Fair Regression under Demographic Parity: A Unified Framework

TL;DR

This paper introduces a versatile and efficient framework for fair regression that enforces demographic parity, applicable to various loss functions, with theoretical guarantees and empirical validation.

Contribution

It presents a unified, computationally efficient approach for fair regression under demographic parity, extending to multiple loss functions with proven asymptotic consistency.

Findings

Effective risk minimization under fairness constraints

Applicable to diverse regression loss functions

Theoretically guarantees convergence and consistency

Abstract

We propose a unified framework for fair regression tasks formulated as risk minimization problems subject to a demographic parity constraint. Unlike many existing approaches that are limited to specific loss functions or rely on challenging non-convex optimization, our framework is applicable to a broad spectrum of regression tasks. Examples include linear regression with squared loss, binary classification with cross-entropy loss, quantile regression with pinball loss, and robust regression with Huber loss. We derive a novel characterization of the fair risk minimizer, which yields a computationally efficient estimation procedure for general loss functions. Theoretically, we establish the asymptotic consistency of the proposed estimator and derive its convergence rates under mild assumptions. We illustrate the method's versatility through detailed discussions of several common loss functions. Numerical results demonstrate that our approach effectively minimizes risk while satisfying fairness constraints across various regression settings.