# Original work Copyright (c) 2017 Geoff Pleiss
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# SOFTWARE.
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# Modified work Copyright 2018 IBM Corporation
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# Licensed under the Apache License, Version 2.0 (the "License"); you may not
# use this file except in compliance with the License. You may obtain a copy of
# the License at http://www.apache.org/licenses/LICENSE-2.0
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import numpy as np
from scipy.optimize import linprog
from aif360.algorithms import Transformer
from aif360.metrics import ClassificationMetric, utils
[docs]class EqOddsPostprocessing(Transformer):
"""Equalized odds postprocessing is a post-processing technique that solves
a linear program to find probabilities with which to change output labels to
optimize equalized odds [8]_ [9]_.
References:
.. [8] M. Hardt, E. Price, and N. Srebro, "Equality of Opportunity in
Supervised Learning," Conference on Neural Information Processing
Systems, 2016.
.. [9] G. Pleiss, M. Raghavan, F. Wu, J. Kleinberg, and
K. Q. Weinberger, "On Fairness and Calibration," Conference on Neural
Information Processing Systems, 2017.
"""
def __init__(self, unprivileged_groups, privileged_groups, seed=None):
"""
Args:
unprivileged_groups (list(dict)): Representation for unprivileged
group.
privileged_groups (list(dict)): Representation for privileged
group.
seed (int, optional): Seed to make `predict` repeatable.
"""
super(EqOddsPostprocessing, self).__init__(
unprivileged_groups=unprivileged_groups,
privileged_groups=privileged_groups,
seed=seed)
self.seed = seed
self.model_params = None
self.unprivileged_groups = unprivileged_groups
self.privileged_groups = privileged_groups
[docs] def fit(self, dataset_true, dataset_pred):
"""Compute parameters for equalizing odds using true and predicted
labels.
Args:
true_dataset (BinaryLabelDataset): Dataset containing true labels.
pred_dataset (BinaryLabelDataset): Dataset containing predicted
labels.
Returns:
EqOddsPostprocessing: Returns self.
"""
metric = ClassificationMetric(dataset_true, dataset_pred,
unprivileged_groups=self.unprivileged_groups,
privileged_groups=self.privileged_groups)
# compute basic statistics
sbr = metric.num_instances(privileged=True) / metric.num_instances()
obr = metric.num_instances(privileged=False) / metric.num_instances()
fpr0 = metric.false_positive_rate(privileged=True)
fpr1 = metric.false_positive_rate(privileged=False)
fnr0 = metric.false_negative_rate(privileged=True)
fnr1 = metric.false_negative_rate(privileged=False)
tpr0 = metric.true_positive_rate(privileged=True)
tpr1 = metric.true_positive_rate(privileged=False)
tnr0 = metric.true_negative_rate(privileged=True)
tnr1 = metric.true_negative_rate(privileged=False)
# linear program has 4 decision variables:
# [Pr[label_tilde = 1 | label_hat = 1, protected_attributes = 0];
# Pr[label_tilde = 1 | label_hat = 0, protected_attributes = 0];
# Pr[label_tilde = 1 | label_hat = 1, protected_attributes = 1];
# Pr[label_tilde = 1 | label_hat = 0, protected_attributes = 1]]
# Coefficients of the linear objective function to be minimized.
c = np.array([fpr0 - tpr0, tnr0 - fnr0, fpr1 - tpr1, tnr1 - fnr1])
# A_ub - 2-D array which, when matrix-multiplied by x, gives the values
# of the upper-bound inequality constraints at x
# b_ub - 1-D array of values representing the upper-bound of each
# inequality constraint (row) in A_ub.
# Just to keep these between zero and one
A_ub = np.array([[ 1, 0, 0, 0],
[-1, 0, 0, 0],
[ 0, 1, 0, 0],
[ 0, -1, 0, 0],
[ 0, 0, 1, 0],
[ 0, 0, -1, 0],
[ 0, 0, 0, 1],
[ 0, 0, 0, -1]], dtype=np.float64)
b_ub = np.array([1, 0, 1, 0, 1, 0, 1, 0], dtype=np.float64)
# Create boolean conditioning vectors for protected groups
cond_vec_priv = utils.compute_boolean_conditioning_vector(
dataset_pred.protected_attributes,
dataset_pred.protected_attribute_names,
self.privileged_groups)
cond_vec_unpriv = utils.compute_boolean_conditioning_vector(
dataset_pred.protected_attributes,
dataset_pred.protected_attribute_names,
self.unprivileged_groups)
sconst = np.ravel(
dataset_pred.labels[cond_vec_priv] == dataset_pred.favorable_label)
sflip = np.ravel(
dataset_pred.labels[cond_vec_priv] == dataset_pred.unfavorable_label)
oconst = np.ravel(
dataset_pred.labels[cond_vec_unpriv] == dataset_pred.favorable_label)
oflip = np.ravel(
dataset_pred.labels[cond_vec_unpriv] == dataset_pred.unfavorable_label)
y_true = dataset_true.labels.ravel()
sm_tn = np.logical_and(sflip,
y_true[cond_vec_priv] == dataset_true.unfavorable_label,
dtype=np.float64)
sm_fn = np.logical_and(sflip,
y_true[cond_vec_priv] == dataset_true.favorable_label,
dtype=np.float64)
sm_fp = np.logical_and(sconst,
y_true[cond_vec_priv] == dataset_true.unfavorable_label,
dtype=np.float64)
sm_tp = np.logical_and(sconst,
y_true[cond_vec_priv] == dataset_true.favorable_label,
dtype=np.float64)
om_tn = np.logical_and(oflip,
y_true[cond_vec_unpriv] == dataset_true.unfavorable_label,
dtype=np.float64)
om_fn = np.logical_and(oflip,
y_true[cond_vec_unpriv] == dataset_true.favorable_label,
dtype=np.float64)
om_fp = np.logical_and(oconst,
y_true[cond_vec_unpriv] == dataset_true.unfavorable_label,
dtype=np.float64)
om_tp = np.logical_and(oconst,
y_true[cond_vec_unpriv] == dataset_true.favorable_label,
dtype=np.float64)
