW5Z9Fr3TfUnjkDjjqqWj9PJNOsW7cOgDZt2oQc\niYhI9cr0xFWlAjWg8N4/cdLy+RSPeEFJq0g1UMIqIpIZtOJazSuua+d+SavjurG4z5l0mfim2lGJ\nVIMJEyYAMHDgwJAjERGpXpm+4qrEtZoTV+cc344ZT/N+v6BV25bV9jkimUw1riKSKTI9ca0VdgDp\nzszo/NtfKWkVqUbjx49n/PjxYYchIpI0zGyYmS0zsx1mNtfMTipn/MnBuB1mttTMrqrsnNVBiauI\npLzs7Gyys7PDDkNEJCmY2WDgCeBB4GhgGvCembUvZfxBwLvBuKOBh4C/mtm5FZ2zuqhUoAaPfBWR\n6vHmm28CMGjQoJAjERGpXvGUCpjZTOAL59zlJe4tAcY7526PMf7PwCDn3CEl7o0EDnfO9azInNVF\nK64ikvKefPJJnnzyybDDEBEJnZnVA7oDk6IeTQJ6lfK2njHGTwSONbO6FZyzWmR8O6wWLVpoQ4dI\nihs+fDigzVkikhHqmNmcEq9HOOdGlHidDdQG1ke9bz3Qp5Q52wCTY4yvE8xnFZizWmR84pqbm/vT\njmQRERGRJFfonDs2jnHRtaAW41554yP3rYwxNVpzmvGJq4ikvnHjxgEwePDgkCMREQldDlCEX0Ut\nqRV7r5hGrCtlfCGwEZ+gJjpntVCNq4ikvGeffZZnn3027DBERELnnCsA5gJ9ox71xXcCiGU6e3/l\n3xeY45zbVcE5q4VWXEUk5b377rthhyAikkweA142s1nAVOAqYD/gOQAzGwPgnLsoGP8ccK2ZPQ48\nD5wIXAycH++cNUWJq4ikvEaNGoUdgohI0nDOjTOzlsCdQFtgITDAObc8GNI+avwyMxvA/2/v7qPl\nqOs7jr8/QAgU5QSRx1AIKiJPbVCqIk+ByqnKKYcHC/E0wm17oECRQ2tUHgQCyFPV8qSAEA8XCBbk\nqfVQFDAFYhFjg5QnITyYYIEECCQlIY83fvvH77dksuzu3d27u3dv9vM6Z86dnfnNzHfmN3vv9878\nZn5wKXAi8CpwSkTc0cA6O2JY3uMq6STga6Qdfxo4NSJ+UaXsBOCBCrN2iYhnC+WOBM4HPgy8CJwZ\nEXcNFovf42o28k2bNg2ASZMmDXMkZmbt5S5fO2wIPS/sRkp0S8PzhXXuDdwK3AyMzz9vk/Splu+A\nmXWdqVOnMnXq1OEOw8zM2qzjV1yb6M1hAumK6xYRsaDKOm8FPhARBxem/Rx4IyK+VGmZEl9xNRv5\nVq1aBcCoUaOGORIzs/byFdcOGmLPC7MkzZM0XdKBZfOq9fjQ0d4czGx4jBo1ykmrmVkP6HRTgVq9\nOZS/G6xkHqmh8JHAEcBsYLqk/Qtltm5knZKOlzRL0qyBgYHG9sDMuk5/fz/9/f3DHYaZmbXZcL1V\noO6eFyJiNilZLXlE0jhgMjCjyXVeC1wLqalAvUGbWXcqJa19fX3DGoeZmbVXpxPXZnpzqGQmMLHw\nuVqPD4Ouc+nSpSFpWQPbLtqA1KuEdSfXT/dqS91IGryQ1cPfne7luulunaifjdu8/q7W0cQ1IlZK\nKvW8cFth1sHAHZWXqmg8qQlBySN5Hd8uW+egvTlERNPNJSTNqrO/YBsGrp/u5brpbq6f7uW66W6u\nn/YbjqYCDfXmIOlUYC7pfa8bApOAw0htXksuB2ZIOh24CzgcOBDYt/27Y2ZmZmad0PHEtdHeHEjJ\n6neAscAyUgJ7SES828djRPxS0kTgW8C5pA4Ijo6ImW3dGTMzMzPrmGHpOWtdIen4/KCXdSHXT/dy\n3XQ310/3ct10N9dP+zlxNTMzM7MRoeNdvpqZmZmZNcOJq5mZmZmNCE5ca5B0kqQ5kpZLelTSfoOU\nPyCXWy7pd5JO6FSsvaiR+pG0jaQfSXpW0mpJ/R0Mtec0WDdHSLpP0huSFkuaKenQTsbbaxqsnwMk\n/VLSm5KW5e/Q5E7G20sa/btTWG5fSQOSnmp3jL2swe/OBElRYfhYJ2Ne1zhxrULS0aTXbF0I7El6\nJ+xPJZW/9aBUfkfgnlxuT+Ai4EpJR1Yqb0PTaP0Ao0kdYFxM6sDC2qSJujkA+E/gkFz+HuCuev9g\nW2OaqJ8lwBXA/sCu5Le3SDqpA+H2lCbqprTcZsCNwPS2B9nDmq0fYDfSW5RKw/PtjHNd54ezqpA0\nE3giIo4rTHseuD0iTq9Q/hLgiIjYqTBtKrBbROzdiZh7SaP1U7bs3cCCiOhrb5S9aSh1Uyj/a+AX\nEfHVNoXZs1pUP3cCKyLiS20Ksyc1Wze5Ph4ndXX+xYjYve3B9qAm8oIJwAPAFhGxoGOBruN8xbUC\nSRsCnwDuK5t1H/CZKovtXaH8vcBekka1NsLe1mT9WAe0sG7eDyxsVVyWtKJ+JO2Zyz7U2uh6W7N1\nk698b026Em5tMsTvzixJ8yRNl3RgWwLsIU5cK/sgsD7wWtn010i/ICrZukr5DfL6rHWaqR/rjCHX\njaR/ALYDbmptaMYQ6kfSy5JWALOAqyLimvaE2LMarhtJewDnAH8dEavbG17Pa+a7Mw84kdTT5xHA\nbGC6pP3bFWQvGI4uX0eS8nYUqjBtsPKVpltrNFo/1jlN1U1uE/5tYGKhNz1rvWbqZz/gfcCngUsk\nzYkI/3PRenXVjaTRwC3A5IiY04nADGjguxMRs0nJaskjksYBk4EZ7QiuFzhxrWwBsJr3/he1Je/9\nb6tkfpXyA8CbLY3Omqkf64ym6yYnrTcBx0TET9oTXs9run4KydGTkrYCpuCr4q3UaN1sQ3pY7npJ\n1+dp6wGSNEDqSr38trY1r1V/d2YCE1sVVC9yU4EKImIl8ChwcNmsg0lPEVbyCPDZCuVnRcSq1kbY\n25qsH+uAZutG0lHANKAvIm5vX4S9rYXfnfVIb+qwFmmibl4B9gDGF4ZrgBfyuH8XtlALvzvjSU0I\nrEm+4lrdvwA35aebHwZOALYl/WJA0o0AEXFMLn8NcLKky4AfAPsAfYCfum2PRusHSePz6KbAH/Ln\nlRHx204G3gMaqhtJE0lX7iYDMySVrmisjIi3Ohx7L2i0fr4CzGHNLc/9SXV1VWfD7gl1102+ILLW\nO1slvU5624Pf5doejX53TgXmAk8DGwKTgMNIbV6tSU5cq4iIWyVtDnyTdEvmKdKtl1K7u+3Lys+R\n9AXgUlJj7FeBUyLijg6G3TMarZ/ssbLPfwm8BIxrV5y9qIm6OYH0u+iyPJQ8BExob7S9p4n6WR+4\nhPQ9GQBeBE4j/7G21mny95p1SBP1syHwHWAssIyUwB4SEfd0KOR1kt/jamZmZmYjgtu4mpmZmdmI\n4MTVzMzMzEYEJ65mZmZmNiI4cTUzMzOzEcGJq5mZmZmNCE5czczMzGxEcOJq1uUk7STpe5KekbRE\n0mJJz0q6TtKnC+XmSgpJc4cx3FIs/TmWyH1zl6ZvJelmSfMkrc7zL5M0rlC+v41xjZE0JQ+H1Rt3\np0iaUNj+YMOUvEzp84Odjncw7azXRuqq7Li2NA4z6yx3QGDWxST9DXA17+1ec+c8bEHqiWWkuBw4\nehi3PwY4J4/fAPzbMMZiZmYNcuJq1qUkHQRMJd0ZCeACUnfCrwM7AF8EPjpsAdYQEX2kLo/LfSL/\nXAR8KCIWFuapzWENqkbcndr+gxSOg6Q+4Pr88YYcX8tJ2igilrdj3WZmreSmAmbd6yLWfEeviIiz\nIuLliFgZEc9HxEXAcbVWIGm8pDslvSDpbUmrJM3P0/YqK7ujpBsl/V7SckmLJD2Vb8luWSh3nKRZ\nkt6StELSK5Lul3Rsocxat3FLt2qBj+QiY4C38vy+WreUJX1c0r/m7ayUtEDSA5I+mee/T9INkp6U\n9Gbex0WSZkg6urCeKcCcwqqPLd9mjSYOm0g6V9LTkpZJWirpMUn/JGmDQrm19kPSMfkYLlNq6nEs\nbSTpIEm/ytt7UdLXJRUT4SmF+A6X9ENJC0jdUZbK7CLppsLxfl3S7ZL+pGxbdZ0vZcscJemJWsdD\n0n6SfiLpjcL5ekv59mscg21zvEvy+XA18P4qZRveBzMbZhHhwYOHLhuALUlXWUvD2DqWmZvLzi1M\nm1i2nuLwDrBLoezTNcrunsv8VY0ytxfW1V+YPg6YUGO5vlym9Lm/sJ7DgVXVlstltq6x7gCOzeWm\n1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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot balanced accuracy, abs(1-disparate impact)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, np.abs(1.0-np.array(disp_imp_arr)), color='r')\n", "ax2.set_ylabel('abs(1-disparate impact)', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], \n", " color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)\n" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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ti7+PVIOrioULF9odgnAzvVqE8u2jvc9Nh9l2KJVN+08w/4/Ec8c0quVPVKOa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\nwESAJk2a6KVLlzrx1NVHze3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/YIrj+AMqu8sJd1d4V7mCOnQw279u2GA2PRDCCjt2mE/7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\nPjaSDgauA/4zhFBf2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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot average odds difference\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, avg_odds_diff_arr, color='r')\n", "ax2.set_ylabel('avg. odds diff.', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2200\n", "Best balanced accuracy: 0.7581\n", "Corresponding abs(1-disparate impact) value: 0.2939\n", "Corresponding average odds difference value: -0.0084\n", "Corresponding statistical parity difference value: -0.0992\n", "Corresponding equal opportunity difference value: 0.0242\n", "Corresponding Theil index value: 0.0938\n" ] } ], "source": [ "lr_thresh_arr_transf_panel19_best = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % lr_thresh_arr_transf_panel19_best)\n", "lr_best_bal_acc_arr_transf_panel19 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel19)\n", "lr_disp_imp_at_best_bal_acc_transf_panel19 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel19)\n", "lr_avg_odds_diff_at_best_bal_acc_transf_panel19 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel19)\n", "\n", "lr_stat_par_diff_at_best_bal_acc_transf_panel19 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel19)\n", "lr_eq_opp_diff_at_best_bal_acc_transf_panel19 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel19)\n", "lr_theil_ind_at_best_bal_acc_transf_panel19 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel19)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.3.3. Testing LR model after reweighing" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Evaluate performance of a given model with a given threshold on a given dataset\n", "\n", "scale = lr_scale_transf_panel19\n", "\n", "dataset = dataset_orig_panel19_test #apply model to this data\n", "model = lr_transf_panel19 #this is the model applied\n", " #lr_transf_panel19 is LR model learned from Panel 19\n", " #transformed data\n", "thresh_arr = lr_thresh_arr_transf_panel19_best # lr_thresh_arr_transf_panel19_best wass threshold for LR\n", " # model with highest balanced accuracy\n", "\n", "\n", "X_data = scale.transform(dataset.features)\n", "y_data = dataset.labels.ravel()\n", "y_data_pred_prob = model.predict_proba(X_data) \n", "\n", " \n", "y_pred = (y_data_pred_prob[:,1] > thresh_arr).astype(np.double)\n", "\n", "dataset_pred = dataset.copy()\n", "dataset_pred.labels = y_pred\n", "\n", "classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", "TPR = classified_metric.true_positive_rate()\n", "TNR = classified_metric.true_negative_rate()\n", "bal_acc = 0.5*(TPR+TNR)\n", " \n", "acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", "\n", "#get results\n", "best_bal_acc = bal_acc\n", "disp_imp_at_best_bal_acc = np.abs(1.0-metric_pred.disparate_impact())\n", "\n", "avg_odds_diff_at_best_bal_acc = classified_metric.average_odds_difference()\n", "\n", "stat_par_diff_at_best_bal_acc = classified_metric.statistical_parity_difference()\n", "eq_opp_diff_at_best_bal_acc = classified_metric.equal_opportunity_difference()\n", "theil_ind_at_best_bal_acc = classified_metric.theil_index()" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2200\n", "Best balanced accuracy: 0.7539\n", "Corresponding abs(1-disparate impact) value: 0.2482\n", "Corresponding average odds difference value: -0.0151\n", "Corresponding statistical parity difference value: -0.0872\n", "Corresponding equal opportunity difference value: -0.0035\n", "Corresponding Theil index value: 0.0966\n" ] } ], "source": [ "lr_thresh_arr_transf_panel19_best_test = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % lr_thresh_arr_transf_panel19_best_test)\n", "lr_best_bal_acc_arr_transf_panel19_best_test = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel19_best_test)\n", "lr_disp_imp_at_best_bal_acc_transf_panel19_best_test = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel19_best_test)\n", "lr_avg_odds_diff_at_best_bal_acc_transf_panel19_best_test = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel19_best_test)\n", "\n", "lr_stat_par_diff_at_best_bal_acc_transf_panel19_best_test = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel19_best_test)\n", "lr_eq_opp_diff_at_best_bal_acc_transf_panel19_best_test = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel19_best_test)\n", "lr_theil_ind_at_best_bal_acc_transf_panel19_best_test = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The fairness metrics for the logistic regression model learnt after reweighing are fairly improved, and thus the model is much more fair relative to the logistic regression model learnt from the original data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.4. Learning Random Forest (RF) classifier from data transformed by reweighing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.4.1. Training RF model after reweighing" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Train model on given dataset\n", "\n", "dataset = dataset_transf_panel19_train # data to train on\n", "\n", "scale = StandardScaler().fit(dataset.features) # remember the scale\n", "\n", "model = RandomForestClassifier(n_estimators = nestimators, min_samples_leaf = minsamplesleaf)\n", "\n", "X_train = scale.transform(dataset.features) #apply the scale\n", "\n", "y_train = dataset.labels.ravel()\n", "\n", "\n", "model.fit(X_train, y_train,\n", " sample_weight=dataset.instance_weights)\n", "y_train_pred = model.predict(X_train)\n", "\n", "#save model\n", "rf_transf_panel19 = model\n", "rf_scale_transf_panel19 = scale" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.4.2. Validating RF model after reweighing" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████| 50/50 [00:00<00:00, 199.99it/s]\n" ] } ], "source": [ "#validate model on given dataset and find threshold for best balanced accuracy\n", "import numpy as np\n", "from tqdm import tqdm\n", "thresh_arr = np.linspace(0.01, 0.5, 50)\n", "\n", "scale = rf_scale_transf_panel19\n", "\n", "model = rf_transf_panel19 #model to validate\n", "dataset = dataset_orig_panel19_validate #data to validate on\n", "\n", "X_validate = scale.transform(dataset.features) #apply the same scale as applied to the training data\n", "y_validate = dataset.labels.ravel()\n", "y_validate_pred_prob = model.predict_proba(X_validate)\n", "\n", "\n", "bal_acc_arr = []\n", "disp_imp_arr = []\n", "avg_odds_diff_arr = []\n", "stat_par_diff = []\n", "eq_opp_diff = []\n", "theil_ind = []\n", " \n", "for thresh in tqdm(thresh_arr):\n", " y_validate_pred = (y_validate_pred_prob[:,1] > thresh).astype(np.double)\n", "\n", " dataset_pred = dataset.copy()\n", " dataset_pred.labels = y_validate_pred\n", "\n", " classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", " bal_acc = 0.5*(classified_metric.true_positive_rate() + classified_metric.true_negative_rate())\n", " \n", " acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", " bal_acc_arr.append(bal_acc)\n", " avg_odds_diff_arr.append(classified_metric.average_odds_difference())\n", " disp_imp_arr.append(metric_pred.disparate_impact())\n", " stat_par_diff.append(classified_metric.statistical_parity_difference())\n", " eq_opp_diff.append(classified_metric.equal_opportunity_difference())\n", " theil_ind.append(classified_metric.theil_index())\n", "\n", " \n", "thresh_arr_best_ind = np.where(bal_acc_arr == np.max(bal_acc_arr))[0][0]\n", "thresh_arr_best = np.array(thresh_arr)[thresh_arr_best_ind]\n", "\n", "best_bal_acc = bal_acc_arr[thresh_arr_best_ind]\n", "disp_imp_at_best_bal_acc = np.abs(1.0-np.array(disp_imp_arr))[thresh_arr_best_ind]\n", "\n", "avg_odds_diff_at_best_bal_acc = avg_odds_diff_arr[thresh_arr_best_ind]\n", "\n", "stat_par_diff_at_best_bal_acc = stat_par_diff[thresh_arr_best_ind]\n", "eq_opp_diff_at_best_bal_acc = eq_opp_diff[thresh_arr_best_ind]\n", "theil_ind_at_best_bal_acc = theil_ind[thresh_arr_best_ind]" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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d+eUX3X5l4kR4440SeYsZM2YAMGrUqBK5vrBeaGQiw+fsJiohna8eb02PJtIy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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot balanced accuracy, abs(1-disparate impact)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, np.abs(1.0-np.array(disp_imp_arr)), color='r')\n", "ax2.set_ylabel('abs(1-disparate impact)', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], \n", " color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)\n" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "data": { "image/png": 