Fair learning with Wasserstein barycenters for non-decomposable performance measures

TL;DR

This paper characterizes optimal fair classifiers under demographic parity, showing that fairness constraints can be incorporated via a regression problem and linking this to optimal transport methods, with implications for awareness and unawareness settings.

Contribution

It provides a fundamental characterization of fair classification under demographic parity, connecting regression, optimal transport, and fairness constraints in a unified framework.

Findings

Maximizing accuracy under demographic parity reduces to a fair regression and thresholding.

Extends results to linear-fractional performance measures like F-score and balanced accuracy.

Establishes an equivalence between awareness and unawareness setups for two sensitive groups.

Abstract

This work provides several fundamental characterizations of the optimal classification function under the demographic parity constraint. In the awareness framework, akin to the classical unconstrained classification case, we show that maximizing accuracy under this fairness constraint is equivalent to solving a corresponding regression problem followed by thresholding at level $1/2$. We extend this result to linear-fractional classification measures (e.g., ${\rm F}$-score, AM measure, balanced accuracy, etc.), highlighting the fundamental role played by the regression problem in this framework. Our results leverage recently developed connection between the demographic parity constraint and the multi-marginal optimal transport formulation. Informally, our result shows that the transition between the unconstrained problems and the fair one is achieved by replacing the conditional expectation of the label by the solution of the fair regression problem. Finally, leveraging our analysis, we demonstrate an equivalence between the awareness and the unawareness setups in the case of two sensitive groups.