Fair Regression under Demographic Parity: A Unified Framework

2026-01-15

AI Summary

This study addresses the problem of risk minimization under demographic parity fairness constraints in regression tasks. The authors propose a general framework that formulates fair regression as a constrained risk minimization problem, accommodating a variety of loss functions including squared loss, cross-entropy, quantile, and Huber losses. The key innovation lies in a novel characterization of the fair risk minimizer, which circumvents the reliance of existing approaches on specific loss structures or non-convex optimization. Theoretical analysis establishes the asymptotic consistency and convergence rates of the resulting estimator. Empirical evaluations demonstrate that the proposed method effectively balances fairness and predictive performance across diverse regression settings.

Technology Category

• Machine Learning: Ethics, Bias, and Fairness
• Philosophy and Ethics of AI: Bias, Fairness & Equity
• Computer Vision: Bias, Fairness & Privacy

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• fair regression
• demographic parity
• risk minimization
• fairness constraint
• regression tasks

Innovation

• fair regression
• demographic parity
• unified framework
• risk minimization
• general loss functions