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vc/6c3bZt29i2bZvZMUQZhfh6MOP+DozsXpcZ6xK4Z9p6TmTIDmqi2MGDcPSo\nTFtwYqqy9xr09fXVmZmZZscou8aNoUED+P13s5M4rQe/3sza2FSWPhVFjUBvs+MIIaz067ajPDt3\nB4He7kwZ2pbWdYLNjuQ4tm+H//3P+N7f3/jy8yv91t8frr0W3Bxgvftnn8GYMRATA40amZ3GIkqp\nLK21r9k5HIUD/FcoLNKrF8ycCfn5sn1hOVi6N5kle5N5tk8TKXKFcFC3tqpFwzB/Rs/azMDP1jPp\ntuYMbF/H7Fjl448/oE4daNasbNcpKoJ33oH//McoZIOD4exZyMiA7OxLPy4qChYtAk873zFy2TKo\nVQsaSs9lZyVTF5xFr17Gi8/GjWYncTqZuQVM/HU3jar58UC3umbHERVk0qRJTJo0yewYwsaa1Qxg\n3sPd6FgvhGfn7uQ/P+90vnm7a9fCTTfBNdfAo4/CqVNXd53ERON3yzPPQL9+cOAAxMZCcjJkZUFB\nAZw5Y5y3d6/x+2fZMnj7bVi5EkaMsO9F0lobHRd69pQNl5yYjOg6i3P/UJcuha5dzU7jVN77cz9H\nz2QzZ0xnPNzkvWFlERMTY3YEUU6CfT2YPqIDby2KYcrKWPYlZfDpPW2co11gfr7xUXzt2kZxOnky\nfPstvPoqjBxp+YYI331nXKewEL78EoYP/3cx6Opq7CYWGPjP4z17GjkmTIDISHjtNVv8yWxv925I\nSZH5uU5Ofms7i5AQY+tCWZBmU7uOpvHlmkMM6ViHdpEhZscRFWjWrFnMmjXL7BiinLi6KJ67qQkf\nD2nNnmPp3PLRX/y5J5nsvEKzo5XNhx8aHXg++sgocrduhRYtYOxYaNsWVq26/OPPnIF77oHBg41p\nD9u2GSOz1o54PvssjBoFr78OU6de/Z+nPC1bZtxW8kJXKeWplPpIKZWqlMpUSs1TStW24HEPKaUO\nKaVylFJblFLdS9wXUnzNfUqpbKVUolLqU6VUhW8lKovRnGUxGhgfL73/Ppw+Db4yT72sCos0t09e\nw7EzOSx9MopAH5n7LIQz2peUzuiZW0g4mYWHqwttIoLoWj+ULg2qcE3tIMdpJXj4sFGcXncd/Prr\nheJUa5gzB556yphmMHAgvPUWhIf/8/ErVsCwYXDsGLz4ojEiW5YFZQUF0L8/LF4M8+cb0ynsyW23\nwY4dxq5oDsTWi9GUUp8CtwL3ASeBd4EgoK3WutR3fkqpgcAs4CHgr+LbEUAzrfVhpVQL4BVgOrAH\nqAVMBo5qrW+wVXZLSKHrTIXuokXQp4+xCOHGG81O4/C+WnOIl+fv4cPBrel/bU2z44gKNnHiRABe\neeUVk5OIipCTX8j6uJOsjT3kbab7AAAgAElEQVTJmoOp7Dmejtbg5+lGh7ohdKlfha4NQmlczR8X\nFzudz3n77UZRuWcPRET8+/6sLKNzwptvGkXwhAkwfrzRP3biRKP4rV8fvvkGOnSwTaaMDGNh2oED\nxmhy69a2uW5ZFRZCaCgMGADTppmdxiq2LHSVUoFACjBCa/1N8bFwIAG4SWu96BKP2wDs0FqPLHHs\nADBHaz3hEo/pC/wGBGmt022R3xIyR9eZdOtmdFxYulQK3TI6npbN24tiiGpUlX7X1DA7jjBBYqLs\npFWZeLm7Et04jOjGYQCczsxjXZxR9K6NPcmyfScAqOLrQfeGoYyNbkDj6v5mRv6nefPgl1+MIra0\nIhfAxwdeesmYijB+vFHcfvklBAQYI5ujRhkdFvz8bJfL3x9++w06dYKbb4b1641uEOUlPd2Yd+vm\nZny5upZ+u327MU2jkk9bANoC7sDicwe01olKqb1AF+Bfha5SyqP4cW9fdNfi4sdcSgCQC2SVMbNV\nKv2Ibnh4uJ45c6bZMWym1WOP4ZqdzRZ7nRPlIA6fyiIjp4BG1fwc52NLIUS5yS/UnM0tIDO3gPTs\nfAq1JtjHg2oBnqa/RrhkZ9NhxAgKvb3Z/PnnaAunGwRt3UqDjz/G49QpYsaP52Q5LmT2PXSI1o8+\nSk5YGFs//JBCWxbTgM/hw9SeM4dqixfjmptr8ePW/vgjeaGOtQFQz54984CSW6FO1Vpf1S99pdQQ\nYAbgrksUhEqpZcABrfXoUh5TEzgKRGmtV5U4PhG4R2vduJTHBAGbgIVa63FXk/VqVfpC16mmLgC8\n8orxjj0lBapU+Jxvp7B4dxKjZm7h2T5NGBtd3+w4Qgg7czozj09XxjJ9bTxoGNY5god7NiDY18Oc\nQM8+a0xJWL3a+GTPGlobHRI8KiD70qXG9LqoKFiwoOzPqTX8+aexNmXhQqNn79Ch0L27MTWhsNCY\nJ3zx7bnvIyONOckOxpKpC0qpV4H/XOFSPYGalF7oLgditNZjSrn2uUK3h9Z6dYnjLwKDtdZNLjrf\nF/gDKAT6aK0rdGtCKXSdrdBds8Z4ofvxR7jzTrPTOJyzuQX0fnclgd7uzH+0m+kjNcI8EyYY08xe\nf/11k5MIe3XsTDbv/bmfuX8fwdfDjdFR9bi/W118PCpwVuDOndCmDdx3n2PMNf36a6NV2X33wVdf\nXV3/2uxsYx7x++8bLcKqVYOHHzbaoVWtavPI9sbCQjcUuNJQ9WGgE7AUCNNap5R4/G6M+bYvlnJt\nD4zpB4O11j+WOP4J0EJrHVXimB+wAFAYc37PXunPZ2syR9fZdOhgzK9aulQK3avw7uL9JKXn8PGQ\nNlLkVnInT540O4KwczWDvHnrrmsZ2aMeby2K4e3F+/l6XQKP9WrIwPbh5f8aUlRktA0LDDTm5jqC\n++6D+Hjjk8fISOPWUsePGy3TpkyB1FRo1coonAcOtP8d2CqY1joVSL3SeUqpLUA+0BuYXXysNtAU\nWHuJa+cVP6438GOJu3oDc0tc2x9YiFHk9jGjyAUZ0XW+EV0wJvwfOAD795udxKHsPJLGrZ/8xZCO\ndXj1tpZmxxFCOJjN8ad48499bIo/Td1QX566oRE3t6yBKq9dt774Ah580BgZHT68fJ6jPGgN998P\n06fDpEnQoAHk5hpfeXkXvi/589Gj8PPPxrSDfv3giSeMKRCVcEezcmov1p9/thcLpkR7MaXUPuBj\nrfXHxT8PBGZitBVbA4wBHgCaa60TiovcxRgL0G4DMko85SmtdZ6t8l+JFLrOWOi++67RL/Hw4X/3\nSRSlKigs4rbJa0hOz2XpU1EEeEnPXCGE9bTWLNt3gv/9EUNMcgZNawTwWK8G3NCsum3bkqWkQJMm\nxmYQK1Y4XsGXlwe33GLMsb0cd3djtNbPD+66C8aNMwrjSqwcCl0v4C1gCOCNMZXhIa11YolzNPCy\n1vqlEsceAp4BagC7gCfOLU5TSkUDyy/xlD211itslf9KpNB1xkJ3+3bjIx1He5dvoi/+OsSk3/bw\nyZA23CztxAQwfvx4AN5+++IOOkJcWWGR5tdtR/lo2UEOpWbSpLo/43o1pE9zGxW8I0bArFnG632z\nZmW/nhkKC42ev25uRjHr4WHcnvtydzd6/Ip/sHWh6+xkjq4zatnSmJC/dKkUuhY4diabdxbHcF2T\nMPq2rG52HGEnsrOzzY4gHJiri+KONrXpf21N5u84xkfLDvLQN3/TuJo/j/ZqQN8WNa6+4F250vjY\nf8IExy1ywehp21KmiYnyJSO6zjiiCzBokLELzdGjjveRVgXSWjNyxhbWHExl8RM9CA/xMTuSEMIJ\nFRZpfttxjA+XHiA2JZOGYX482qshN7esgas1BW9envGJXXa20XHAR16zKhsZ0bWOfCbgrHr1Mlao\n7ttndhK7tnhPMkv2JvNE74ZS5Aohyo2ri+LWVrVY/EQUHw42tsEd9+1Wbnx/Fb9uO0phkYWDTu+8\nA3v3wiefSJErhAVkRNdZR3Tj4ow9yz/6CB55xOw0dklrzU0frCa/sIhFj/fATdqJiRIef/xxAN5/\n/32TkwhnVFSkWbDrOB8uPcD+5LM0CPPjmRsb07tZtUt3aYiPh6ZNjc46c+ZUaF5hP2RE1zqm/GZX\nSj2klDqklMpRSm1RSnW/zLnTlVK6lK/Mi86LKr5WjlIqTin1r908KpV69YwehUuXmp3Ebi2POcG+\npAweim4gRa4QokK5uChuuaYmfzzWg0+GtKFIa0bN3MJdU9axJeFU6Q967z1jAdd771VsWCEcWIWP\n6Bb3XpuF0Xvtr+LbEUAzrfXhUs4PxGh3UdIaYJXWekTxOXUxWlt8CUwGuhXfDtJaz+UynHZEF4z+\ninPnGo21XV3NTmN37vx0LcfTcljxdLRsDiGEMFVBYRE/bD7Ce0v2k5KRyw3NqvFMnyY0CPMzTkhL\ng9q14Y47jE0SRKUlI7rWMeO3+5PAdK3151rrvVrrR4HjwNjSTtZap2mtk859AfWBesDnJU4bAxzT\nWj9afM3Pga+B8eX7R7FzvXrBmTPw999mJ7E7Gw+dYnPCaUb1qCdFrhDCdG6uLgzpWIeVT0fzVO9G\nrI09yY3vr2LCTzs5kZ4DX34JZ8/CY4+ZHVUIh1Khv+GL90dui7FbRkmLgS4WXmYksFtrXXJrus6l\nXHMR0E4pVXk7/193nXE7bhxs3GhuFjszecVBqvh6cHc72VBDlO7hhx/m4YcfNjuGqGR8PNx4tFdD\nVj4dzb2dIpizJZGeby4l7c13KOjaDdq0MTuiEA6looeyQgFXIPmi48nAFRuYFk9juIt/juZS/NjS\nrulW/JwXX2eUUmqzUmpzQUGBhdEdULVqxqYRsbHQsSPcfTccPGh2KtPtPpbGipgU7u9WF28PmdIh\nSuft7Y2398WzpoSoGFX8PHmpf3OWPBnFE9n7CEw+ynPh1/HFX4c4eTbX7HhCOAyL5ugqRUet2VDm\nJ1OqJnAU6KG1Xl3i+IvAYK11kys8/mHgHaCm1vpUieP7gZla60kljkUBK4AaxVMeSuXUc3TPSU+H\nt9822tLk5cHo0TBxIoSFmZ3MFI9+u5Xl+06w5rnrCPSuvAP+QggHERVF3qF47v/vbP6KO4NS0KZO\nMNc3rcb1TcNoEOZ36U4NwunIHF3rWDqiu04pdijFo0oRXIbnSwUK+ffobRj/HpEtzUhgbskit1jS\nJa5ZAJy8ipzOJSAAXnnFGM194AGYMsVoPfbKK8acr0okPjWT33cc455OdaTIFULYv7//hlWr8Hj8\nMWaO7MLv47rxeK9G5BUU8eYf++j93iqi317BpN/2sDY2lfzCIrMTC2FXLB3RLQLOnZgL/AxM05rl\nVj+hUhuA7VrrUSWO7ccoYCdc5nEdgfVAT631iovuexO4TWvduMSxqUBLrXXny+WpFCO6F4uJgeef\nh59+MqY3vPSSUQC7O3/hN+Gnncz9+wh/PduTMH8vs+MIOzZqlPESNXXqVJOTiErtvvuM1+ojRyAw\n8B93JaXlsHRfMkv2JLMm9iR5BUUEeLkR3TiM65tVo1eTMHw93UwKLsqLjOhax9IR3feAI4ACvIBB\nwBKlOKAUzyl15fm1JbwLDFdKPaiUaqqU+gCoCUwBUErNUErNKOVxI4EDwMpS7psC1FZKvV98zQeB\n4cDbVuSqPBo3NtqOrV0LDRvC2LHQogUsWmR2snKVnJ7D3C1HuKttbSlyxRVVqVKFKlWqmB1DVGZJ\nSfDddzBixL+KXIDqgV7c0zGCr0Z0YNvE3nx2b1tubF6dNQdTGfftVjq/vpT//bHP6NogRCVlVR9d\npegGDAYGYEwNAGOktxD4Ffg/rdl25euoh4BngBoY/W+f0FqvKr5vBYDWOrrE+f4YLche0Vr/7xLX\njMIoyJsDx4A3tdZTrpSlUo7olqQ1zJ8Pzz5rLFpbtQo6darYDCtWwKFDxot5OXptwV6mrY5jxfie\n1KkiW2cKIezcSy8ZU8xiYoxBCQsVFmk2x59i+tp4/tidhLuLC7e2qsnIHvVoVM2//PKKCiEjuta5\nqg0jlCIcmAFEYRS6qvi2ALhba361ZcjyVOkL3XNOnYJ27SA/H7ZsqbiFaj/8APfcA56ekJEB5bSg\nIi0rny5vLKVX02rn95kXQgi7lZMDERHQoYMxGHGVEk5m8sVfh/hhcyI5+UVEN67KqO716Fy/iixg\nc1BS6FrH2hHd3hibM/TDaBN27l/JViAAYzOHPVrTwsY5y40UuiVs3QpduhhfixaBWznP7friCxg1\nCnx8jEVxJ05A1arl8lQfLT3AO3/uZ+Fj3WlaI6BcnkM4lxHFnzB89dVXJicRldL06canXEuWGJv/\nlNHpzDxmrU/g63XxpJ7No3nNAEb1qEffljX+sWlOUZEmOSOHwyezSDydTeKpLOPrdBZnsvK5o01t\nhnWOkLm/JpJC1zqWLkZ7GhiFsSMZGAVuETAPeE9rViuFL0brMB+t8SinvDYnhe5Fzr24PvccvP56\n+T3Pe+/Bk0/CjTcazzdoEGzYYIxe2Fh2XiFd31xGq/Agvhze3ubXF85p4sSJALzyyismJxGVjtbQ\nujUUFsKOHTb9pCsnv5Bfth7l89VxxKZkUjPQi+4Nq3I8PYfEU1kcPZ1NXonODUpB9QAvwoON6V4b\n409RxdeD0VH1uLdTpPQiN4EUutaxtuuCAtKBL4EPtSb+ovP2AQ21xmH+y5dCtxSjR8PUqfDzz3Db\nbba9ttbw8svG1513wjffwP790LKlsehi4EDbPh/w1ZpDvDx/D3PGdKZdZIjNry+EEDa1YgX07AnT\nphkdccpBUZFmxf4TTF0Vx/7ks9QK8iY8xJvwEB/Cg30ID/GhTogPNYO88HS78Ct9S8Jp3l+yn9UH\nUgn182RMVD2GdorAy91hfu07PCl0rWNNoRsHfAR8oTWlNl9VipqAu9Yk2DRlOZJCtxS5udC9u7EA\nYtMmaNTINtfV2hjFff99YxR36lRjesTZs+Dvb4wgP/ecbZ6rWF5BEdFvLadWsDc/jrF0l2khhDDR\nbbfBmjVw+DDY6e58m+JP8d6f+1kbe5Iwf0/GRtdncIc6UvBWACl0rWNpe7HbMUZqP7hUkQugNccc\nqcgVl+DpCXPmGH11BwwAW7wRKCyEBx80itzHHjNGKs7NAfbzM+bmHjpU9ue5yK/bjnIsLYeHohvY\n/NrCuQ0dOpShQ4eaHUNUNrGxMG8ejBljt0UuQPvIEGaP7MT3ozpRN9SXl+fvIfqtFcxcF09uQaHZ\n8YQ4z9JCdwUQrhShJQ8qRahS1FGKfzf4E46tTh349lvYvdtYMHYV3TnOy8sz5uB++SW8+KIxP9fl\nov/06ta1eaFbVKSZsjKWpjUCiG5cPovchPNq3LgxjRs3vvKJQtjSxx8bgwBjx5qdxCId61Xh+9Gd\nmT2yI+Eh3rzw6256vrWC5TEnzI4mBGB5ofslcAgYctHxQcXHv7BlKGEneveGSZNg9mzjxfdqZGXB\nrbcaI8Tvvmv0hSxtYUU5FLqL9yQTm5LJ2Oj60kZHWO2FF17ghRdeMDuGqEzS041uNHffDTVrmp3G\nKl3qh/LD6M7MeqAjAd7ujJ65hU3xp8yOJYTFhW7H4tu5Fx3/CWOBWkeEc5owAfr1M+bWrl1r3WPT\n0qBPH6NV2bRp8MQTlz63bl1ISDCmONiA1ppPVxwkoooPfVtYs3GfEEKY5KuvjH7ijz9udpKropSi\nW8NQZo/sRO0gbx78ejMHT2SYHUtUcpYWuuc+9z1z0fG0i+4XzsbFBWbMMBqX33UXJCdf/vyzZ2Hh\nQhg/Htq0gXXrjG4KV1o5XLeusVnFsWM2ib029iTbj6Qxqkc93Fwt/c9ciAsGDRrEoEGDzI4hKovC\nQvjwQ+ja1di8x4GF+Hrw9f0dcHd14b4vN5EsWxALE1laAZx7S3bDRcfP/XzJBWrCCQQFwdy5cPq0\n0f6roODCfXl5sHq1MSWhe3cIDoa+feGjj4x5vgsWGB/DXUlkpHFro+kLnyw/SFV/Twa0qW2T64nK\np1WrVrRq1crsGKKy+O03iItz2NHci4WH+DB9RHvOZOVx35cbSc/JNzuSqKQsbS+2GLgeYwT3HWAv\n0BR4EggElmjNjeWYs9xIezErzJwJw4YZfXYbNIClS40iNzPTmHfbtq2xg0+vXsaohI+P5dc+cMBo\nYzZ9Otx3X5lirtqfwrAvN/Lfm5vyYPd6V36AEEKYrWdPo9CNjS3/XSkr0Kr9Kdw/fRMd64Xw1fAO\neLjJJ2xlJe3FrGPpv6YpGIVuAPByieMKYyOJT22cS9ije++F9eth8mTj56ZNjX64110H0dHGaO7V\nqlPHKJbLOKJbWKR5bcFewkO8ubdzRJmuJYQQFWLbNmOTiLfecqoiF6BHo6q8OeAanvpxO8/M2c67\nd7fCxUUWB4uKY9G/KK35SSnexRjBvdg7WvOLbWMJu/X++3DLLXDttbZdFezpCbVqQXx8mS4z9+8j\n7EvK4OMhrf+xm48Q1howYAAAc+devAZXCBs4cQKWL4dly4wpXr6+5bYLmtkGtK1NUnoOby2KoVqg\nFxNuamp2JFGJWPzWUWvGK8X3QH+gGpAMzNOaTeUVTtghd3e46abyuXYZW4xl5xXyzuIYWoUHcXPL\nGjYMJiqjzp07mx1BOJO0NFi1ypjytWwZ7NxpHA8IgKgoY4OIsnwqZuceiq7P8bRsPlsZR/UAL0Z0\nrWt2JFFJWPUZSXFRK4WtKB916xojHFdp2uo4ktNz+XhIG+mbK8ps/PjxZkcQjm7LFmMh77JlsHmz\n0VnBy8tYw/Daa8a0r7ZtnW66QmmUUrzcvwUn0nN55bc9VAvwoq8MSIgKYPG/LqVwA/oCjYF/7Uuo\nNa/YMJeojOrWNRa85eWBh4dVD03JyGXKylhubF6N9pEh5RRQCCEstH8/dCxuMd+hg9GT/LrroHNn\no9ithFxdFB8Obs090zbw+PfbCPXzpENdeb0WFlLqXKN9jdYW168WnagUYRjbAF9uP0wpdEXZ1K1r\nbDV8+LDR1cEK7y/ZT25BEc/2aVJO4URl079/fwDmzZtnchLhkF591XjDfuCAsf5AAODl7sq0Ye0Y\nMGUtD369iblju9Cwmr/ZsYRjuKqPai2tiF8GLldBXLlHmRBXUrd4ztahQ1YVugeSM/huUyL3doqg\nXlW/cgonKptevXqZHUE4qgMH4JtvjJ64UuT+S7CvB1+P6MAdn66l/8draBUeRJuIINrUCaZ1nWBC\nfK37RE9UGoe5inrT0kL3huKLTwdGFH//GPBo8fdvWPvEQvxLyULXCm8s3IePuyvjejUsh1Cisnrs\nscfMjiAc1auvGp1knn7a7CR2KzzEh29HdmLGunj+PnyaKSvjKCwyapjIKj5G0RsRTJs6QTSu5i87\nXArQOvJqHmZpoXvuLelzGIUuWvOxUiwHdgKy/ZQou5o1ja4OVhS6a2NTWbrvBM/2aSKjAEII8x08\naIzmjhsH1aubncauNQjz45VbWwCQlVfAjiNpbD18hr8Pn2bVgRR+2noUAB8PV1qFB3Fb61r0v7Ym\nXu7SOtLpKPUuxtzbp1BqGABaz7DJpS3cGS0T8ALcgWyMArl68ffpwBGtqWOLQBVNdkazMw0bGquQ\nv/vuiqcWFWn6f/IXp87msWx8tLz4CZu6qbiN3sKFC01OIhzK8OHw/ffGG3YpdK+a1prEU9lsTTzN\n3wmn+etgKrEpmQT5uHN3u3CGdoygThUrdt90Ik65M5pSRUARWrv943sbsPQiJzFGdQOBJIwR3G+A\nnOL7nbf5n6hYkZEWj+j+uv0ou46m897Aa6XIFTbXr18/syMIR3PwIMyaJaO5NqCUok4VH+pU8eHW\nVrXQWrM+7hQz18fzxV+H+Hx1HNGNqjKscyRRjarKbmuOrwhQKBVY/LPN/kItHdH9E7gO6IgxN/ce\n/jkh+C+tibJVqIokI7p2ZtQo+OUXY9egy8jJL6TXOysJ9nVn3sPd5EVOCGG+ESOMT6NkNLdcJaXl\nMHvjYb7deJiUjFzqhPgwtFMd7m4XTpCP809hc9IR3WMYm5GdwRg81UDCJc7WaF3f0ktbOqL7OXAQ\nY/rCyxiL06oW35cCPG7pEwpxWXXrQkoKnD0LfpfuoPDVmniOnsnmrbuukSJXCGG+2FijD/ijj0qR\nW86qB3rxZO9GPNKzAYt2JzFzXQKvLdjHO4v30//amtzQvDp1Q30ID/GRreAdx3JgMBdmCCgg8hLn\nWtV5waIR3X89SBEA9AQKgDVac8bqi9gJGdG1M999B4MHG9tjtmhR6iknz+YS/dYKOtQN4Yvh7Ss4\noKgsrr/+egCWLFlichLhEO6/H779FuLioIbs+FXR9h5PZ+b6BH7ZepSsPGNfARcFNYO8qRvqS2QV\nXyJDfakb6kNkFV/CQ3xwd9BODk46ohsGfAi0ARpgFLOHL3m+1hbvIX3FEV2l8AT2FP94s9bs05p0\n4FdLn0QIi51rMRYff8lC96NlB8nKL2RCX9kcQpSfgQMHmh1BOIrYWJgxAx55RIpckzStEcBrt7fk\nP32bcuDEWeJTMzlU/BV/MpNfth0lI6fg/PmuLorW4UF8PqwdwdKxx3xanwAGAecWpllVzF7OFQtd\nrclViiqAPxBniycV4pKu0Es3LuUss9YnMLB9OA3CZDcdUX5GjhxpdgThKF57Ddzc4JlnzE5S6fl6\nutEqPIhW4UH/OK615lRmHvEnMzmUmkVsylm+WH2Ih2f/zdf3d3DY0V2nUbK92IX9GmzC0jm6S4Db\ngWuBTbZ6ciH+pWpV8PG5ZKH75h/78HRz4fHrZXMIIYQdiIuDr7+Ghx82eoELu6SUooqfJ1X8PGkb\nEQJAvVBfnp6zg0m/7Tnfz1eY5nGMzgtPAV8Vf2+TPrqWFrrvA1HAt0rxH2AbRg/d87S+zFwKISyl\nlDGqW0qhu+PIGRbtTubJ3o0I8/cyIZyoTKKjowFYsWKFqTmEnTs3mvvss2YnEVa6q104B06cZeqq\nOBpW8+feThFmR6rMyq29mKWF7iqMYeQQYHYp92srriXE5V2i0J21PgEfD1dGdI2s+Eyi0hk+fLjZ\nEYS9O3TIGM0dO1ZGcx3Us32acCA5g5fm7aZ+VV+61A81O1JldQKjvdiFKbJKXWq6rFXtxayZlKKu\n8CWEbZwrdEt0BEnPyWf+9uP0v7Ym/l7uJoYTlcXw4cOl2BWX99pr4Ooqo7kOzNVF8eHg1tQN9eWh\nb/4m4aR0YTLJcoxa8uL2Ypf6spilo7BfW3NRIcqkbl1IT4fTpyHEmEv167ZjZOcXMriDQ+40LRxQ\nfn4+AO7u8sZKlOLQIZg+HcaMgVq1zE4jysDfy51pw9px2+Q1PPD1Zn5+qIsMqFS8JwBXjPZi50Zr\nbTIl1qJCV2tG2OLJhLBIyc4LISForZm94TDNagRwTe3Ayz9WCBvp3bs3IHN0xSW89hq4uMBzz5md\nRNhAZKgvk+9pw7AvNjLu261Mu689rrIZUcX5d3sxbav2YtJPQ9ifyEjjtnie7o4jaew9ns7gjnVQ\nSl54RMV48MEHefDBB82OIexRfLwxmjtqlIzmOpEu9UN5qX9zlsek8OYf+8yOU5n1BK6z1cUsGtFV\nii+vcIrWmgdskEeIf/XS/XbjYbzdXbm1lSz2EBVn6NChZkcQ9urcaK7MzXU6QztFEJOUwdRVcTSq\n5s+dbWubHalyUMqYl6j1YeDQP46VxjjPIpbO0R3OpZv3quL7pNAVthEYCMHBcOgQGTn5zNt+jH7X\n1iBA5kyJCpSVlQWAj4+PyUmEXcjPhz17YPNm+OorGD0aaksR5Iwm9mtGbMpZnv9pJ3VDfc733RXl\nKh6jxZhb8feX2zDCqk5f1rQEk8+MRcUp7rwwb/sxsvJkEZqoeH379gVkjm6llJkJO3bA1q0Xvnbu\nhLw84/6aNWVurhNzd3Vh8j1tuPWTNYyeuYVfH+lGrSBvs2NVBuoS35eJpYXuxROC3YB6wAtAa+AW\nWwUSAjAK3d27+XbjYZrWCPjXdo5ClLexY8eaHUFUpGXLYNo0o6iNibnQ3jAkBFq3hnHjjNvWraFR\nI6OtmHBaQT4efHFfO27/ZC0jv97M832bUjvYmxpBXni6yd99OZjBhVHckt+XmdL66q+lFH5AKvCL\n1sWr5RyMr6+vzsyUvnl25+mnKfroY+o99iOTbmvBvZ0jzU4khHBmzZvDsWPQo8eFgrZ1awgPN3Zs\nFJXS8pgTjPx6MwVFRq2kFIT5e1IryJvawT7UCvamdrD3hZ+DvPH2KN9CWCmVpbX2LdcncSJl3c3M\nDaPq7mODLEJcULcuLrk5hOemcWtrWdUsKl5aWhoAgYHS0s7pHTlizL99+2146imz0wg70rNxGGsn\nXEfsiUyOnsnmyOksjp7O5sjpbLYlnmHhruPkF14YMOxSvwqzR3YyMbG4WFm6LngBXQFPIM2WoYTI\nrl0Hb2BgaIEsQhOmuI9GmAEAACAASURBVPXWWwGZo1sp/PmncXvjjebmEHYpzN+LMH+vUu8rLNKc\nyMg5X/wGeJd1/LCSUupK3b1K0mhtcQOEsnZdOPd5zgJLn1AISyzN8eEW4Gb/XLOjiEpq3LhxZkcQ\nFWXxYqhRw5i+IIQVXF0UNQK9qRHoTbtIs9M4tOFYNi/X6k5fZe26kAt8CzxuxXWEuKKvjmpuASLT\nk82OIiqpO+64w+wIoiIUFhojurfcInNxhTBXufwDvNquCwC5WpNkyzBCAOw6msaW5ByyqoThEx9v\ndhxRSaWmpgIQGhpqchJRrrZuhZMn4YYbzE4iRGXWs8T3/sBnwBngHeAIUBt4CggFRlpzYYsKXa1J\nsOaiQpTF7I2H8XRzwaNh/fO7owlR0e68805A5ug6vcWLjdvrrzc3hxCVmdYrz3+v1GSgOtANrQ+V\nOL4SOAD0A+ZZemlLF6P1AToAW7Vmfonj/YFWwEat+cPSJxXiUjJzC/h161FuuaYmbofqwtq1ZkcS\nldRTsvq+cli82GgjFhZmdhIhhOHu4tvsi46f+/kOrBjVtXTqwkSgI3DTRcfPAi8B60AKXVF287cf\nIzOvkCEdw2FHXfj+eygoADdZySoqVr9+/cyOIMpbRobxZvrJJ81OIoS4wLP4di5Kvc6FqQvntiO0\nqhWTpdVDk+LbdRcd31h829SaJxXiUr7deJhG1fxoUyfY2B2tsBASE43vhahASUnGEoTq1aubnESU\nm5UrIT9f2ooJYV8WYYzadgJ+veg+XXy/xVwsPM+n+NbvouP+F90vxFXbdTSN7UfSGNyhDkqpC8Wt\nzNMVJhg0aBCDBjnkho/CUosWgY8PdOlidhIhTKOU8lRKfaSUSlVKZSql5imlalvwuIeUUoeUUjlK\nqS1Kqe6XOE8ppf5QSmml1J0WRHoUiMHownDxVwxgVe9HS0d0jwN1gP8Aj5Q4/nzx7TFrnlSI0ny3\nyViEdvu5ndCk0BUmeu655658knBsixdDdDR4el7xVCGc2PvArcBg4CTwLvCbUqqt1rqwtAcopQYC\nHwAPAX8V3y78f/buOzzKKnvg+PeEUEORjihIE6SIKCLSAiKEsoAFFVR0xYaCLuqqP2VF1l0su5YV\nu6KAKxYUVAQFAiigJCggyFKlSBNCCT2UkOT+/rgzMgxJ5p2Ueaecz/PM8yZvPeO65sydc88VkWbG\nmK1+p/8VyPU+uTJmJyIXA7cCXYGqwF7gO+C/GHM8iPfmONGdg23Oe68ISdiMugnQEDuMPCeYhyrl\n72hmFl8u28GfLjybs8qVsjvr1IESJUBbjCkX9OypK5tHtc2b4ddfYehQtyNRyjUiUgmb3w02xsz2\n7LsF2AJ0I+8ygYeACcaYsZ7f7xeRnsC9wOM+978UGA60Bpw3xrfJ7DueV6E4LV14DjvxDGxy29uz\nFSDDc1ypApv+y06OnMjixrZ1T+2Mj7fJro7oKhds27aNbdu2uR2GKi7eZX+1f66Kba2xk7uSvTuM\nMduANUCuNT0iUspzXbLfoWTfa0SkAnZRsSHGmN1FG7ZzTvvobvSM5L7H6RPPVgN3GsOm4gguFKpU\nqaJ9MsPA4T0ZjLjYkLF5BfM2n9p/UeXKxC1fzjL930iF2AMP2AUfX375ZZcjUcWh2YcfUrF6dRal\npcEuXYFRRZR4EVni8/s7xpiCjnzWwpYV7PXbv8tzLDfVgBKcOUK7CzsK7PUWMNMY800BYysSjns2\nGcMioLkIDYGawC5j2FiQh4rIUOAR4GxgFfCAMeb7fM4vBTwB3ALUxv7DfMEY84rn+G3A+FwuLWsC\n1HLs27ePLl26FOBdqKKyeschbpv5PSP7NKdLR7/uChdfDDNm6P9GKuReeOEFAP13LxplZcEvv8C1\n19LliisCn69UeMkyxlya3wkiMho7ryo/+f3LL9jS1Pz4H//jGk/5w0VAvnGGQtDNST3JbYESXAi6\ngNnrY6AOcDd2VYyaQFm/c45iyyl8Yg2uYFm549Ml2ygVH8e13klovurXh5074dgxKOv/P7lSxaeb\nrpQVvZYsgQMHtK2YimYvAxMDnLMV28KrBHaUdo/PsRrAgjyu24sdBfYf8a3BqVHeK4FmwBER8T1n\nkoikGmM6BnoDRcVRja4IE0XIFuFJv/1PePYH+ofp648CZmPMGmPM/diuDvfm/mxJwg6F9zbGzDbG\nbDbG/GiMmed3qjHGpPm+gohJuSQnxzBzZRpdGlenckKpM0/wdl7YoqtQq9DatGkTmzZFbFWWyk9y\nMojAlVe6HYlSxcIYs9cYszbA6yiwFDgJdPde62kt1hTIdWlSY0ym57rufoe6+1zzN6AldvVc7wvg\nYWw3hZBxOhmtg2f7gd/+idih6g444LSA2c/VwGLgIRHZLiLrReQVEfHv6VtWRLZ4zpkutjWFCnO/\nbD9A2qHj9GyRRymQthhTLrn99tu5/fbb3Q5DFYfkZLj0Uqha1e1IlHKVMeYgdv7V8yLSzZM7fQCs\nwKejloisFRHf9rIvAbeJyJ0i0lRExmBLS9/y3Pd3Y8xK35fnum3GmOBHEEQEkeoFeY9OSxfO9mz9\nR0m9Q9ROlw5yWsDsqwHQETgB9AfOAl7F/gP1Nh5eB9wO/IJdxGI4sFBELjLGrHcYm3LBzFVpxMcJ\nV15QM/cTNNFVLnnqqafcDkEVh4MHYdEi0D7JSnk9CGQBk7BloXOBW/166DbB5nAAGGMmiUhV7Pyp\ns4GV2G/eC//1q0gvbP3wIoz5HFvv+wZQDpFlQG+C6OLgNNE9jm0/0Q741md/O5/jwcizgDkXcZ5j\nN3k+eeD5VDFLRGoaY3YZY1LxWZ5YRFKA5djVNc5YQUNE7sbW+1KqVC5fl6uQMMYwa2Ua7RpWpVK5\nPJaurlnTNnPXRFeFWOfOnd0OQRWH776zS4trWzGlgD/mM93veeV1juSy7w1sAur0OWfcIw9DsW1s\nb0OkLPA6kOA5djHwD+Aep891WrrwP2wyOkGEQSK0FmEQttOB8Rx3wkkBs7+dwO/eJNdjjWdbN5fz\n8XwKWQKcn8fxd4wxlxpjLo2PD3o+nioiv+46wub0o3mXLQDExUG9eproqpBbt24d69atczsMVdRm\nzYLy5eHyy92ORCmVu5ae7Q/AZUB5bN43HZuLBjWL1GmiO8GzPQd4H/jJs63jdzxfDguY/S