A Statistical Test for Probabilistic Fairness

TL;DR

This paper introduces a new statistical test based on optimal transport theory to assess the fairness of classifiers, providing both theoretical guarantees and interpretability features.

Contribution

It proposes a novel hypothesis testing framework for probabilistic fairness using optimal transport geometry, applicable to pre-trained classifiers.

Findings

The test is asymptotically correct both theoretically and empirically.

It quantifies the distance to the fairness manifold in feature space.

The framework offers interpretability by identifying data perturbations to achieve fairness.

Abstract

Algorithms are now routinely used to make consequential decisions that affect human lives. Examples include college admissions, medical interventions or law enforcement. While algorithms empower us to harness all information hidden in vast amounts of data, they may inadvertently amplify existing biases in the available datasets. This concern has sparked increasing interest in fair machine learning, which aims to quantify and mitigate algorithmic discrimination. Indeed, machine learning models should undergo intensive tests to detect algorithmic biases before being deployed at scale. In this paper, we use ideas from the theory of optimal transport to propose a statistical hypothesis test for detecting unfair classifiers. Leveraging the geometry of the feature space, the test statistic quantifies the distance of the empirical distribution supported on the test samples to the manifold of distributions that render a pre-trained classifier fair. We develop a rigorous hypothesis testing mechanism for assessing the probabilistic fairness of any pre-trained logistic classifier, and we show both theoretically as well as empirically that the proposed test is asymptotically correct. In addition, the proposed framework offers interpretability by identifying the most favorable perturbation of the data so that the given classifier becomes fair.