Obtaining fairness using optimal transport theory

TL;DR

This paper proposes a method to enhance fairness in binary classification by modifying input data through optimal transport theory, addressing biases related to protected variables and analyzing fairness definitions like Disparate Impact and Balanced Error Rate.

Contribution

It introduces a novel approach using optimal transport to modify data for fairness, providing a new tool to mitigate discrimination in algorithms.

Findings

Effective data modification improves fairness metrics

Analysis of fairness definitions clarifies their relationship

Method reduces bias in binary classifiers

Abstract

Statistical algorithms are usually helping in making decisions in many aspects of our lives. But, how do we know if these algorithms are biased and commit unfair discrimination of a particular group of people, typically a minority? \textit{Fairness} is generally studied in a probabilistic framework where it is assumed that there exists a protected variable, whose use as an input of the algorithm may imply discrimination. There are different definitions of Fairness in the literature. In this paper we focus on two of them which are called Disparate Impact (DI) and Balanced Error Rate (BER). Both are based on the outcome of the algorithm across the different groups determined by the protected variable. The relationship between these two notions is also studied. The goals of this paper are to detect when a binary classification rule lacks fairness and to try to fight against the potential discrimination attributable to it. This can be done by modifying either the classifiers or the data itself. Our work falls into the second category and modifies the input data using optimal transport theory.