0EavvV\n5Db2bHMdIhc7xa8lNklWYWrmyjREoHuzPMoWvOrX10RXhdyQIUMYMmSI22GoopacDF27gn6bp1S4\n8tbi/o7t3AC2i8SfPT/XDuZmTheMeE+EntgaWX+TjWFcEM98CfhARH7CJrH34FPALCL/tc803ll5\nHwEjgfEi8ndsje4Y+1xboyEio4BF2NZjFbHlCi3Jo5ODCg8zV6XRum5lalQok/+J9evDjz+GJiil\nPJ555hm3Q1BFbeNG2LQJHnrI7UiUUnnLBEoDVbG5nMHOxTruc9yxYBaMuF6EG4C+eBaMAL4yhs+C\neaCDAua6fucfEZFu2Aloi4H9wJeA70yCs7DrIdcCDgLLgERjzE/BxKZCZ0t6Bmt2HuKJPzUNfHL9\n+rB/v51EUqlS8QenFNC+fV6NYFTESvY0/NH6XKXC2VagObZ0oTanSmS9zfaDWk44qAJVY/gU+NR3\nnwjlgf7G8L7z++RdwGyM6ZLLvnVAnv9lMsY8iJ01qCLErFW2gUeP5g4adng7L2zeDBddVHxBKeVj\n5UrbDadFixYuR6KKTHKyrflv1MjtSJRSefsIeAbwLpU6B2P2I3KV5/efg7lZgWZiiRAH9AQGAf2A\nMuA80VVq5so0mteuSJ0q5QKf7NtiTBNdFSL33WdbRs6bN8/dQFTROHkS5s6FG2+0i0UopcLVv7CN\nCzoBv2G7LIDNWd8DpgRzs6ASXRHaYJPbgZzqp+ZkPWSl/rDr0HF+3nqAv3ZvHPhk0F66yhXPP/+8\n2yGoovTjj3D4sJYtKBXujDHA856X7/53gXeDvV3ARFeE+sDN2ATX267L9+PwMWzNrFKOJK+2neTy\nbSvmq3JlqFhRE10VUm3atHE7BFWUkpNtu8KuXd2ORCkVQnkmuiIMAW7h1KIQcHqCC3Ykt6YxHCmG\n2FSUmrUyjQbVE2hUw38V5zyIaIsxFXLLly8HoFWrVgHOVBEhORnatrUfnJVS4UUkO/BJfzAY47gi\nIb8T38Qmst7kNhO77vEUYCMwD0CTXBWMA0czSd2UzpDEBkgwdXL168N6Xc1Zhc4DDzwAaI1uVNi3\nDxYvhpEj3Y5EKZW7Yiucd5IRG2Ac8IgxHAAQoXlxBaSi25w1u8nOMc66LfiqX9+OyBijE0lUSLz8\n8stuh6CKyrffQk6O1ucqFb62cvp8r6rYFdFOAume30sCRwmyvZjTldFuB9aK8KYI3TwPUypoM1em\ncXalMrQ8N8h+uPXqwdGjsGdPscSllL9WrVpp2UK0mDXL1vlfdpnbkSilcmNMPYypjzH1geuwSe+L\nQCWMqQ1UAv7jOfvmYG6dX6L7L2AbdjhZgBrA3cAsbBNfpYKScSKLBev30KN5reDKFkA7L6iQW7x4\nMYsXL3Y7DFVYxthvg668EuIL1FFTKRVaL2NHc/+BMXY1NLv9O1AOeCGYm+WZ6BrD48ZQD+iC7Vt2\ngFNJbzk8Q8wibBPh2eDeg4pF89btITMrx3m3BV+a6KoQe+SRR3jkkUfcDkMV1q+/wtatWragVORo\n7dn6fwXT1rO9OJibBfx4awwLgAUiDMMu/3sLdrGIUp5TzgEeBR4P5sEq9sxalUbVhFK0qVcl+Ivr\n1bNbTXRViLz22mtuh6CKgnfZ3x493I1DKeXUHuBcYBoi3wDbPb/3xg6yBlXD6Ph7HGPIxHZcmCJC\nZeyiEYM4vf2YUrk6kZXNt2t306fl2ZSIK8BksvLloXp1TXRVyOjSv1EiOdku+ev9VkgpFe7exC4B\nXBq4xme/d4Gy14O5mdPJaKcxhv3G8KYxdAAaYesmlMpTyoZ0jpzIokdByha86teHzZuLLCal8pOS\nkkJKSorbYajCyMyE777TsgWlIokxz2GX/T3BqZJZAY5j63b/HcztCl2ZbwybgH8W9j4qus1cmUaF\n0vG0b1i14DepXx+WLi26oJTKx4gRIwDtoxvRli2DjAy44gq3I1FKBcOYvyPyH2zVQFVgL7AIYw4G\neyudgqqKXVZ2DrPX7KJr0xqUji9R8BvVrw+ffw7Z2VCiEPdRyoG3337b7RBUYaWm2m379u7GoZQK\nnk1qZxb2NproqmK3ePN+9mVkBr9IhL/69eHkSdixA+rUKZrglMpDkyZN3A5BFVZKCtStC7Vrux2J\nUio/Ik8Gdb4x/3B6qia6qtjNWpVG6fg4OjeuXrgbNW5stzfeCMOGwbXXQunShQ9QqVzMnz8fgM6d\nO7sciSqw1FTo2NHtKJRSgf2d01dGC8RxolugyWhKOWWMYdaqNBIbVyehdCE/V3XuDC++aEd0b7oJ\nzj0XHn0UNmwommCV8jFq1ChGjRrldhiqoLZtg+3boZ02BlIqQojDV1A00VXFasX2g+w8eJyehS1b\nABCBhx6yie2sWdCpE7z0Epx/PnTvDlOm2NIGpYrAuHHjGDdunNthqILS+lylIslgn9fdwE4gDRgN\n3OPZpmF76N4TzI3zHGITITGYG3kWllDqNDNXpREfJ1zZtEbR3TQuzrYLSkqyo7vvvQdjx8J110Gt\nWnDHHXDXXXDeeUX3TBVzGjRo4HYIqjBSU6FsWbjoIrcjUUoFYsz7f/wsMhqoBVyCMb/47P8CWAqc\nH8ytxZjcSyJEyMF5vYQxJjLrfRMSEkxGRobbYUQlYwxdX5zPuZXL8sEdbQNfUBjZ2TBjBrz9Nnz9\ntd332mswdGjxPldFrTlz5gDQrVs3lyNRBdK2ra3hX6BjMCq6iMhRY0yC23EUG5EdQE2gGsbs99lf\nBdtmbBfGnO30doFKF5zWSxRgqSsV7dbvPsJvezMK323BiRIloE8fmDbNLirRujW8+mrxP1dFrdGj\nRzN69Gi3w1AFceyY7aGrZQtKRaKzPNuxiLRA5CxEWgBjPfsrBnOz/EZh3/f7PQk7lLyQU+sOdwDS\ngenBPFTFhpkr0xCBpGY1Q/vgunXhlltg+HBbz9uoUWifr6LCBx984HYIqqCWLrX1+joRTalI9APQ\nDbv87zV+x4znuGN5jugaw2DvC5iDTXIHGEOiMdxkDInAjdgVKxYG81AVG2auTOOSupWpUbFM6B/e\np4/dTtfPYKpg6tSpQx3t1xyZvBPRNNFVKhLdj510llv1wB7gL8HczGnXhSc8W/8VKr7xPPiRYB6q\not/uw8dZvfNQ0U5CC0aDBtCsmSa6qsBmzpzJzJmFXpRHuSElBRo2hBou/fdHKVVwxqwDWgD/An4C\nNgI/As8BF3qOO+Z0Alk9z3Yo8G+f/cM8W53erk6TujEdgI6NqrkXRN++tu/uwYNQqZJ7caiI9Nxz\nzwHQs2dPlyNRQTHGjugmJbkdiVKqoIzZAzxeFLdymuj+is2unxXhr9j+ZmcD1bD1Er8WRTAqeqRs\nSKdimXia13YxwezTB/71L0hOhuuvdy8OFZE++eQTt0NQBbF5M+zapWULSkU6kcuB3kANYDcwHWN+\nCvY2TksX/gbkYMsUqgEXeraCTXRHBPtgFd0WbtzL5Q2qUiLOxYYc7dpBlSq2E4NSQapVqxa1aoWg\nY4gqWikpdquJrlKRS+RN7PyvvwF3ebapiLwe7K0cJbrGMB3oia2RMJxKcBcBScbwdbAPVtFr276j\nbN9/jA5uli2AbTnWuzd8843ts6tUEKZNm8Y0/ZAUeVJToXx5aNHC7UiUUgUhchswhNwno92DyK3B\n3M7xEsDGMNcY2mH7l9UBKhpDe2P4NpgHqui3cMNeADo0qupyJNg63fR0WLTI7UhUhHnxxRd58cUX\n3Q5DBSslBS67DOIjcg0jpZRdAhhgC/AAtsXYcGAzNtkdEszNgvovgQjx2FrdqsYwI5hrVexYuDGd\nGhVK07B6ebdDgR497B+8adOgQwe3o1ERZPLkyW6HoIKVkQErVsDjRTKHRSnljhbYqoG+GLPyj70i\n3wErPMcdczyiK8L1wO9AKjDNs2+uCJtE0OmtCrDL/qZu3Ev7hlURCYMF8ypVgsREbTOmglatWjWq\nVXO5/EYFZ/FiW6ak9blKRbJSnu12v/3b/Y474ijRFaET8DGnJqB5M5ivsa3HrgvmoSp6/brrCHuP\nZNLe7fpcX337wqpV8NtvbkeiIsjnn3/O559/7nYYKhjeiWiXX+5uHEqpwtjm2b6AiF0OWKQS8Lzf\ncUecjug+7jnXv0nvHM9WPz4r4FR9bvuGYVCf6+VdJU0nFqkgvPLKK7zyyituh6GCkZoKF1xgu60o\npSLVdOyA6mAgHZGDwD7gdmxJQ1B/zJ0mupfjrZc43SbP9pxgHqqiV8rGdM6rWo5zK5dzO5RTGjWy\nf/y0fEEFYerUqUydOtXtMJRT3oUitGxBqUg3GtjKqQqCCj4/bwGeDuZmThPdBM92q9/+sn5bFcOy\nsnP4cVN6eI3mevXpA/PmwaFDbkeiIkSlSpWopCvqRY71622Hlfbt3Y5EKVUYxqQDbYH3sAuUZXm2\nY4F2GLMvmNs5TXR/92z9Pyo/7Nn6FwyrGLRyxyEOn8iifcMwqs/16tsXTp6E2bPdjkRFiEmTJjFp\n0iS3w1BOpabarY7oKhX5jNmFMXdhzDkYU8qzHYIxu4K9ldNEdxZ2yPhL7w4R1mITXeM5rmKctz63\nXTiO6LZvD5Ura52ucuzNN9/kzTffdDsM5VRKiu2y0rSp25EopcKI0z66o7GdFapiE1uA87HJbzrw\nbNGHpiJNysa9XFCrAtXKl3Y7lDPFx0OvXvD117b9UIkSbkekwtw333zjdggqGKmptttCnOOumUqp\nGOB0CeDfgQ5AMpCDTXBzPL938hxXMez4yWyWbN4fnmULXn37wt698NNPbkeiIkC5cuUoVy6MJlWq\nvB08CCtXatmCUuoMjldGM4ZfgZ4ilAGqAPuM4XixRaYiys9b93MiKyc8lv3NS48ediR32jT9g6gC\nmjhxIgCDBg1yORIV0E8/2a4LOhFNKeXH6YIRlUSoK0I1YzhuDDuM4bgI1Tz7dWpyjEvZkE6JOOGy\n+mHcv7JyZejUSduMKUfeffdd3n33XbfDUE6kpIAItG3rdiRKqTDjtJhpHPAbcJPf/oGe/e8VZVAq\n8qRs3EvLcytRoUxJt0PJX58+8L//wZYtbkeiwtzs2bOZrV06IkNqKrRoARUruh2JUirMOE10vR+T\np/jt/xxbr6sfo2PY4eMn+WX7wfDsn+uvr2fNE+2+oAIoWbIkJUuG+Qc3BTk5sGiRliMpFe1E6v7x\nCoLTRLe6Z3vAb/9Bv+MqBi3evI/sHEOHcJ6I5tW4sX1p+YIKYMKECUyYMMHtMFQga9bYyWhan6tU\ntNuMrSLYFOC80zhNdA97tkl++72/HwnmoSq6LNyQTqn4OC45r7LboTjTpw989x0cPhz4XBWzNNGN\nELpQhFKxxLsUsGNOuy78DHQDxonQHFgDNAUewvbVXRrMQ1V0WbhhL5eeV5kyJSOkN23fvvDSSzBn\nDlxzjdvRqDA1b948t0NQTqSkQNWqcP75bkeilCpeCzi1loNjThPdt7CJbkXgKZ/94nmoLh8Uo9KP\nnGBt2mEe6dHE7VCc69DBrqA0bZomukpFutRUO5orQQ3yKKUijTFdCnKZ0wUjPgde4tSQse/Q8YvG\nnFoaWMWW1E3pAJExEc2rZMlTq6Tl5LgdjQpTY8eOZezYsW6HofKzbx+sXatlC0qpPAWzYMTDIkwC\n+gE1gV3AV8awuLiCU+Fv4YZ0KpSO58JzIqyVcp8+8MknsHix9t5UuZo0aRIAd911l8uRqDwtWmS3\nOhFNqeghkpjPUQOkY8xqp7dznOgCeJJaTWzVH1I37qVtgyrEl4iw9eV79Tq1SpomuioXc+bMcTsE\nFUhqqv3/cZs2bkeilCo68whUiyuyA7gHY74OdDPHia4IFYDewHlAGf/jxvAPp/dS0eH3A8fYnH6U\nW9rVczuU4FWpYmt1p0+H0aPdjkYpVRApKXDRRZCQ4HYkSqmiFajo/hzgc0TaYMyK/E50lOiK0Ab4\nBshvfVdNdGNMyoa9AHRoFEH1ub769IFHH4WtW6FuUP2nVQx44403ABg6dKjLkahcZWXBTz/Bn//s\ndiRKqaL1PtAdqA2kAFuBOkB7YCewDNsgoRS2+9dt+d3M6ffNLwNVOXMyWtD9zFT0SNmYTtWEUjSp\nWcHtUArGu0ra1wG/+VAxaNq0aUzTFfTC18qVcOSITkRTKvrMBc4GBmJMR4y5CWM6ATd79k8CrsHm\nn50D3cxp6UJLbL3EfOwywBkUoJeZih7GGBZu2Eu7hlWRSG3r06QJNGxo63TvvdftaFSYmTFjhtsh\nqPx4F4rQiWhKRZsnPNtv/PZPxya3IzCmGSIHgVqBbuZ0RNe79O+1xvC6MUwwhvd9Xw7vA4CIDBWR\n30TkuIgsFZFOAc4vJSL/8FxzQkS2ishf/M7pLyKrPcdXi4g2SC1GG/dksPvwCTo0ioBlf/MiYssX\nvv0Wjh93OxqlVDBSU6FmTahXz+1IlFJF6zzPdrjfSNo9nm19z/YwkBXoZk4T3f96ti0cnp8nERkA\njAGeAS7G1l/MEJH8iiQ/BnoCdwNNgOuBP4qPRaQddij7Q6CVZ/uZiOh0+mKSstFTn9swghNdgCuu\ngBMnbK2fUj7GjBnDmDFj3A5D5SUlxY7mRuo3SkqpvKzzbP8B7EZkOSK7gH9hqwnWIVIC2+p2R6Cb\nOS1d2AwcBKaK8J4niJO+JxjzRzIcyEPABGOMtxP7/SLSE7gXeNz/ZBFJwhYdNzTG7PWJx9cDwHfG\nmKc9vz8tIld49t/oMC4VhJQN6ZxzVlnqVCnrdiiF06mT/UO5YAEk5te6T8WauXPnAjB8+HCXI1Fn\n2L0bNm6EIUPcjkQpVfRGAFOBEtgmCN5GCIIdwX0c6AqUBBYGupnTRPdtTtXk/jWX4wYCJ7oiUgpo\nDbzgdygZO5suN1dje/c+JCK3AseAGcAIY8wRzzntgFf9rpsF3BcoJhW87BxD6qZ0ejSvGbn1uV5V\nqsCFF8L8+fDEE4HPVzHjq6++cjsElZeFnr9tOhFNqehjzDeIdAeeBtpiqw9ygFTgbxgzH5F4oAJw\nItDtgunyn1fHhWA6L1TDZui7/PbvIu+C4gZAR+AioD82ee0JTPA5p1Yw9xSRu0VkiYgsycoKWN6h\n/KzecYiDx05Gdn2ur8RE+zXoyZOBz1VKuSsjA0aMgLPPhksvdTsapSKeiJQWkVdFZK+IZIjIVyJy\nroPrAs63EpHLRGS2iBwRkcMikiIigZMHY+ZhTAdsMlsHqODpwDDfczwLYzIwJmAS53REd7DD85zy\n79gguezzivMcu8kYcxBARO4DZolITWOMN8F1fE9jzDvAOwAJCQnaPSJI3vrcdg0itH+uv86d4bXX\nYOlSuPxyt6NRYeKFF+wXTw8//LDLkajTPPAArFsHs2dDmTPWLlJKBe9l4CpsqWc68BIwXURaG2Oy\nc7vAZ77VUOAHz3aGiDQzxmz1nNMW++3688CDQCZ2rlf+o0oi84D3gMkYcwz4vTBvzlGiG2xXhXzs\nBbI5c6S1BmeOyHrtBH73Jrkeazzbup7r0oK8pyqEhRvTOb9GeWpUjJI/Mp08H0IXLNBEV/0h1du+\nSoWPTz+Fd9+Fxx+HK690OxqlIp6IVALuAAYbY2Z79t0CbMHOj5qVx6VO5lv9B3jdZ/4UwK8OwkoE\nOgGvIjIJGIcxPwbxtk4TTOlCoRljMoGl2BUvfHXHdl/IzUKgtoiU99nX2LPd4tmmBnlPVUCZWTks\n/m0f7RtGyWgu2BZFF1xg63SV8pgyZQpTpkxxOwzltXkz3H23/TD61FNuR6NUtGiNndSV7N1hjNmG\nHVDMde6Uz3yrJD9tCwAAIABJREFUZL9Df8y3EpEa2PlTO0XkBxHZJSLfi4iTT6iZ2G/lKwJ3AimI\nrELkIUSqB/XucF66gAi3YIeemwD+Q3nGGMf3egn4QER+wiax92CXeXvLPkf+67nhrZ7zPwJGAuNF\n5O/AWdjh8snGmN2ec8YAC0TkceAL7IoZV2Bre/NVpUoV5s2b5zB0lZGZzdALTnBe6TTmzdsb+III\n0bhRI2p89x0/zJ0LJUq4HY5SyodkZdFq+HASsrJY8pe/cHxhwInWSkWzeBFZ4vP7O56SzIKohf2m\n3f8Pen5zp/Kbb9XN83MDz/Yp4BHssr3XY8tOWxtjfsknpprAtcBNQBfPs5piSyCeReRrjLk2/7d1\niqPkVIQbsGsPGwq55K8xZpKIVMWufHE2sBLobYzxjs7W9Tv/iIh0w3ZVWAzsB74EHvM5J0VEBgKj\nsf9QNwIDjIOh7n379tGlS5fCvKWY8sw3axi/+jd+HtmZCmVKuh1O0dmxA6ZPp0vlynDJJW5Ho8LA\nc889B8Bjjz0W4ExV7P72N1i9Gj75hMsHDHA7GqXclmWMyXcmpoiMBv4W4D5X5HcLAq+Am9/cKG/F\nwNvGmHGen5eJSBfsAGfey5HaUtXxwHhEagIDsPXDbbGjz1cFiOs0Tkdhh3m2x4By2DeyD6iKXTXt\nQB7X5coY8wbwRh7HuuSybx2QFOCek4HJwcShgmOMYdaqNNo3rBZdSS6c6qE7f74mugqA5cuXux2C\nArty4bPPwh13gCa5Sjn1MjAxwDlbgcuxI6bVgD0+x2oAC/K4zsl8q52e7Wq/c9bgN6AZwBFsvrnf\n88ygv3J1mui2xCa33fDUvRpDdRFGYtt99Q32wSry/LrrCFvSj3J3YoPAJ0eac8+FBg3shLQHH3Q7\nGhUGPvnkE7dDUHv2wKBB0KQJ6Cp1SjnmWWArYH2hiCzFdkHoji0VxdNarCl5zHMyxmR6rusOfOZz\nqDvgndiwGbtqWRO/yxsD/wsQVEmgN7Z0oQ+nymW9I8Z5JeC5cproJni2P3seggglgBexpQKvADoF\nNsolr0pDBLo3rel2KMUjMRG++gpyciAupPM0lVL+jIHBg2HfPpgxAxISAl+jlAqKMeagiLwHPC8i\nuznVXmwFMMd7noisBV4zxrzm2ZXvfCtjjBGR54GnRGQFtkb3BuwIcqDFvHYBlbyP9my3YxcmG4cx\nm4J5j04T3UNAZc8DD2Mb+PbCLgsMtm5CRbnk1bu4uM5Z0dNWzF/nzjBhgq0FbNHC7WiUy/75z38C\nMHLkSJcjiVGvvAJffw2vvgoXXeR2NEpFswexS+tOAsoCc4Fb/XroNsGWNwCO5lthjHnZ06HhRWyp\n6yqgV4CJaGCbDoBd9ewrYByQjDEFWvfAaaK7A5vo1sDWV1yGXYfYa19BHq4ix44Dx/jf7wd5rNcF\nbodSfHzrdDXRjXnr1q1zO4TYtWwZPPoo9OsHw4YFPl8pVWDGmOPA/Z5XXuec0Yggv/lWPuf8G/h3\nkCEtx05Gm4gx+4O89gxOE91l2NUs2mKHjv1HcItqQQkVpmavtvXlSc2itGwBoH59W6u7YIH+cVVM\nnBhoHocqFkeO2Eln1avDuHEghWr0o5SKNMYU6Yxwp4nuUOBR4LAxHBWhErbdQxa2b+2/ijIoFX6S\nV6fRqEZ5GlQvH/jkSCViyxfmzLH1gfoHVqnQu/9+2LDBdluoGkUL0yilnBOJx05Ia4ItpzidMf9w\neiunSwBnABk+vz8HPOf0ISqyHTiayaJN+xgSjd0W/CUmwocfwvr10Lhx4PNV1HryyScB+Mc/HP/3\nVBXWRx/ZOvknngDtb65UbLKrqs3jzI4Nvgqf6IoE1ecMY9gazPkqcny7djfZOYak5nktkhJFOne2\n2/nzNdGNcdu2bXM7hNiycqVd4rd9exg1yu1olFLueQrIb0JQUJPS8hvR3RzEzUyAe6kIlrxqFzUr\nlqblOZUCnxzpGjeGmjVtne5dd7kdjXLR+PHj3Q4hduzfD1dfDRUqwGefQbz+OVEqhiVh88oJwGDP\nz8Oxk+UMQVYUBGoWKkG8VBQ6fjKb+b/uoXuzmsTFxcD/zCK2fGH+fFunq5QqXtnZcPPNsGULTJ4M\ntWu7HZFSyl3neLan1l+3/XuvxS44cW4wN8vvY7N2UlD8sH4vx05m0yMWyha8EhPtqNKWLVCvntvR\nKJc8/vjjADz77LMuRxLl/v53uyDEG29Ahw5uR6OUcl82UBK7eMVJIB6R6oC3R+/dwGinN8sz0TWG\nwYUIUkWJ5NVpVCgTT9v6MTT72bdOVxPdmJWenu52CNHviy9g9Gi4/Xa45x63o1FKhYd07KhuJSAN\nO4L7IXDcc7xyMDfTQiiVp+wcw5w1u+l6QQ1KxcfQkrjNm0OVKjbR/fOf3Y5GueSdd95xO4TotmYN\n3HortGkDr7+u7fyUUl7rsIluQ2ABcDNwpeeYAX4O5maOE10RmgBDyL2nmTHmjyBUlFiyeR/7MjJJ\nahZDZQsAcXHQqZOdkKaUKnoHD9rJZ+XKwZQpUCZKlxVXShXEWGADUAbbgSEJqO45tgd4IJibOUp0\nRWiN7WlWLrfDBNnqQUWG5NW7KFUijs5Nqgc+OdokJsLUqfD773DOOYHPV1Hn4YcfBuCFF15wOZIo\nk5MDt9wCmzbB3LlQp47bESmlwokxnwKf/vG7yPnAFdhFyhZizIFgbuf0++gRQALabSFmGGNIXp1G\nh0ZVKV86BitcvHW6Oqobs44dO8axY8fcDiP6/POfMG0avPSS/UCplFL5MeYQxkzFmK+DTXLBeaLb\nHjtqe6/3sUBL4CvgV6BI1yVW7lubdpht+47FxiIRubnoItvTc/58tyNRLnn99dd5/fXX3Q4junz1\nle2y8Oc/w333uR2NUioGOE10vVPuP/TuMIaV2BYPjYEHizgu5bLkVbsQgW5Na7odijvi46FjRx3R\nVaqorF0LgwZB69bw5ps6+UwpFRJOE13v93fHvT97JqeV9OzvV8RxKZclr06jdd3KVK9Q2u1Q3NO5\ns50Zvnu325EoFzzwwAM88EBQcx5UXg4dgmuugdKl4fPPoaz/fGallCoeThNd71/6KtilgQG+A1I9\nP+cUYUzKZdv3H2XVjkMkNY/R0Vwvb/3g99+7G4dSkSwnx5YqrF8Pn34Kdeu6HZFSKoY4nWX0P6AB\nti53OtAU8GZBBkgu+tCUW5JX7QKge6y1FfPXurVtfzR/PvTv73Y0KsRefvllt0OIfMbAvffCl1/C\nf/4DV1zhdkRKqRjjdET3KeAm7GjuaGxi6y2wmgsML/LIlGuSV6fRuGZ56ldLcDsUd5UqBe3aaZ2u\nUgVhDAwfDu+8A489Zn9WSqkQc5ToGsMvxjDJGDYYw2Fj6IktY6hkDEnGsKd4w1Shsj8jk59+2xd7\ni0TkpXNnWLEC9u93OxIVYsOGDWPYsGFuhxGZjIFHH4VXX4UHH4RnntHJZ0opVxRmXddSwImiCkSF\nh7lrd5Nj0Ppcr8RE+0f7hx/cjkSFWNmyZSmrk6YK5skn4YUXYOhQePFFTXKVUq7Jt0ZXhEuAgdhl\n2L40hm9FuBN4Fjuie1yEN43h4eIPVYVC8qo0alUsw4XnVHI7lPDQtq0tYZg/H/r2dTsaFUK6IloB\njR5tX3feaUd0NclVSrkoz0RXhI7Y+lvvOcNEeB54FDsBTYCywIMibDCGt4o7WFW8jmVms2D9Hm64\ntA6if5ysMmVssqsLR6hYkJ0Nt90GWVkwYgRceGFw17/wAowcaZf4festiCvMl4ZKKVV4+f1X6BFs\nn1zf5X4f8RwTYK/Pz7cUV4AqdL5fv4fjJ3O0Ptdf587w889w+LDbkagQuvvuu7n77rvdDiO0Ro6E\niRPtCmYtW9puI8uXO7v21VfhkUfghhtg3DgoUaJ4Y1VKKQfyS3QvxY7czgKGAjOwSa0BbjSGGsDN\nnnObFWeQKjRmrdpFxTLxtG1Qxe1Qwktiou0FunCh25GoEKpatSpVq1YNfGK0+PJLePZZuPtu2L7d\n1tnOnQsXXwxXXw1Ll+Z97TvvwF/+YheFmDjRriyolFJhQIwxuR8QTmDLFiobwyERKgH7sYluGWM4\nKUIp7GppOcY47skbVhISEkxGRobbYbguKzuHS5+ewxVNavCfAa3cDie8ZGTAWWfZ0apnnnE7GqWK\n3vr1cOml0KSJXSCltGdFxAMH4JVXbA/cAwegTx876nvZZaeuff99GDwYeve2q56VKuXOe1AqRojI\nUWNMjPf/dC6/Ed2SAMZwyLM96D1gDCc920zPLi3ojHCLN+/nwNGTJDXTbgtnSEiwi0dona6KRhkZ\ncO21ULIkTJ58KskF+wHvySdhyxZ4+mlISbE16716waJF8PHHcPvt0K2bvVaTXKVUmAk4CivCk072\nqciWvDqNUvFxJDau7nYo4alzZzuqdfSoXS1NRb3BgwcDMH78eJcjKUbG2FKFVatg1qy8l+etWNFO\nTrv/fnjjDTvprF0721EhMdGWPZQpE9rYlVLKASflBqN8fja57FNR4If1e2lbvwoJpSOyAqX4JSbC\nv/8Nqalw5ZVuR6NCoE6dOm6HUPxeew0++siO1nbvHvj8ChXg//4Phg2zXRVWr7alDfrhTykVpvKr\n0c0J4j7GGCJyiq3W6MKewydo8/QcHu3ZhKFdGrkdTng6fBiqVNE6XRU9Fi6ELl1sbe0XX2grMKUi\nhNboBie/4bunQhaFctWiTekAtG9YzeVIwliFCvar2uRkTXRV5EtLg+uvh3r17GQyTXKVUlEqz0TX\nGE10Y0XKxnTKl46nRe2KbocS3pKS7MScPXugutYyR7tBgwYBMHHiRJcjKWInT8KAAbaLwsyZdsKZ\nUkpFKf0Yr1i0KZ3L6lchvoT+65CvpCQ7eWfuXLcjUSHQpEkTmjRp4nYYRe/xx2HBAtv7tmVLt6NR\nSqlipTOPYtzOg8f4bW8GN7fNY7a1OqV1a6hc2ZYvDBzodjSqmI0cOdLtEIreZ5/Biy/CffeBZ8Ra\nKaWimQ7hxbjUjbY+9/IGMbQCVEGVKGH7hSYn25FdpSLJmjV2YYd27Wyyq5RSMUAT3RiXujGdSmVL\n0uxsrc91JCkJfv/dJg0qqg0cOJCB0TJyf+iQXRQiIcGO6urCDkqpGKGlCzEudVM6lzeoQlycLm7n\niLfXaHIyNGvmbiyqWLVqFSVLYefk2DKF9ethzhw45xy3I1JKqZDRRDeGbdt3lO37j3Fnx/puhxI5\nzjsPGje2ie4DD7gdjSpGjz32mNshFI2RI2HaNHj1Vds3VymlYoiWLsQwb31uO+2fG5ykJJg3D06c\ncDsSpfI3aZLt+3znnXY1M6WUijGa6Maw1E3pVE0oReOa5d0OJbIkJcGxY3ZlqUj1889w662Qmel2\nJGGrf//+9O/f3+0wCu7nn+3ksw4d4PXXQbQ8SSkVezTRjVHGGFI3pnN5w6qI/gEMTpcuEB9vyxci\n1fPPwwcfRPZ7KGbt2rWjXbt2bodRMLt2wdVXQ7VqMGWKTj5TSsUsTXRj1G97M0g7dJx22lYseBUq\nQPv2kZskHjkCU6fanz/5xN1YwtjDDz/Mww8/7HYYwcvMhP79Ye9e+PJLqFnT7YiUUso1mujGqNRN\n3vpcTXQLJCkJli2D3bvdjiR4U6fa0ouWLU/9rKKDMbYWd+FCGD8eLrnE7YiUUspVmujGqNSN6dSs\nWJoG1RLcDiUyJSXZ7Zw57sZREB99BHXr2vKFI0dgxgy3IwpL/fr1o1+/fm6HEZzXX4d334URI2DA\nALejUUop12miG4OMMSzalE67BlqfW2CXXAJVqkRe+cKePTBrFtx4I3TtCtWra/lCHq688kquvPJK\nt8Nw7ttvbcu7vn3hn/90OxqllAoL2kc3Bq3ffYS9RzK1bKEw/JcDjpQPDJMnQ3Y23HSTnVB33XUw\nYYId2S2v3Td8DR8+3O0QnNu0Ca6/Hpo0gYkTIU7HMJRSCnRENyZ5++e21/65hZOUBDt3wqpVbkfi\n3EcfQYsWtj4XYOBAW6M7fbq7camCO3wYrrrKfuCaOhUq6nLeSinlpYluDErZuJdzzipLnSrl3A4l\nsvkuBxwJtmyBH36wo7leHTtC7dpavpCLXr160atXL7fDyF9Oju2HvGYNfPopNGrkdkRKKRVWNNGN\nMTk5hh9/26dlC0Whbl244AKYPdvtSJz5+GO7HTjw1L64OPuV94wZcPCgO3GFqb59+9K3b1+3w8jf\nq6/aFmIvvmhLaZRSSp1GjDFux+CqhIQEk5GR4XYYIbNqx0H+9MoPvHTDRVx7ybluhxP5hg+HsWNh\n3z4oU8btaPLXsqXtAey/otuiRdCuHbz/vh0dVJHBGGjcGM4+G+bPj5w6caVUoYjIUWOMtkxyyJUR\nXREZKiK/ichxEVkqIp3yObeLiJhcXhf4nHNbHueEeeYRet76XB3RLSKRshzw//5nX75lC15t28J5\n52n5QqRZuBA2bIA77tAkVyml8hDyRFdEBgBjgGeAi4EUYIaI1A1waXPgbJ/Xer/jR/2On22MOV6E\noUeF1I3p1KtajrMrlXU7lOjQuTOULBn+dboff2w7RVx//ZnHRGzP1dmzIT099LGFqW7dutEtnMsB\nxo+3nTKuu87tSJRSKmy5MaL