# A_eq - 2-D array which, when matrix-multiplied by x,
# gives the values of the equality constraints at x
# b_eq - 1-D array of values representing the RHS of each equality
# constraint (row) in A_eq.
# Used to impose equality of odds constraint
A_eq = [[(np.mean(sconst*sm_tp) - np.mean(sflip*sm_tp)) / sbr,
(np.mean(sflip*sm_fn) - np.mean(sconst*sm_fn)) / sbr,
(np.mean(oflip*om_tp) - np.mean(oconst*om_tp)) / obr,
(np.mean(oconst*om_fn) - np.mean(oflip*om_fn)) / obr],
[(np.mean(sconst*sm_fp) - np.mean(sflip*sm_fp)) / (1-sbr),
(np.mean(sflip*sm_tn) - np.mean(sconst*sm_tn)) / (1-sbr),
(np.mean(oflip*om_fp) - np.mean(oconst*om_fp)) / (1-obr),
(np.mean(oconst*om_tn) - np.mean(oflip*om_tn)) / (1-obr)]]
b_eq = [(np.mean(oflip*om_tp) + np.mean(oconst*om_fn)) / obr
- (np.mean(sflip*sm_tp) + np.mean(sconst*sm_fn)) / sbr,
(np.mean(oflip*om_fp) + np.mean(oconst*om_tn)) / (1-obr)
- (np.mean(sflip*sm_fp) + np.mean(sconst*sm_tn)) / (1-sbr)]
# Linear program
self.model_params = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq)
return self
[docs] def predict(self, dataset):
"""Perturb the predicted labels to obtain new labels that satisfy
equalized odds constraints.
Args:
dataset (BinaryLabelDataset): Dataset containing labels that needs
to be transformed.
dataset (BinaryLabelDataset): Transformed dataset.
"""
if self.seed is not None:
np.random.seed(self.seed)
# Get the model parameters output from fit
sp2p, sn2p, op2p, on2p = self.model_params.x
# Create boolean conditioning vectors for protected groups
cond_vec_priv = utils.compute_boolean_conditioning_vector(
dataset.protected_attributes, dataset.protected_attribute_names,
self.privileged_groups)
cond_vec_unpriv = utils.compute_boolean_conditioning_vector(
dataset.protected_attributes, dataset.protected_attribute_names,
self.unprivileged_groups)
# Randomly flip labels according to the probabilities in model_params
self_fair_pred = dataset.labels[cond_vec_priv].copy()
self_pp_indices, _ = np.nonzero(
dataset.labels[cond_vec_priv] == dataset.favorable_label)
self_pn_indices, _ = np.nonzero(
dataset.labels[cond_vec_priv] == dataset.unfavorable_label)
np.random.shuffle(self_pp_indices)
np.random.shuffle(self_pn_indices)
n2p_indices = self_pn_indices[:int(len(self_pn_indices) * sn2p)]
self_fair_pred[n2p_indices] = dataset.favorable_label
p2n_indices = self_pp_indices[:int(len(self_pp_indices) * (1 - sp2p))]
self_fair_pred[p2n_indices] = dataset.unfavorable_label
othr_fair_pred = dataset.labels[cond_vec_unpriv].copy()
othr_pp_indices, _ = np.nonzero(
dataset.labels[cond_vec_unpriv] == dataset.favorable_label)
othr_pn_indices, _ = np.nonzero(
dataset.labels[cond_vec_unpriv] == dataset.unfavorable_label)
np.random.shuffle(othr_pp_indices)
np.random.shuffle(othr_pn_indices)
n2p_indices = othr_pn_indices[:int(len(othr_pn_indices) * on2p)]
othr_fair_pred[n2p_indices] = dataset.favorable_label
p2n_indices = othr_pp_indices[:int(len(othr_pp_indices) * (1 - op2p))]
othr_fair_pred[p2n_indices] = dataset.unfavorable_label
# Mutated, fairer dataset with new labels
dataset_new = dataset.copy()
new_labels = np.zeros_like(dataset.labels, dtype=np.float64)
new_labels[cond_vec_priv] = self_fair_pred
new_labels[cond_vec_unpriv] = othr_fair_pred
dataset_new.labels = new_labels
return dataset_new
[docs] def fit_predict(self, dataset_true, dataset_pred):
"""fit and predict methods sequentially."""
return self.fit(dataset_true, dataset_pred).predict(dataset_pred)