7EDDBGDPWGLPGGHM/sBO4N8B1u40xaT6vbL/jxu94WrFEH8GysnP4\nSetzi1b58tChQ3gnusbYbgvdu0ONGrmfM2AAZGXB55+HNrYwNmDAAAaE66ILGRl28tkNN0CCfoOp\nlFJ5CWmiKyKlgNaAf1aQDLQPcPkSEdkpInNF5IpcjpcVkS0isl1EpovIxUURczRZteMQh09k0U7b\nihWtpCRYvhx27XI7ktylptqOC7mVLXhdfLGdsT9pUujiCnN33XUXd911l9th5G7yZNv7+Lbb3I5E\nKaXCWqhHdKsBJQD/jGAXUCuPa7yjvf2Ba4F1wFwRSfQ5Zx1wO3AVcCNwHFgoIufndkMRuVtElojI\nkqysrIK+l4iT4qnPvbxBFZcjiTLhvhzwRx/ZiXJXX533OSK2G8N334Vvwq5OGT/efjDp2NHtSJRS\nKqy51V7Mv9WD5LLPnmjMOmPMW8aYpcaYVGPMUGAm8LDPOanGmPeNMcuNMd8DA4CNwP153PMdY8yl\nxphL4+NjZ3G41E3pNKpRnhoVdI5ekbr4YqhaNTzLF06etF9x9+tnOy7kZ8AA25d18uTQxBbmunTp\nQpcuXdwO40ybNtkuC7fdppPQlFIqgFAnunuBbM4cva3BmaO8+fkRyHW0FsBTv7skv3NiTWZWDks2\n76O91ucWvbg4W//qXQ44nMydC3v25F+24NWiBTRrpuULHrfddhu3hWNpwPvv2wRXW8EppVRAIU10\njTGZwFKgu9+h7tjuC061wpY05EpEBGiZ3zmxZsX2AxzNzKZdA010i0VSEqSlwcqVbkdyuo8+grPO\ngp49nZ0/cKBdPW379uKNKwKEZaKbk2MT3e7doU4dt6NRSqmw50bpwkvAbSJyp4g0FZExQG3gLQAR\n+a+I/Nd7sog8ICJXi8j5ItJcRJ4FrgZe8zlnlIj0EJEGItIKeA+b6L4VyjcWzrz9c9tqols8wnE5\n4KNH4YsvbEux0qWdXTNggB2V/uyz4o0tApw8eZKTJ0+6HcbpvvvOTiwcPNjtSJRSKiKEPNE1xkwC\nHgCeAJYDHYHexpgtnlPqel5epYAXgBXA957z/2SM8e2DdBbwDrAG28HhHCDRGPNTMb6ViJK6KZ2m\nZ1ekSkIpt0OJTueea7/2D6dEd/p0OzPfSdmCV+PG0KqVli8A3bt3p3t3/y+fXDZ+PFSqBFdd5XYk\nSikVEVyZiWWMeQN4I49jXfx+/zfw7wD3exB4sKjiizbHT2azZMt+BrU9z+1Qolv37vD223altLJh\nsCDHhx/COedApzwXHszdwIHw2GPw229Qv37xxBYB7rzzTrdDON3Bg7bP8Z//HB7/fimlVARwq+uC\nCqFlWw+QmZWjC0UUt6QkOH7c1ri6bd8+mDHDJq0lSgR37Q032O2nnxZ9XBFk0KBBDBo0yO0wTvn0\nU/shSssWlFLKMU10Y0DqpnTiBC6rr/1zi1U4LQc8ZYptLRZM2YJX/frQtm3Mly8cPXqUo0ePuh3G\nKePH2/KYNm3cjkQppSKGJroxIHXjXlqcU4lKZUu6HUp0S0iwDfzDIdH96CNo0sT2+C2IAQNg2TL4\n9deijSuC9O7dm969e7sdhrV2rV3hbvBg7Z2rlFJB0EQ3yh3LzGb5tgPaVixUkpJgxQrY6WJnu+3b\n7YICN91U8KTo+uvtNoZHde+9917uvfdet8OwJkywJSjhVEqhlIoKIlJaRF4Vkb0ikiEiX4nIuQ6u\nGyoiv4nIcRFZKiKd/I7XEpEPRCTNc99fROTm4nsnudNEN8ot2bKPk9mGy7U+NzTCYTngSZNsi7Ab\nbyz4Pc49105iK8pE9+RJO5mqVy+oXt0uZhHGBgwYwIABA9wOA7Ky4L//tf/cauW1UrpSShXYy0B/\n4EagE1ARmC4ieU7wEJEBwBjgGeBi7FoIM0TEt2vWf4GmwFXAhZ7fPxCRxOJ4E3nRRDfKpWxMJz5O\naFNP63NDolUrm8S9955NUNzw0Ue2jvP8Qi4MOGAArFpV+EUwNm6Exx+3Cxz0729HvCtXhj/9CaZN\nK9y9i9HBgwc5ePCg22HA7Nn2GwKdhKaUKmIiUgm4A3jEGDPbGPMzcAt2LYJu+Vz6EDDBGDPWGLPG\nGHM/dpEu36/B2gOvG2N+NMZsMsa8CGwDLiuWN5MHTXSjXOrGdFqeW4nypV3pJBd74uLg6adt6cB9\n94V+SeC1a+Hnnws2Cc3fddfZ91OQUd0TJ+x13bpBo0bw73/DZZfBV1/ZBQ8WLYKWLeHaa8O2POKq\nq67iqqLuV7t6tV3dLBjjx0O1atCnT9HGopRS0BooiV2DAABjzDbsugTtc7tAREp5rvOfkJLsd80P\nwA0iUlVE4kTkKqA6ENKvPGM++6lSpQrz5s1zO4xikZ1j6HbWYapXKB217zEsnX8+DW68kbpvv81G\nY9hWmBICQDIzOefLL4k/cgRTokS+r8pLl1JDhNQ6dcgsgv/NL2rVitITJvBT166O6n3Lbt1K7a+/\npuasWZQ6eJDjNWuyc/Bg0nr14kT16vYkT/u1EqNGceGIEVS68UbWLV1KWrhM/PLo2rUrQJH9f6fa\nggW0GDWK9MsuY+3jj3PyrLMCXhN/6BDtv/ySHf36sSElmFXSlVJRLF5Elvj8/o4x5p0C3qsWkA3s\n9du/y3MsN9WAEp5z/K/xHQW+AfjEc+8s4ARwozFmeQFjLRAxoR5xCjMJCQkmIyPD7TCKxZSl2/nr\nZ7/w5bAOtKoT+I+qKkI5OXDzzfDJJ/Dxx7afbUEcPAjXXGOXfnWqVy/45puCPc/f2LFw993wf/9n\nW6cdOXLqlZFx+u+HD9uJcPHx0K+fva5bt/z7+B49akd1Z82CMWPgL38pmrjDUWKiHdE9cgSqVrX/\nXiQGKFV77TW4/35Yvhwuuig0cSqlwpqIHDXGJAQ4ZzTwtwC3ugKoja2dLWl8EkIR+Q5YZ4y5J5d7\n1wZ+x65A+73P/lHYRPYCz++vAJcDj2OT3auxJQ+JxphfAr7RIqKJbhQnunf/dwkrth8k5bGuxMVp\nS6KQO37crpb20092clqwK5SlpdmkdeVKO+v+5pttAp2VZSd2ZWWd+Tp50k4kK1OmaN5Dejo0bGgT\n7rg4KF/etlErXz73V9OmcMstwU2aOnHCTpz74gtb9jFiRNHEXkh799oBjmrVqhX+ZsuWwSWXwIsv\nQteudlGOjRvhqads/XJeHwZat7b/my9bVvgYlFJRwWGiWw078pqfrdhEdC5Qwxizx+f6VcBkY8yo\nXO5dCjiKTWo/89n/OtDCGNNZRBoCG4BWvkmtiMwBNhtjQrb0ZMyXLkSro5lZzP91DwPb1NEk1y1l\nysCXX0L79nDVVZCSAhdc4Oza9euhRw/YvRumT7c/g002S5Wyr1CoWtUm3MbY91McPVxLl7arfg0e\nDH/7mx0ZfuYZ1/vFXnfddUARlS688gqUKwe33w5nnQVLl8I998DIkbaee+JEqFnz9GtWrLD11mPG\nFP75SqmYYozZy5nlCGcQkaXASaA78JFn37nYbgm51ksZYzI913UHPvM51B2Y4vm5nGeb7Xd5NiGe\nH6aJbpRa8OseTmTl0KO5tiNyVdWqdineyy+H3r1t03//hMbf0qV2JNcY+PZbO4nLTUU1Opyf+Hh4\n/307Kvzcc/br/TFjbGLvkr/+9a9Fc6Pdu20njDvusEkuQIUKNrnt2tVOWmzVCj780P7uNWGCLRcp\niomFSimVC2PMQRF5D3heRHYD6cBLwAp8Jo2JyFrgNWPMa55dL2Fbhf0ELATuwZZBvOU5vhY7ovuG\niDzsue/V2GS4iGf55k+7LkSpmSvTOKtcSV32Nxw0aGBHZdPSbO1qfsvKzp4NXbrY0b+FC91PckMp\nLg7eeAMeftjWpt5xB2T7DwaETt++fenbt2/hbzR2LGRm2lpbXyL2PS5ebBPgbt3g73+37/nkSZsI\n9+tnOy4opVTxeRD4HJiETVqPAH2NMb7/AW6CTymEMWYS8ADwBLAc6Aj0NsZs8Rw/CfQG9gDTsInz\nrcBgY0xI+0pqjW4U1uhmZuXQevRsejSvxQvX6wSWsDF1qp1Y1q8fTJlyZl3mJ5/ArbfaOtcZM6B2\nbXfidJsx8M9/wqhRdoW2iRNDV6rhIy0tDYBahVmk4eRJqFcPWrSwE+7ykpEBw4bZUe0uXWwN79Ch\n9gPSn/5U8OcrpaKOkxpddYqO6Eah1E3pHD6eRU8tWwgvV10FL79sE96HHjr92JgxdkJWu3a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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot average odds difference\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, avg_odds_diff_arr, color='r')\n", "ax2.set_ylabel('avg. odds diff.', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2400\n", "Best balanced accuracy: 0.7690\n", "Corresponding abs(1-disparate impact) value: 0.4350\n", "Corresponding average odds difference value: -0.0874\n", "Corresponding statistical parity difference value: -0.1651\n", "Corresponding equal opportunity difference value: -0.0773\n", "Corresponding Theil index value: 0.0906\n" ] } ], "source": [ "rf_thresh_arr_transf_panel19_best = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % rf_thresh_arr_transf_panel19_best)\n", "rf_best_bal_acc_arr_transf_panel19 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % rf_best_bal_acc_arr_transf_panel19)\n", "rf_disp_imp_at_best_bal_acc_transf_panel19 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % rf_disp_imp_at_best_bal_acc_transf_panel19)\n", "rf_avg_odds_diff_at_best_bal_acc_transf_panel19 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % rf_avg_odds_diff_at_best_bal_acc_transf_panel19)\n", "\n", "rf_stat_par_diff_at_best_bal_acc_transf_panel19 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % rf_stat_par_diff_at_best_bal_acc_transf_panel19)\n", "rf_eq_opp_diff_at_best_bal_acc_transf_panel19 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % rf_eq_opp_diff_at_best_bal_acc_transf_panel19)\n", "rf_theil_ind_at_best_bal_acc_transf_panel19 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % rf_theil_ind_at_best_bal_acc_transf_panel19)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.3.4.3. Testing RF model after reweighing" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Evaluate performance of a given model with a given threshold on a given dataset\n", "\n", "scale = rf_scale_transf_panel19\n", "\n", "dataset = dataset_orig_panel19_test #apply model to this data\n", "model = rf_transf_panel19 #this is the model applied\n", " #lr_transf_panel19 is LR model learned from Panel 19\n", " #transformed data\n", "thresh_arr = rf_thresh_arr_transf_panel19_best # lr_thresh_arr_transf_panel19_best wass threshold for LR\n", " # model with highest balanced accuracy\n", "\n", "\n", "X_data = scale.transform(dataset.features)\n", "y_data = dataset.labels.ravel()\n", "y_data_pred_prob = model.predict_proba(X_data) \n", "\n", " \n", "y_pred = (y_data_pred_prob[:,1] > thresh_arr).astype(np.double)\n", "\n", "dataset_pred = dataset.copy()\n", "dataset_pred.labels = y_pred\n", "\n", "classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", "TPR = classified_metric.true_positive_rate()\n", "TNR = classified_metric.true_negative_rate()\n", "bal_acc = 0.5*(TPR+TNR)\n", " \n", "acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", "\n", "#get results\n", "best_bal_acc = bal_acc\n", "disp_imp_at_best_bal_acc = np.abs(1.0-metric_pred.disparate_impact())\n", "\n", "avg_odds_diff_at_best_bal_acc = classified_metric.average_odds_difference()\n", "\n", "stat_par_diff_at_best_bal_acc = classified_metric.statistical_parity_difference()\n", "eq_opp_diff_at_best_bal_acc = classified_metric.equal_opportunity_difference()\n", "theil_ind_at_best_bal_acc = classified_metric.theil_index()" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2400\n", "Best balanced accuracy: 0.7573\n", "Corresponding abs(1-disparate impact) value: 0.4361\n", "Corresponding average odds difference value: -0.0942\n", "Corresponding statistical parity difference value: -0.1713\n", "Corresponding equal opportunity difference value: -0.0730\n", "Corresponding Theil index value: 0.0965\n" ] } ], "source": [ "rf_thresh_arr_transf_panel19_best_test = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % rf_thresh_arr_transf_panel19_best_test)\n", "rf_best_bal_acc_arr_transf_panel19_best_test = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % rf_best_bal_acc_arr_transf_panel19_best_test)\n", "rf_disp_imp_at_best_bal_acc_transf_panel19_best_test = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % rf_disp_imp_at_best_bal_acc_transf_panel19_best_test)\n", "rf_avg_odds_diff_at_best_bal_acc_transf_panel19_best_test = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % rf_avg_odds_diff_at_best_bal_acc_transf_panel19_best_test)\n", "\n", "rf_stat_par_diff_at_best_bal_acc_transf_panel19_best_test = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % rf_stat_par_diff_at_best_bal_acc_transf_panel19_best_test)\n", "rf_eq_opp_diff_at_best_bal_acc_transf_panel19_best_test = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % rf_eq_opp_diff_at_best_bal_acc_transf_panel19_best_test)\n", "rf_theil_ind_at_best_bal_acc_transf_panel19_best_test = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % rf_theil_ind_at_best_bal_acc_transf_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once again, the model learnt from the transformed data is fairer than that learnt from the original data. However, the random forest model learnt from the transformed data is still relatively unfair as compared to the logistic regression model learnt from the transformed data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "### 3.4. Bias Mitigation using in-processing technique - Prejudice Remover (PR)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.4.1. Training PR model" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": true }, "outputs": [], "source": [ "model = PrejudiceRemover(sensitive_attr=sens_attr, eta = 25.0)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Train model on given dataset\n", "\n", "dataset = dataset_orig_panel19_train # data to train on\n", "\n", "tr_dataset = dataset.copy(deepcopy=True)\n", "scale = StandardScaler().fit(tr_dataset.features) # remember the scale\n", "\n", "tr_dataset.features = scale.transform(tr_dataset.features)\n", " \n", "\n", "\n", "model.fit(tr_dataset)\n", "\n", "#save model\n", "ks_orig_panel19 = model\n", "ks_scale_orig_panel19 = scale" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.4.2. Validating PR model" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████| 50/50 [00:00<00:00, 187.26it/s]\n" ] } ], "source": [ "#validate model on given dataset and find threshold for best balanced accuracy\n", "import numpy as np\n", "from tqdm import tqdm\n", "thresh_arr = np.linspace(0.01, 0.5, 50)\n", "\n", "dataset = dataset_orig_panel19_validate #data to validate on\n", "\n", "model = ks_orig_panel19\n", "scale = ks_scale_orig_panel19\n", "\n", "te_dataset= dataset.copy(deepcopy=True)\n", "te_dataset.features = scale.transform(te_dataset.features)\n", "pred_dataset = model.predict(te_dataset)\n", "\n", "y_validate_pred_prob = pred_dataset.scores\n", "\n", "\n", "bal_acc_arr = []\n", "disp_imp_arr = []\n", "avg_odds_diff_arr = []\n", "stat_par_diff = []\n", "eq_opp_diff = []\n", "theil_ind = []\n", " \n", "for thresh in tqdm(thresh_arr):\n", " y_validate_pred = (y_validate_pred_prob[:,1] > thresh).astype(np.double)\n", "\n", " dataset_pred = dataset.copy()\n", " dataset_pred.labels = y_validate_pred\n", "\n", " classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", " bal_acc = 0.5*(classified_metric.true_positive_rate() + classified_metric.true_negative_rate())\n", " \n", " acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", " bal_acc_arr.append(bal_acc)\n", " avg_odds_diff_arr.append(classified_metric.average_odds_difference())\n", " disp_imp_arr.append(metric_pred.disparate_impact())\n", " stat_par_diff.append(classified_metric.statistical_parity_difference())\n", " eq_opp_diff.append(classified_metric.equal_opportunity_difference())\n", " theil_ind.append(classified_metric.theil_index())\n", "\n", " \n", "thresh_arr_best_ind = np.where(bal_acc_arr == np.max(bal_acc_arr))[0][0]\n", "thresh_arr_best = np.array(thresh_arr)[thresh_arr_best_ind]\n", "\n", "best_bal_acc = bal_acc_arr[thresh_arr_best_ind]\n", "disp_imp_at_best_bal_acc = np.abs(1.0-np.array(disp_imp_arr))[thresh_arr_best_ind]\n", "\n", "avg_odds_diff_at_best_bal_acc = avg_odds_diff_arr[thresh_arr_best_ind]\n", "\n", "stat_par_diff_at_best_bal_acc = stat_par_diff[thresh_arr_best_ind]\n", "eq_opp_diff_at_best_bal_acc = eq_opp_diff[thresh_arr_best_ind]\n", "theil_ind_at_best_bal_acc = theil_ind[thresh_arr_best_ind]" ] }, { "cell_type": "code", "execution_count": 38, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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H4cUXbXLYu7fT0aRPy5bw5ZewYIFtY6ZUBunMrRt05jZ7iY8X+kz8myW7Qpny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\nyhgzgCgRecD16ylAscQtWV1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B1j8EAt2BhcawxxgGG0Np92M33bCFw+8BDYCVwFxjTMUU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\npBauJdjBK2HetsB+REtIk3O9vpxSVZZs2EH/E5qUzQ1HjIBPPoEXXkj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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot balanced accuracy, abs(1-disparate impact)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, np.abs(1.0-np.array(disp_imp_arr)), color='r')\n", "ax2.set_ylabel('abs(1-disparate impact)', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], \n", " color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)\n" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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/s40dQWHM7N+YZpWLERMXT0ycJjYunugUfh0Xr6lVuiC5vd2k3njy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4PubrjxRvjIR6CzMybDpWpthXHjYOutS99HA1m6dCkAo0fn+9bIzMysPoQQOti89GEzkuYBG4Aj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\nRL7MtxgvwXIAAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot average odds difference\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, avg_odds_diff_arr, color='r')\n", "ax2.set_ylabel('avg. odds diff.', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.1200\n", "Best balanced accuracy: 0.7009\n", "Corresponding abs(1-disparate impact) value: 0.2416\n", "Corresponding average odds difference value: 0.0041\n", "Corresponding statistical parity difference value: -0.0898\n", "Corresponding equal opportunity difference value: 0.0660\n", "Corresponding Theil index value: 0.1071\n" ] } ], "source": [ "ks_thresh_arr_orig_panel19_best = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % ks_thresh_arr_orig_panel19_best)\n", "ks_best_bal_acc_arr_orig_panel19 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % ks_best_bal_acc_arr_orig_panel19)\n", "ks_disp_imp_at_best_bal_acc_orig_panel19 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % ks_disp_imp_at_best_bal_acc_orig_panel19)\n", "ks_avg_odds_diff_at_best_bal_acc_orig_panel19 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % ks_avg_odds_diff_at_best_bal_acc_orig_panel19)\n", "\n", "ks_stat_par_diff_at_best_bal_acc_orig_panel19 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % ks_stat_par_diff_at_best_bal_acc_orig_panel19)\n", "ks_eq_opp_diff_at_best_bal_acc_orig_panel19 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % ks_eq_opp_diff_at_best_bal_acc_orig_panel19)\n", "ks_theil_ind_at_best_bal_acc_orig_panel19 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % ks_theil_ind_at_best_bal_acc_orig_panel19)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.4.3. Testing PR model" ] }, { "cell_type": "code", "execution_count": 41, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Test model on given dataset and find threshold for best balanced accuracy\n", "import numpy as np\n", "from tqdm import tqdm\n", "thresh_arr = np.linspace(0.01, 0.75, 75)\n", "\n", "dataset = dataset_orig_panel19_test #data to test on\n", "scale = ks_scale_orig_panel19\n", "model = ks_orig_panel19\n", "\n", "thresh_arr = ks_thresh_arr_orig_panel19_best\n", "\n", "te_dataset= dataset.copy(deepcopy=True)\n", "te_dataset.features = scale.transform(te_dataset.features)\n", "pred_dataset = model.predict(te_dataset)\n", "\n", "y_data_pred_prob = pred_dataset.scores\n", "\n", "\n", "y_data_pred = (y_data_pred_prob[:,1] > thresh_arr).astype(np.double)\n", "\n", "dataset_pred = dataset.copy()\n", "dataset_pred.labels = y_data_pred\n", "\n", "classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", "bal_acc = 0.5*(classified_metric.true_positive_rate() + classified_metric.true_negative_rate())\n", " \n", "acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", "\n", "best_bal_acc = bal_acc\n", "disp_imp_at_best_bal_acc = np.abs(1.0-metric_pred.disparate_impact())\n", "\n", "avg_odds_diff_at_best_bal_acc = classified_metric.average_odds_difference()\n", "\n", "stat_par_diff_at_best_bal_acc = classified_metric.statistical_parity_difference()\n", "eq_opp_diff_at_best_bal_acc = classified_metric.equal_opportunity_difference()\n", "theil_ind_at_best_bal_acc = classified_metric.theil_index()" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.1200\n", "Best balanced accuracy: 0.7087\n", "Corresponding abs(1-disparate impact) value: 0.1952\n", "Corresponding average odds difference value: 0.0157\n", "Corresponding statistical parity difference value: -0.0720\n", "Corresponding equal opportunity difference value: 0.0698\n", "Corresponding Theil index value: 0.1064\n" ] } ], "source": [ "ks_thresh_arr_orig_panel19_best_test = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % ks_thresh_arr_orig_panel19_best_test)\n", "ks_best_bal_acc_arr_orig_panel19_best_test = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % ks_best_bal_acc_arr_orig_panel19_best_test)\n", "ks_disp_imp_at_best_bal_acc_orig_panel19_best_test = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % ks_disp_imp_at_best_bal_acc_orig_panel19_best_test)\n", "ks_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % ks_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test)\n", "\n", "ks_stat_par_diff_at_best_bal_acc_orig_panel19_best_test = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % ks_stat_par_diff_at_best_bal_acc_orig_panel19_best_test)\n", "ks_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % ks_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test)\n", "ks_theil_ind_at_best_bal_acc_orig_panel19_best_test = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % ks_theil_ind_at_best_bal_acc_orig_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As in the case of re-weighing, prejudice remover has resulted in a fair model. However, it hs come at an expense of relative lower balanced accuracy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.5. Bias mitigation using pre-processing technique - Disparate Impact (DIR) Remover" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.5.1. Training DIR model" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Train model on given dataset\n", "\n", "dataset = dataset_orig_panel19_train # data to train on\n", "\n", "tr_dataset = dataset.copy(deepcopy=True)\n", "scale = MinMaxScaler().fit(tr_dataset.features) # remember the scale\n", "\n", "tr_dataset.features = scale.transform(tr_dataset.features)\n", "index = tr_dataset.feature_names.index(sens_attr) \n", "\n", "di = DisparateImpactRemover(repair_level=1.0)\n", "train_repd = di.fit_transform(tr_dataset) #repair training dataset\n", "\n", "X_tr = np.delete(train_repd.features, index, axis=1)\n", " \n", "\n", "y_tr = train_repd.labels.ravel()\n", " \n", "model = LogisticRegression(random_state = 1, class_weight='balanced')\n", "model.fit(X_tr, y_tr)\n", "\n", "di_scale_orig_panel19 = scale\n", "di_orig_panel19 = model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.5.2. Validating DIR model" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████| 75/75 [00:00<00:00, 142.04it/s]\n" ] } ], "source": [ "#validate model on given dataset and find threshold for best balanced accuracy\n", "import numpy as np\n", "from tqdm import tqdm\n", "\n", "scale = di_scale_orig_panel19\n", "model = di_orig_panel19\n", "\n", "thresh_arr = np.linspace(0.01, 0.75, 75)\n", "\n", "dataset = dataset_orig_panel19_validate #data to validate on\n", "\n", "te_dataset= dataset.copy(deepcopy=True)\n", "te_dataset.features = scale.transform(te_dataset.features)\n", "\n", "validate_repd = di.fit_transform(te_dataset) #repair validate dataset\n", "\n", "X_te = np.delete(validate_repd.features, index, axis=1)\n", " \n", "\n", "y_te_pred_prob = model.predict_proba(X_te)\n", "\n", "\n", "bal_acc_arr = []\n", "disp_imp_arr = []\n", "avg_odds_diff_arr = []\n", "stat_par_diff = []\n", "eq_opp_diff = []\n", "theil_ind = []\n", " \n", "for thresh in tqdm(thresh_arr):\n", " y_te_pred = (y_te_pred_prob[:,1] > thresh).astype(np.double)\n", "\n", " validate_repd_pred = validate_repd.copy()\n", " validate_repd_pred.labels = y_te_pred\n", "\n", " classified_metric = ClassificationMetric(validate_repd, \n", " validate_repd_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " metric_pred = BinaryLabelDatasetMetric(validate_repd_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", " bal_acc = 0.5*(classified_metric.true_positive_rate() + classified_metric.true_negative_rate())\n", " \n", " acc = accuracy_score(y_true=validate_repd.labels,\n", " y_pred=validate_repd_pred.labels)\n", " bal_acc_arr.append(bal_acc)\n", " avg_odds_diff_arr.append(classified_metric.average_odds_difference())\n", " disp_imp_arr.append(metric_pred.disparate_impact())\n", " stat_par_diff.append(classified_metric.statistical_parity_difference())\n", " eq_opp_diff.append(classified_metric.equal_opportunity_difference())\n", " theil_ind.append(classified_metric.theil_index())\n", " \n", "thresh_arr_best_ind = np.where(bal_acc_arr == np.max(bal_acc_arr))[0][0]\n", "thresh_arr_best = np.array(thresh_arr)[thresh_arr_best_ind]\n", "\n", "best_bal_acc = bal_acc_arr[thresh_arr_best_ind]\n", "disp_imp_at_best_bal_acc = np.abs(1.0-np.array(disp_imp_arr))[thresh_arr_best_ind]\n", "\n", "avg_odds_diff_at_best_bal_acc = avg_odds_diff_arr[thresh_arr_best_ind]\n", "\n", "stat_par_diff_at_best_bal_acc = stat_par_diff[thresh_arr_best_ind]\n", "eq_opp_diff_at_best_bal_acc = eq_opp_diff[thresh_arr_best_ind]\n", "theil_ind_at_best_bal_acc = theil_ind[thresh_arr_best_ind]" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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7b6JkkMyjdMoff8B998Frr8GYMVZHI8R1jp27xN3jV3F7vXJMH9DK43/RlKTU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\nck3mlAp3YXml1Ky4t6O1nxOr73FlgL6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0PFAB2IpzOzC7D2gD7AM+AJ7EufSoq8vnjk4H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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot balanced accuracy, abs(1-disparate impact)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, np.abs(1.0-np.array(disp_imp_arr)), color='r')\n", "ax2.set_ylabel('abs(1-disparate impact)', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], \n", " color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)\n" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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gSREfK4FErNHZmAL3V+bMEds8x7CK1oIjvmfcIyJlgLxZnFeVdJELWugGhuHD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\ninbggLQVS61sQakAkWKiawyNka4KzwH9gaXGMByZP1wUqdHNCzxjDI9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6awgLg/ffh5Yt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\nD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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot average odds difference\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, avg_odds_diff_arr, color='r')\n", "ax2.set_ylabel('avg. odds diff.', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.5500\n", "Best balanced accuracy: 0.7696\n", "Corresponding abs(1-disparate impact) value: 0.4911\n", "Corresponding average odds difference value: -0.1083\n", "Corresponding statistical parity difference value: -0.1881\n", "Corresponding equal opportunity difference value: -0.0944\n", "Corresponding Theil index value: 0.0916\n" ] } ], "source": [ "di_thresh_arr_orig_panel19_best = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % di_thresh_arr_orig_panel19_best)\n", "di_best_bal_acc_arr_orig_panel19 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % di_best_bal_acc_arr_orig_panel19)\n", "di_disp_imp_at_best_bal_acc_orig_panel19 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % di_disp_imp_at_best_bal_acc_orig_panel19)\n", "di_avg_odds_diff_at_best_bal_acc_orig_panel19 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % di_avg_odds_diff_at_best_bal_acc_orig_panel19)\n", "\n", "di_stat_par_diff_at_best_bal_acc_orig_panel19 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % di_stat_par_diff_at_best_bal_acc_orig_panel19)\n", "di_eq_opp_diff_at_best_bal_acc_orig_panel19 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % di_eq_opp_diff_at_best_bal_acc_orig_panel19)\n", "di_theil_ind_at_best_bal_acc_orig_panel19 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % di_theil_ind_at_best_bal_acc_orig_panel19)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### 3.5.3. Testing DIR model" ] }, { "cell_type": "code", "execution_count": 48, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Test model on given dataset and find threshold for best balanced accuracy\n", "import numpy as np\n", "from tqdm import tqdm\n", "thresh_arr = np.linspace(0.01, 0.75, 75)\n", "\n", "dataset = dataset_orig_panel19_test #data to test on\n", "scale = di_scale_orig_panel19\n", "model = di_orig_panel19\n", "\n", "te_dataset= dataset.copy(deepcopy=True)\n", "te_dataset.features = scale.transform(te_dataset.features)\n", "\n", "di = DisparateImpactRemover(repair_level=1.0)\n", "\n", "test_repd = di.fit_transform(te_dataset) #repair test dataset\n", "\n", "index = te_dataset.feature_names.index(sens_attr) \n", "X_te = np.delete(test_repd.features, index, axis=1)\n", " \n", "\n", "y_te_pred_prob = model.predict_proba(X_te)\n", "\n", "thresh_arr = di_thresh_arr_orig_panel19_best \n", "\n", "y_te_pred = (y_te_pred_prob[:,1] > thresh).astype(np.double)\n", "\n", "test_repd_pred = test_repd.copy()\n", "test_repd_pred.labels = y_te_pred\n", "\n", "classified_metric = ClassificationMetric(test_repd, \n", " test_repd_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "metric_pred = BinaryLabelDatasetMetric(test_repd_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", "bal_acc = 0.5*(classified_metric.true_positive_rate() + classified_metric.true_negative_rate())\n", " \n", "acc = accuracy_score(y_true=test_repd.labels,\n", " y_pred=test_repd_pred.labels)\n", "\n", "best_bal_acc = bal_acc\n", "disp_imp_at_best_bal_acc = np.abs(1.0-metric_pred.disparate_impact())\n", "\n", "avg_odds_diff_at_best_bal_acc = classified_metric.average_odds_difference()\n", "\n", "stat_par_diff_at_best_bal_acc = classified_metric.statistical_parity_difference()\n", "eq_opp_diff_at_best_bal_acc = classified_metric.equal_opportunity_difference()\n", "theil_ind_at_best_bal_acc = classified_metric.theil_index()" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.5500\n", "Best balanced accuracy: 0.7233\n", "Corresponding abs(1-disparate impact) value: 0.5133\n", "Corresponding average odds difference value: -0.0898\n", "Corresponding statistical parity difference value: -0.1213\n", "Corresponding equal opportunity difference value: -0.1282\n", "Corresponding Theil index value: 0.1126\n" ] } ], "source": [ "di_thresh_arr_orig_panel19_best_test = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % di_thresh_arr_orig_panel19_best_test)\n", "di_best_bal_acc_arr_orig_panel19_best_test = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % di_best_bal_acc_arr_orig_panel19_best_test)\n", "di_disp_imp_at_best_bal_acc_orig_panel19_best_test = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % di_disp_imp_at_best_bal_acc_orig_panel19_best_test)\n", "di_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % di_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test)\n", "\n", "di_stat_par_diff_at_best_bal_acc_orig_panel19_best_test = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % di_stat_par_diff_at_best_bal_acc_orig_panel19_best_test)\n", "di_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % di_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test)\n", "di_theil_ind_at_best_bal_acc_orig_panel19_best_test = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % di_theil_ind_at_best_bal_acc_orig_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While disparate impact remover resulted in a model that is relatively fairer than, for examaple, the logistic regression model learnt from original data, it is quite unfair with an bs(1-disparate impact) value much higher than the typically desired value of < 0.2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3.6. Summary of Model Learning Results" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Logistic Regression classifier 'without' bias mitigation" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.1900\n", "Best balanced accuracy: 0.7759\n", "Corresponding abs(1-disparate impact) value: 0.5738\n", "Corresponding average odds difference value: -0.2057\n", "Corresponding statistical parity difference value: -0.2612\n", "Corresponding equal opportunity difference value: -0.2228\n", "Corresponding Theil index value: 0.0921\n" ] } ], "source": [ "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % lr_thresh_arr_orig_panel19_best_test)\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_orig_panel19_best_test)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_orig_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Random Forest classifier 'without' bias mitigation" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2200\n", "Best balanced accuracy: 0.7682\n", "Corresponding abs(1-disparate impact) value: 0.5021\n", "Corresponding average odds difference value: -0.1409\n", "Corresponding statistical parity difference value: -0.2182\n", "Corresponding equal opportunity difference value: -0.1222\n", "Corresponding Theil index value: 0.0933\n" ] } ], "source": [ "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % rf_thresh_arr_orig_panel19_best_test)\n", "print(\"Best balanced accuracy: %6.4f\" % rf_best_bal_acc_arr_orig_panel19_best_test)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % rf_disp_imp_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding average odds difference value: %6.4f\" % rf_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % rf_stat_par_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % rf_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding Theil index value: %6.4f\" % rf_theil_ind_at_best_bal_acc_orig_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Logistic Regression classifier 'with' bias mitigation" ] }, { "cell_type": "code", "execution_count": 52, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2200\n", "Best balanced accuracy: 0.7539\n", "Corresponding abs(1-disparate impact) value: 0.2482\n", "Corresponding average odds difference value: -0.0151\n", "Corresponding statistical parity difference value: -0.0872\n", "Corresponding equal opportunity difference value: -0.0035\n", "Corresponding Theil index value: 0.0966\n" ] } ], "source": [ "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % lr_thresh_arr_transf_panel19_best_test)\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel19_best_test)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Random Forest classifier 'with' bias mitigation" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2400\n", "Best balanced accuracy: 0.7573\n", "Corresponding abs(1-disparate impact) value: 0.4361\n", "Corresponding average odds difference value: -0.0942\n", "Corresponding statistical parity difference value: -0.1713\n", "Corresponding equal opportunity difference value: -0.0730\n", "Corresponding Theil index value: 0.0965\n" ] } ], "source": [ "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % rf_thresh_arr_transf_panel19_best_test)\n", "print(\"Best balanced accuracy: %6.4f\" % rf_best_bal_acc_arr_transf_panel19_best_test)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % rf_disp_imp_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding average odds difference value: %6.4f\" % rf_avg_odds_diff_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % rf_stat_par_diff_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % rf_eq_opp_diff_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding Theil index value: %6.4f\" % rf_theil_ind_at_best_bal_acc_transf_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Model learnt using in-processing Bias Mitigation (Kamishima)" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.1200\n", "Best balanced accuracy: 0.7087\n", "Corresponding abs(1-disparate impact) value: 0.1952\n", "Corresponding average odds difference value: 0.0157\n", "Corresponding statistical parity difference value: -0.0720\n", "Corresponding equal opportunity difference value: 0.0698\n", "Corresponding Theil index value: 0.1064\n" ] } ], "source": [ "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % ks_thresh_arr_orig_panel19_best_test)\n", "print(\"Best balanced accuracy: %6.4f\" % ks_best_bal_acc_arr_orig_panel19_best_test)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % ks_disp_imp_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding average odds difference value: %6.4f\" % ks_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % ks_stat_par_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % ks_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding Theil index value: %6.4f\" % ks_theil_ind_at_best_bal_acc_orig_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Model learnt using Disparate Impact Remover" ] }, { "cell_type": "code", "execution_count": 55, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.5500\n", "Best balanced accuracy: 0.7233\n", "Corresponding abs(1-disparate impact) value: 0.5133\n", "Corresponding average odds difference value: -0.0898\n", "Corresponding statistical parity difference value: -0.1213\n", "Corresponding equal opportunity difference value: -0.1282\n", "Corresponding Theil index value: 0.1126\n" ] } ], "source": [ "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % di_thresh_arr_orig_panel19_best_test)\n", "print(\"Best balanced accuracy: %6.4f\" % di_best_bal_acc_arr_orig_panel19_best_test)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % di_disp_imp_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding average odds difference value: %6.4f\" % di_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % di_stat_par_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % di_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding Theil index value: %6.4f\" % di_theil_ind_at_best_bal_acc_orig_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of all the models, the logistic regression model gives the best balance in terms of balanced accuracy and fairness. While the model learnt by prejudice remover is slightly fairer, it has much lower accuracy. All other models are quite unfair compared to the logistic model. Hence, we take the logistic regression model learnt from data transformed by re-weighing and 'deploy' it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Deploying model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.1. Testing learned model on 2015 Panel 20 deployment data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "code", "execution_count": 56, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.random.seed(seed)\n", "dataset_orig_panel20 = MEPSDataset20()\n", "dataset_orig_panel20_train, dataset_orig_panel20_validate, dataset_orig_panel20_deploy \\\n", " = dataset_orig_panel20.split([split_1,split_2], shuffle=shuffle) \n", "\n", "#now align them with the 2014 datasets\n", "dataset_orig_panel20_train = dataset_orig_panel19_train.align_datasets(dataset_orig_panel20_train)\n", "dataset_orig_panel20_validate = dataset_orig_panel19_train.align_datasets(dataset_orig_panel20_validate)\n", "dataset_orig_panel20_deploy = dataset_orig_panel19_train.align_datasets(dataset_orig_panel20_deploy)" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Training Dataset shape" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(8785, 138)\n" ] }, { "data": { "text/markdown": [ "#### Validation Dataset shape" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(5271, 138)\n" ] }, { "data": { "text/markdown": [ "#### Deployment Dataset shape" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(3514, 138)\n" ] }, { "data": { "text/markdown": [ "#### Favorable and unfavorable labels" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "1.0 0.0\n" ] }, { "data": { "text/markdown": [ "#### Protected attribute names" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "['RACE']\n" ] }, { "data": { "text/markdown": [ "#### Privileged and unprivileged protected attribute values" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[array([1.])] [array([0.])]\n" ] }, { "data": { "text/markdown": [ "#### Dataset feature names" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "['RACE', 'AGE', 'PCS42', 'K6SUM42', 'MCS42', 'REGION=1', 'REGION=2', 'REGION=3', 'REGION=4', 'SEX=1', 'SEX=2', 'MARRY=1', 'MARRY=2', 'MARRY=3', 'MARRY=4', 'MARRY=5', 'MARRY=6', 'MARRY=7', 'MARRY=8', 'MARRY=9', 'MARRY=10', 'FTSTU=-1', 'FTSTU=1', 'FTSTU=2', 'FTSTU=3', 'ACTDTY=1', 'ACTDTY=2', 'ACTDTY=3', 'ACTDTY=4', 'HONRDC=1', 'HONRDC=2', 'HONRDC=3', 'HONRDC=4', 'RTHLTH=-1', 'RTHLTH=1', 'RTHLTH=2', 'RTHLTH=3', 'RTHLTH=4', 'RTHLTH=5', 'MNHLTH=-1', 'MNHLTH=1', 'MNHLTH=2', 'MNHLTH=3', 'MNHLTH=4', 'MNHLTH=5', 'HIBPDX=-1', 'HIBPDX=1', 'HIBPDX=2', 'CHDDX=-1', 'CHDDX=1', 'CHDDX=2', 'ANGIDX=-1', 'ANGIDX=1', 'ANGIDX=2', 'MIDX=-1', 'MIDX=1', 'MIDX=2', 'OHRTDX=-1', 'OHRTDX=1', 'OHRTDX=2', 'STRKDX=-1', 'STRKDX=1', 'STRKDX=2', 'EMPHDX=-1', 'EMPHDX=1', 'EMPHDX=2', 'CHBRON=-1', 'CHBRON=1', 'CHBRON=2', 'CHOLDX=-1', 'CHOLDX=1', 'CHOLDX=2', 'CANCERDX=-1', 'CANCERDX=1', 'CANCERDX=2', 'DIABDX=-1', 'DIABDX=1', 'DIABDX=2', 'JTPAIN=-1', 'JTPAIN=1', 'JTPAIN=2', 'ARTHDX=-1', 'ARTHDX=1', 'ARTHDX=2', 'ARTHTYPE=-1', 'ARTHTYPE=1', 'ARTHTYPE=2', 'ARTHTYPE=3', 'ASTHDX=1', 'ASTHDX=2', 'ADHDADDX=-1', 'ADHDADDX=1', 'ADHDADDX=2', 'PREGNT=-1', 'PREGNT=1', 'PREGNT=2', 'WLKLIM=-1', 'WLKLIM=1', 'WLKLIM=2', 'ACTLIM=-1', 'ACTLIM=1', 'ACTLIM=2', 'SOCLIM=-1', 'SOCLIM=1', 'SOCLIM=2', 'COGLIM=-1', 'COGLIM=1', 'COGLIM=2', 'DFHEAR42=-1', 'DFHEAR42=1', 'DFHEAR42=2', 'DFSEE42=-1', 'DFSEE42=1', 'DFSEE42=2', 'ADSMOK42=-1', 'ADSMOK42=1', 'ADSMOK42=2', 'PHQ242=-1', 'PHQ242=0', 'PHQ242=1', 'PHQ242=2', 'PHQ242=3', 'PHQ242=4', 'PHQ242=5', 'PHQ242=6', 'EMPST=-1', 'EMPST=1', 'EMPST=2', 'EMPST=3', 'EMPST=4', 'POVCAT=1', 'POVCAT=2', 'POVCAT=3', 'POVCAT=4', 'POVCAT=5', 'INSCOV=1', 'INSCOV=2', 'INSCOV=3']\n" ] } ], "source": [ "# print out some labels, names, etc.\n", "display(Markdown(\"#### Training Dataset shape\"))\n", "print(dataset_orig_panel20_train.features.shape)\n", "display(Markdown(\"#### Validation Dataset shape\"))\n", "print(dataset_orig_panel20_validate.features.shape)\n", "display(Markdown(\"#### Deployment Dataset shape\"))\n", "print(dataset_orig_panel20_deploy.features.shape)\n", "display(Markdown(\"#### Favorable and unfavorable labels\"))\n", "print(dataset_orig_panel20_train.favorable_label, dataset_orig_panel20_train.unfavorable_label)\n", "display(Markdown(\"#### Protected attribute names\"))\n", "print(dataset_orig_panel20_train.protected_attribute_names)\n", "display(Markdown(\"#### Privileged and unprivileged protected attribute values\"))\n", "print(dataset_orig_panel20_train.privileged_protected_attributes, \n", " dataset_orig_panel20_train.unprivileged_protected_attributes)\n", "display(Markdown(\"#### Dataset feature names\"))\n", "print(dataset_orig_panel20_train.feature_names)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Original training dataset" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean outcomes between privileged and unprivileged groups = -0.135347\n" ] } ], "source": [ "# Metric for the original dataset\n", "sens_idx = dataset_orig_panel20_deploy.protected_attribute_names.index(sens_attr)\n", "privileged_groups = [{sens_attr:dataset_orig_panel20_deploy.privileged_protected_attributes[sens_idx][0]}]\n", "unprivileged_groups = [{sens_attr:dataset_orig_panel20_deploy.unprivileged_protected_attributes[sens_idx][0]}]\n", "metric_orig_panel20_deploy = BinaryLabelDatasetMetric(dataset_orig_panel20_deploy, \n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "display(Markdown(\"#### Original training dataset\"))\n", "print(\"Difference in mean outcomes between privileged and unprivileged groups = %f\" % \\\n", " metric_orig_panel20_deploy.mean_difference())" ] }, { "cell_type": "code", "execution_count": 59, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Evaluate performance of a given model with a given threshold on a given dataset\n", "\n", "scale = lr_scale_transf_panel19\n", "\n", "dataset = dataset_orig_panel20_deploy #apply model to this data\n", "model = lr_transf_panel19 #this is the model applied\n", " #lr_transf_panel19 is LR model learned from Panel panel19 (panel1914)\n", " #transformed data\n", "thresh_arr = lr_thresh_arr_transf_panel19_best # lr_thresh_arr_transf_panel19_best wass threshold for LR\n", " # model with highest balanced accuracy\n", "\n", "X_data = scale.transform(dataset.features)\n", "y_data = dataset.labels.ravel()\n", "y_data_pred_prob = model.predict_proba(X_data) \n", "\n", " \n", "y_pred = (y_data_pred_prob[:,1] > thresh_arr).astype(np.double)\n", "\n", "dataset_pred = dataset.copy()\n", "dataset_pred.labels = y_pred\n", "\n", "classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", "TPR = classified_metric.true_positive_rate()\n", "TNR = classified_metric.true_negative_rate()\n", "bal_acc = 0.5*(TPR+TNR)\n", "acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", "\n", "#get results\n", "best_bal_acc = bal_acc\n", "avg_odds_diff_at_best_bal_acc = classified_metric.average_odds_difference()\n", "disp_imp_at_best_bal_acc = np.abs(1.0 - metric_pred.disparate_impact())\n", "stat_par_diff_at_best_bal_acc = classified_metric.statistical_parity_difference()\n", "eq_opp_diff_at_best_bal_acc = classified_metric.equal_opportunity_difference()\n", "theil_ind_at_best_bal_acc = classified_metric.theil_index()" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best balanced accuracy: 0.7289\n", "Corresponding abs(1-disparate impact) value: 0.1106\n", "Corresponding average odds difference value: 0.0696\n", "Corresponding statistical parity difference value: -0.0341\n", "Corresponding equal opportunity difference value: 0.1315\n", "Corresponding Theil index value: 0.1038\n" ] } ], "source": [ "lr_best_bal_acc_arr_transf_panel19_deploy_panel20 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel19_deploy_panel20)\n", "lr_disp_imp_at_best_bal_acc_transf_panel19_deploy_panel20 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel19_deploy_panel20)\n", "lr_avg_odds_diff_at_best_bal_acc_transf_panel19_deploy_panel20 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel19_deploy_panel20)\n", "\n", "lr_stat_par_diff_at_best_bal_acc_transf_panel19_deploy_panel20 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel19_deploy_panel20)\n", "lr_eq_opp_diff_at_best_bal_acc_transf_panel19_deploy_panel20 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel19_deploy_panel20)\n", "lr_theil_ind_at_best_bal_acc_transf_panel19_deploy_panel20 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel19_deploy_panel20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deployed model tested on the 2015 Panel 20 data still exhibits fairness as well as maintains accuracy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.2. Generating explanations for model predictions on 2015 Panel 20 deployment data using LIME" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This section shows how LIME can be integrated with AIF 360 to get explanations for model predictions." ] }, { "cell_type": "code", "execution_count": 61, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2200\n" ] }, { "data": { "text/html": [ "\n", " \n", " \n", "
\n", " \n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Actual label: [0.]\n" ] }, { "data": { "text/html": [ "\n", " \n", " \n", "
\n", " \n", " \n", " " ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Actual label: [0.]\n" ] } ], "source": [ "scale = lr_scale_transf_panel19\n", "\n", "train_dataset = dataset_transf_panel19_train #data the deployed model (lr from transformed data)\n", "test_dataset = dataset_orig_panel20_deploy #the data model i sbeing tested on\n", "model = lr_transf_panel19 #this is the model applied\n", " #lr_transf_panel19 is LR model learned from Panel panel19 (panel1914)\n", " #transformed data\n", "thresh_arr = lr_thresh_arr_transf_panel19_best # lr_thresh_arr_transf_panel19_best wass threshold for LR\n", "\n", "#First, you call LimeEncode.fit(..) to fit the encoder to the aif360 dataset. \n", "limeData = LimeEncoder().fit(train_dataset)\n", "\n", "#The 'transform' method then is used to convert aif360 features to lime compatible features. \n", "s_train = limeData.transform(train_dataset.features)\n", "s_test = limeData.transform(test_dataset.features)\n", "\n", "\n", "#The LimeTabularExplainer takes as input the lime compatible data along with various other arguments to create a lime explainer\n", "explainer = lime.lime_tabular.LimeTabularExplainer(s_train ,class_names=limeData.s_class_names, \n", " feature_names = limeData.s_feature_names,\n", " categorical_features=limeData.s_categorical_features, \n", " categorical_names=limeData.s_categorical_names, \n", " kernel_width=3, verbose=False,discretize_continuous=True)\n", "\n", "#The inverse_transform function is used to transform lime compatible data back to aif360 compatible data since that is needed\n", "# by the model to make predictions. The function below is used to produce \n", "#the predictions for any perturbed data that is produce by lime\n", "s_predict_fn = lambda x: model.predict_proba(scale.transform(limeData.inverse_transform(x)))\n", "\n", "#the explain_instance method can then be used to produce explanations for any instance in the test dataset\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % thresh_arr)\n", "i = 0\n", "exp = explainer.explain_instance(s_test[i], s_predict_fn, num_features=10)\n", "exp.show_in_notebook(show_all=False)\n", "print(\"Actual label: \" + str(test_dataset.labels[i]))\n", "\n", "i = 2\n", "exp = explainer.explain_instance(s_test[i], s_predict_fn, num_features=10)\n", "exp.show_in_notebook(show_all=False)\n", "print(\"Actual label: \" + str(test_dataset.labels[i]))\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "See [LIME documentation](https://github.com/marcotcr/lime) for detailed description of results. In short, the left hand side shows the label predictions made by the model, the middle shows the features that are important to the instance in question and their contributions (weights) to the label prediction, while the right hand side shows the actual values of the features in the particular instance." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.3. Testing learned model on 2016 Panel 21 deployment data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Load the Panel 21 data, and split it again into 3 parts: train, validate, and deploy. We test the deployed model against the deployment data. If a new model needs to be learnt, it will be learnt from the train/validate data and then tested again on the deployment data." ] }, { "cell_type": "code", "execution_count": 62, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.random.seed(seed)\n", "dataset_orig_panel21 = MEPSDataset21()\n", "dataset_orig_panel21_train, dataset_orig_panel21_validate, dataset_orig_panel21_deploy \\\n", " = dataset_orig_panel21.split([split_1,split_2], shuffle=shuffle) \n", "\n", "#now align them with the panel19 datasets\n", "dataset_orig_panel21_train = dataset_orig_panel19_train.align_datasets(dataset_orig_panel21_train)\n", "dataset_orig_panel21_validate = dataset_orig_panel19_train.align_datasets(dataset_orig_panel21_validate)\n", "dataset_orig_panel21_deploy = dataset_orig_panel19_train.align_datasets(dataset_orig_panel21_deploy)" ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Training Dataset shape" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(7837, 138)\n" ] }, { "data": { "text/markdown": [ "#### Validation Dataset shape" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(4703, 138)\n" ] }, { "data": { "text/markdown": [ "#### Deployment Dataset shape" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "(3135, 138)\n" ] }, { "data": { "text/markdown": [ "#### Favorable and unfavorable labels" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "1.0 0.0\n" ] }, { "data": { "text/markdown": [ "#### Protected attribute names" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "['RACE']\n" ] }, { "data": { "text/markdown": [ "#### Privileged and unprivileged protected attribute values" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "[array([1.])] [array([0.])]\n" ] }, { "data": { "text/markdown": [ "#### Dataset feature names" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "['RACE', 'AGE', 'PCS42', 'K6SUM42', 'MCS42', 'REGION=1', 'REGION=2', 'REGION=3', 'REGION=4', 'SEX=1', 'SEX=2', 'MARRY=1', 'MARRY=2', 'MARRY=3', 'MARRY=4', 'MARRY=5', 'MARRY=6', 'MARRY=7', 'MARRY=8', 'MARRY=9', 'MARRY=10', 'FTSTU=-1', 'FTSTU=1', 'FTSTU=2', 'FTSTU=3', 'ACTDTY=1', 'ACTDTY=2', 'ACTDTY=3', 'ACTDTY=4', 'HONRDC=1', 'HONRDC=2', 'HONRDC=3', 'HONRDC=4', 'RTHLTH=-1', 'RTHLTH=1', 'RTHLTH=2', 'RTHLTH=3', 'RTHLTH=4', 'RTHLTH=5', 'MNHLTH=-1', 'MNHLTH=1', 'MNHLTH=2', 'MNHLTH=3', 'MNHLTH=4', 'MNHLTH=5', 'HIBPDX=-1', 'HIBPDX=1', 'HIBPDX=2', 'CHDDX=-1', 'CHDDX=1', 'CHDDX=2', 'ANGIDX=-1', 'ANGIDX=1', 'ANGIDX=2', 'MIDX=-1', 'MIDX=1', 'MIDX=2', 'OHRTDX=-1', 'OHRTDX=1', 'OHRTDX=2', 'STRKDX=-1', 'STRKDX=1', 'STRKDX=2', 'EMPHDX=-1', 'EMPHDX=1', 'EMPHDX=2', 'CHBRON=-1', 'CHBRON=1', 'CHBRON=2', 'CHOLDX=-1', 'CHOLDX=1', 'CHOLDX=2', 'CANCERDX=-1', 'CANCERDX=1', 'CANCERDX=2', 'DIABDX=-1', 'DIABDX=1', 'DIABDX=2', 'JTPAIN=-1', 'JTPAIN=1', 'JTPAIN=2', 'ARTHDX=-1', 'ARTHDX=1', 'ARTHDX=2', 'ARTHTYPE=-1', 'ARTHTYPE=1', 'ARTHTYPE=2', 'ARTHTYPE=3', 'ASTHDX=1', 'ASTHDX=2', 'ADHDADDX=-1', 'ADHDADDX=1', 'ADHDADDX=2', 'PREGNT=-1', 'PREGNT=1', 'PREGNT=2', 'WLKLIM=-1', 'WLKLIM=1', 'WLKLIM=2', 'ACTLIM=-1', 'ACTLIM=1', 'ACTLIM=2', 'SOCLIM=-1', 'SOCLIM=1', 'SOCLIM=2', 'COGLIM=-1', 'COGLIM=1', 'COGLIM=2', 'DFHEAR42=-1', 'DFHEAR42=1', 'DFHEAR42=2', 'DFSEE42=-1', 'DFSEE42=1', 'DFSEE42=2', 'ADSMOK42=-1', 'ADSMOK42=1', 'ADSMOK42=2', 'PHQ242=-1', 'PHQ242=0', 'PHQ242=1', 'PHQ242=2', 'PHQ242=3', 'PHQ242=4', 'PHQ242=5', 'PHQ242=6', 'EMPST=-1', 'EMPST=1', 'EMPST=2', 'EMPST=3', 'EMPST=4', 'POVCAT=1', 'POVCAT=2', 'POVCAT=3', 'POVCAT=4', 'POVCAT=5', 'INSCOV=1', 'INSCOV=2', 'INSCOV=3']\n" ] } ], "source": [ "# print out some labels, names, etc.\n", "display(Markdown(\"#### Training Dataset shape\"))\n", "print(dataset_orig_panel21_train.features.shape)\n", "display(Markdown(\"#### Validation Dataset shape\"))\n", "print(dataset_orig_panel21_validate.features.shape)\n", "display(Markdown(\"#### Deployment Dataset shape\"))\n", "print(dataset_orig_panel21_deploy.features.shape)\n", "display(Markdown(\"#### Favorable and unfavorable labels\"))\n", "print(dataset_orig_panel21_train.favorable_label, dataset_orig_panel21_train.unfavorable_label)\n", "display(Markdown(\"#### Protected attribute names\"))\n", "print(dataset_orig_panel21_train.protected_attribute_names)\n", "display(Markdown(\"#### Privileged and unprivileged protected attribute values\"))\n", "print(dataset_orig_panel21_train.privileged_protected_attributes, \n", " dataset_orig_panel21_train.unprivileged_protected_attributes)\n", "display(Markdown(\"#### Dataset feature names\"))\n", "print(dataset_orig_panel21_train.feature_names)" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Original training dataset" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean outcomes between privileged and unprivileged groups = -0.098749\n" ] } ], "source": [ "# Metric for the original dataset\n", "sens_idx = dataset_orig_panel21_deploy.protected_attribute_names.index(sens_attr)\n", "privileged_groups = [{sens_attr:dataset_orig_panel21_deploy.privileged_protected_attributes[sens_idx][0]}]\n", "unprivileged_groups = [{sens_attr:dataset_orig_panel21_deploy.unprivileged_protected_attributes[sens_idx][0]}]\n", "metric_orig_panel21_deploy = BinaryLabelDatasetMetric(dataset_orig_panel21_deploy, \n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "display(Markdown(\"#### Original training dataset\"))\n", "print(\"Difference in mean outcomes between privileged and unprivileged groups = %f\" % \\\n", " metric_orig_panel21_deploy.mean_difference())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, the logistic regression classifier learnt from the panel 19 data after reweighing is tested against the panel 21 deployment data." ] }, { "cell_type": "code", "execution_count": 65, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Evaluate performance of a given model with a given threshold on a given dataset\n", "\n", "scale = lr_scale_transf_panel19\n", "\n", "dataset = dataset_orig_panel21_deploy #apply model to this data\n", "model = lr_transf_panel19 #this is the model applied\n", " #lr_transf_panel19 is LR model learned from Panel 19\n", " #transformed data\n", "thresh_arr = lr_thresh_arr_transf_panel19_best # lr_thresh_arr_transf_panel19_best wass threshold for LR\n", " # model with highest balanced accuracy\n", "\n", "X_data = scale.transform(dataset.features)\n", "y_data = dataset.labels.ravel()\n", "y_data_pred_prob = model.predict_proba(X_data) \n", "\n", " \n", "y_pred = (y_data_pred_prob[:,1] > thresh_arr).astype(np.double)\n", "\n", "dataset_pred = dataset.copy()\n", "dataset_pred.labels = y_pred\n", "\n", "classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", "TPR = classified_metric.true_positive_rate()\n", "TNR = classified_metric.true_negative_rate()\n", "bal_acc = 0.5*(TPR+TNR)\n", "acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", "\n", "#get results\n", "best_bal_acc = bal_acc\n", "avg_odds_diff_at_best_bal_acc = classified_metric.average_odds_difference()\n", "disp_imp_at_best_bal_acc = np.abs(1.0 - metric_pred.disparate_impact())\n", "stat_par_diff_at_best_bal_acc = classified_metric.statistical_parity_difference()\n", "eq_opp_diff_at_best_bal_acc = classified_metric.equal_opportunity_difference()\n", "theil_ind_at_best_bal_acc = classified_metric.theil_index()" ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best balanced accuracy: 0.7269\n", "Corresponding abs(1-disparate impact) value: 0.2257\n", "Corresponding average odds difference value: -0.0101\n", "Corresponding statistical parity difference value: -0.0719\n", "Corresponding equal opportunity difference value: 0.0142\n", "Corresponding Theil index value: 0.0967\n" ] } ], "source": [ "lr_best_bal_acc_arr_transf_panel19_deploy_panel21 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel19_deploy_panel21)\n", "lr_disp_imp_at_best_bal_acc_transf_panel19_deploy_panel21 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel19_deploy_panel21)\n", "lr_avg_odds_diff_at_best_bal_acc_transf_panel19_deploy_panel21 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel19_deploy_panel21)\n", "\n", "lr_stat_par_diff_at_best_bal_acc_transf_panel19_deploy_panel21 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel19_deploy_panel21)\n", "lr_eq_opp_diff_at_best_bal_acc_transf_panel19_deploy_panel21 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel19_deploy_panel21)\n", "lr_theil_ind_at_best_bal_acc_transf_panel19_deploy_panel21 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel19_deploy_panel21)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compared to the 2015 panel 20 deployment data results, the abs(1 - disparate impact) fairness metric shows a noticable drift upwards. While still within specs, it may be worthwhile to re-learn the model. So even though the model is still relatively fair and accurate, we go ahead and re-learn the model from the 2016 Panel 21 data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Re-learning model (from 2016 Panel 21 data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Train and evaluate new model on 'transformed' 2016 training/test data**" ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "collapsed": true }, "outputs": [], "source": [ "RW = Reweighing(unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "RW.fit(dataset_orig_panel21_train)\n", "dataset_transf_panel21_train = RW.transform(dataset_orig_panel21_train)" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "data": { "text/markdown": [ "#### Transformed training dataset" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean outcomes between privileged and unprivileged groups = -0.000000\n" ] } ], "source": [ "metric_transf_panel21_train = BinaryLabelDatasetMetric(dataset_transf_panel21_train, \n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "display(Markdown(\"#### Transformed training dataset\"))\n", "print(\"Difference in mean outcomes between privileged and unprivileged groups = %f\" % metric_transf_panel21_train.mean_difference())" ] }, { "cell_type": "code", "execution_count": 69, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Train model on given dataset\n", "dataset = dataset_transf_panel21_train # data to train on\n", "\n", "scale = StandardScaler().fit(dataset.features)\n", "\n", "model = LogisticRegression(random_state = 1) # model to learn\n", "\n", "X_train = scale.transform(dataset.features)\n", "y_train = dataset.labels.ravel()\n", "\n", "\n", "model.fit(X_train, y_train,\n", " sample_weight=dataset.instance_weights)\n", "y_train_pred = model.predict(X_train)\n", "\n", "#save model\n", "lr_transf_panel21 = model\n", "scale_transf_panel21 = scale" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "100%|█████████████████████████████████████████| 50/50 [00:00<00:00, 176.67it/s]\n" ] } ], "source": [ "#validate model on given dataset and find threshold for best balanced accuracy\n", "import numpy as np\n", "from tqdm import tqdm\n", "thresh_arr = np.linspace(0.01, 0.5, 50)\n", "\n", "scale = scale_transf_panel21\n", "\n", "model = lr_transf_panel21 #model to validate\n", "dataset = dataset_orig_panel21_validate #data to validate on\n", "\n", "X_validate = scale.transform(dataset.features)\n", "y_validate = dataset.labels.ravel()\n", "y_validate_pred_prob = model.predict_proba(X_validate)\n", "\n", "\n", "bal_acc_arr = []\n", "disp_imp_arr = []\n", "avg_odds_diff_arr = []\n", "stat_par_diff = []\n", "eq_opp_diff = []\n", "theil_ind = []\n", " \n", "for thresh in tqdm(thresh_arr):\n", " y_validate_pred = (y_validate_pred_prob[:,1] > thresh).astype(np.double)\n", "\n", " dataset_pred = dataset.copy()\n", " dataset_pred.labels = y_validate_pred\n", "\n", " classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", " bal_acc = 0.5*(classified_metric.true_positive_rate() + classified_metric.true_negative_rate())\n", " \n", " acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", " bal_acc_arr.append(bal_acc)\n", " avg_odds_diff_arr.append(classified_metric.average_odds_difference())\n", " disp_imp_arr.append(metric_pred.disparate_impact())\n", " stat_par_diff.append(classified_metric.statistical_parity_difference())\n", " eq_opp_diff.append(classified_metric.equal_opportunity_difference())\n", " theil_ind.append(classified_metric.theil_index())\n", "\n", " \n", "thresh_arr_best_ind = np.where(bal_acc_arr == np.max(bal_acc_arr))[0][0]\n", "thresh_arr_best = np.array(thresh_arr)[thresh_arr_best_ind]\n", "\n", "best_bal_acc = bal_acc_arr[thresh_arr_best_ind]\n", "disp_imp_at_best_bal_acc = np.abs(1.0-np.array(disp_imp_arr))[thresh_arr_best_ind]\n", "\n", "avg_odds_diff_at_best_bal_acc = avg_odds_diff_arr[thresh_arr_best_ind]\n", "\n", "stat_par_diff_at_best_bal_acc = stat_par_diff[thresh_arr_best_ind]\n", "eq_opp_diff_at_best_bal_acc = eq_opp_diff[thresh_arr_best_ind]\n", "theil_ind_at_best_bal_acc = theil_ind[thresh_arr_best_ind]" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "image/png": 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yMu5KCOHw8ju4hgLJ3Ly66sPNK6bpeRxYorW+csPxyxlcMwkIy0adooDYfCKE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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot balanced accuracy, abs(1-disparate impact)\n", "\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, np.abs(1.0-np.array(disp_imp_arr)), color='r')\n", "ax2.set_ylabel('abs(1-disparate impact)', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], \n", " color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)\n" ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "image/png": 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5TN7o6c7p/dtYsd+yuIKcnWlbUMDmWbM4a8Zsdy20cOFCAK677jqTIxGNgP90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/CmeXMoX14D3Suv9Hs2MG6cHuNhNdwYEzecc/uB/oGP/K7JtaLmnHsTeDOf69cBMbFj1lIX4tR3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\nRU5ErkJggg==\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#Plot average odds difference\n", "fig, ax1 = plt.subplots(figsize=(10,7))\n", "ax1.plot(thresh_arr, bal_acc_arr)\n", "ax1.set_xlabel('Classification Thresholds', fontsize=16, fontweight='bold')\n", "ax1.set_ylabel('Balanced Accuracy', color='b', fontsize=16, fontweight='bold')\n", "ax1.xaxis.set_tick_params(labelsize=14)\n", "ax1.yaxis.set_tick_params(labelsize=14)\n", "\n", "\n", "ax2 = ax1.twinx()\n", "ax2.plot(thresh_arr, avg_odds_diff_arr, color='r')\n", "ax2.set_ylabel('avg. odds diff.', color='r', fontsize=16, fontweight='bold')\n", "\n", "ax2.axvline(np.array(thresh_arr)[thresh_arr_best_ind], color='k', linestyle=':')\n", "ax2.yaxis.set_tick_params(labelsize=14)\n", "ax2.grid(True)" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Threshold corresponding to Best balanced accuracy: 0.2000\n", "Best balanced accuracy: 0.7321\n", "Corresponding abs(1-disparate impact) value: 0.2266\n", "Corresponding average odds difference value: -0.0211\n", "Corresponding statistical parity difference value: -0.0773\n", "Corresponding equal opportunity difference value: -0.0288\n", "Corresponding Theil index value: 0.0977\n" ] } ], "source": [ "lr_thresh_arr_transf_panel21_best = thresh_arr_best\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % lr_thresh_arr_transf_panel21_best)\n", "lr_best_bal_acc_arr_transf_panel21 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel21)\n", "lr_disp_imp_at_best_bal_acc_transf_panel21 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel21)\n", "lr_avg_odds_diff_at_best_bal_acc_transf_panel21 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel21)\n", "\n", "lr_stat_par_diff_at_best_bal_acc_transf_panel21 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel21)\n", "lr_eq_opp_diff_at_best_bal_acc_transf_panel21 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel21)\n", "lr_theil_ind_at_best_bal_acc_transf_panel21 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel21)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The new model is both relatively fair as well as accurate so we deploy and test against the 2017 deployment data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 6. Re-deploying model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Evaluate new 2016 transformed data model and evaluate again on 2016 deployment data**" ] }, { "cell_type": "code", "execution_count": 74, "metadata": { "collapsed": true }, "outputs": [], "source": [ "#Evaluate performance of a given model with a given threshold on a given dataset\n", "\n", "scale = scale_transf_panel21\n", "\n", "dataset = dataset_orig_panel21_deploy #apply model to this data\n", "model = lr_transf_panel21 #this is the model applied\n", " #lr_transf_panel21 is new LR model learned from Panel 21 (2016) data\n", " #transformed data\n", "thresh_arr = lr_thresh_arr_transf_panel21_best # lr_thresh_arr_transf_panel21_best was threshold for LR\n", " # model with highest balanced accuracy\n", "\n", "\n", "X_data = scale.transform(dataset.features)\n", "y_data = dataset.labels.ravel()\n", "y_data_pred_prob = model.predict_proba(X_data) \n", "\n", " \n", "y_pred = (y_data_pred_prob[:,1] > thresh_arr).astype(np.double)\n", "\n", "dataset_pred = dataset.copy()\n", "dataset_pred.labels = y_pred\n", "\n", "classified_metric = ClassificationMetric(dataset, \n", " dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", "metric_pred = BinaryLabelDatasetMetric(dataset_pred,\n", " unprivileged_groups=unprivileged_groups,\n", " privileged_groups=privileged_groups)\n", " \n", "TPR = classified_metric.true_positive_rate()\n", "TNR = classified_metric.true_negative_rate()\n", "bal_acc = 0.5*(TPR+TNR)\n", " \n", "acc = accuracy_score(y_true=dataset.labels,\n", " y_pred=dataset_pred.labels)\n", "\n", "#get results\n", "best_bal_acc = bal_acc\n", "avg_odds_diff_at_best_bal_acc = classified_metric.average_odds_difference()\n", "disp_imp_at_best_bal_acc = np.abs(1.0 - metric_pred.disparate_impact())\n", "stat_par_diff_at_best_bal_acc = classified_metric.statistical_parity_difference()\n", "eq_opp_diff_at_best_bal_acc = classified_metric.equal_opportunity_difference()\n", "theil_ind_at_best_bal_acc = classified_metric.theil_index()" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best balanced accuracy: 0.7473\n", "Corresponding abs(1-disparate impact) value: 0.1406\n", "Corresponding average odds difference value: -0.0025\n", "Corresponding statistical parity difference value: -0.0474\n", "Corresponding equal opportunity difference value: -0.0082\n", "Corresponding Theil index value: 0.0916\n" ] } ], "source": [ "lr_best_bal_acc_arr_transf_panel21_deploy_panel21 = best_bal_acc\n", "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel21_deploy_panel21)\n", "lr_disp_imp_at_best_bal_acc_transf_panel21_deploy_panel21 = disp_imp_at_best_bal_acc\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel21_deploy_panel21)\n", "lr_avg_odds_diff_at_best_bal_acc_transf_panel21_deploy_panel21 = avg_odds_diff_at_best_bal_acc\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel21_deploy_panel21)\n", "\n", "lr_stat_par_diff_at_best_bal_acc_transf_panel21_deploy_panel21 = stat_par_diff_at_best_bal_acc\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel21_deploy_panel21)\n", "lr_eq_opp_diff_at_best_bal_acc_transf_panel21_deploy_panel21 = eq_opp_diff_at_best_bal_acc\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel21_deploy_panel21)\n", "lr_theil_ind_at_best_bal_acc_transf_panel21_deploy_panel21 = theil_ind_at_best_bal_acc\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel21_deploy_panel21)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The new transformed 2016 data model is again within original accuracy/fairness specs so is deployed" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 7. SUMMARY" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Back to TOC](#toc)
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Logistic Regression classifier 'without' bias mitigation learnt from 2015 (Panel 19) training data" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best balanced accuracy: 0.7759\n", "Corresponding abs(1-disparate impact) value: 0.5738\n", "Corresponding average odds difference value: -0.2057\n", "Corresponding statistical parity difference value: -0.2612\n", "Corresponding equal opportunity difference value: -0.2228\n", "Corresponding Theil index value: 0.0921\n" ] } ], "source": [ "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_orig_panel19_best_test)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_orig_panel19_best_test)\n", "\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_orig_panel19_best_test)\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_orig_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Logistic Regression classifier 'with' bias mitigation learnt from 2015 (Panel 19) training data. This is the model that is 'deployed'" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best balanced accuracy: 0.7539\n", "Corresponding abs(1-disparate impact) value: 0.2482\n", "Corresponding average odds difference value: -0.0151\n", "Corresponding statistical parity difference value: -0.0872\n", "Corresponding equal opportunity difference value: -0.0035\n", "Corresponding Theil index value: 0.0966\n" ] } ], "source": [ "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel19_best_test)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel19_best_test)\n", "\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel19_best_test)\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel19_best_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deployed model evaluated on 2015 (Panel 20) deployment data" ] }, { "cell_type": "code", "execution_count": 78, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best balanced accuracy: 0.7289\n", "Corresponding abs(1-disparate impact) value: 0.1106\n", "Corresponding average odds difference value: 0.0696\n", "Corresponding statistical parity difference value: -0.0341\n", "Corresponding equal opportunity difference value: 0.1315\n", "Corresponding Theil index value: 0.1038\n" ] } ], "source": [ "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel19_deploy_panel20)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel19_deploy_panel20)\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel19_deploy_panel20)\n", "\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel19_deploy_panel20)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel19_deploy_panel20)\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel19_deploy_panel20)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Deployed model evaluated on 2016 (Panel 21) deployment data" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best balanced accuracy: 0.7269\n", "Corresponding abs(1-disparate impact) value: 0.2257\n", "Corresponding average odds difference value: -0.0101\n", "Corresponding statistical parity difference value: -0.0719\n", "Corresponding equal opportunity difference value: 0.0142\n", "Corresponding Theil index value: 0.0967\n" ] } ], "source": [ "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel19_deploy_panel21)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel19_deploy_panel21)\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel19_deploy_panel21)\n", "\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel19_deploy_panel21)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel19_deploy_panel21)\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel19_deploy_panel21)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "While model accuracy/fairness metrics are still fine, a drift upwards in (1-disparate impact) metric is observed. A new Logistic Regression classifier with bias mitigation is learned from 2016 (Panel 21) training data to see if a better model can be learnt." ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best balanced accuracy: 0.7321\n", "Threshold corresponding to Best balanced accuracy: 0.2000\n", "Corresponding abs(1-disparate impact) value: 0.2266\n", "Corresponding average odds difference value: -0.0211\n", "Corresponding statistical parity difference value: -0.0773\n", "Corresponding equal opportunity difference value: -0.0288\n", "Corresponding Theil index value: 0.0977\n" ] } ], "source": [ "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel21)\n", "print(\"Threshold corresponding to Best balanced accuracy: %6.4f\" % lr_thresh_arr_transf_panel21_best)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel21)\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel21)\n", "\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel21)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel21)\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel21)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This new model is evaluated on 2016 (Panel 21) deployment data." ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Best balanced accuracy: 0.7473\n", "Corresponding abs(1-disparate impact) value: 0.1406\n", "Corresponding average odds difference value: -0.0025\n", "Corresponding statistical parity difference value: -0.0474\n", "Corresponding equal opportunity difference value: -0.0082\n", "Corresponding Theil index value: 0.0916\n" ] } ], "source": [ "print(\"Best balanced accuracy: %6.4f\" % lr_best_bal_acc_arr_transf_panel21_deploy_panel21)\n", "print(\"Corresponding abs(1-disparate impact) value: %6.4f\" % lr_disp_imp_at_best_bal_acc_transf_panel21_deploy_panel21)\n", "print(\"Corresponding average odds difference value: %6.4f\" % lr_avg_odds_diff_at_best_bal_acc_transf_panel21_deploy_panel21)\n", "\n", "print(\"Corresponding statistical parity difference value: %6.4f\" % lr_stat_par_diff_at_best_bal_acc_transf_panel21_deploy_panel21)\n", "print(\"Corresponding equal opportunity difference value: %6.4f\" % lr_eq_opp_diff_at_best_bal_acc_transf_panel21_deploy_panel21)\n", "print(\"Corresponding Theil index value: %6.4f\" % lr_theil_ind_at_best_bal_acc_transf_panel21_deploy_panel21)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "New model is again within accuracy/fairness specs" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.6" } }, "nbformat": 4, "nbformat_minor": 2 }