Fair regression under localized demographic parity constraints

2026-03-26

AI Summary

This work addresses the excessive strictness of traditional demographic parity (DP) in regression tasks, which enforces identical prediction distributions across all sensitive groups and often incurs significant accuracy loss. To mitigate this, the authors propose a localized DP constraint that enforces equality of group-wise cumulative distribution functions (CDFs) only at pre-specified critical quantiles or decision-relevant score thresholds. By discretizing the prediction space, they derive a closed-form optimal fair predictor via Lagrangian duality, rigorously quantify the discretization error, and prove convergence to the continuous optimum as the grid is refined. The resulting model-agnostic post-processing algorithm leverages both labeled and unlabeled data for calibration and provides finite-sample guarantees on constraint violation and risk upper bounds. Experiments on synthetic and real-world datasets demonstrate that the method achieves precise fairness correction at decision-critical thresholds while preserving high predictive performance.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• 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

Demographic parity (DP) is a widely used group fairness criterion requiring predictive distributions to be invariant across sensitive groups. While natural in classification, full distributional DP is often overly restrictive in regression and can lead to substantial accuracy loss. We propose a relaxation of DP tailored to regression, enforcing parity only at a finite set of quantile levels and/or score thresholds. Concretely, we introduce a novel (${\ell}$, Z)-fair predictor, which imposes groupwise CDF constraints of the form F f |S=s (z m ) = ${\ell}$ m for prescribed pairs (${\ell}$ m , z m ). For this setting, we derive closed-form characterizations of the optimal fair discretized predictor via a Lagrangian dual formulation and quantify the discretization cost, showing that the risk gap to the continuous optimum vanishes as the grid is refined. We further develop a model-agnostic post-processing algorithm based on two samples (labeled for learning a base regressor and unlabeled for calibration), and establish finite-sample guarantees on constraint violation and excess penalized risk. In addition, we introduce two alternative frameworks where we match group and marginal CDF values at selected score thresholds. In both settings, we provide closed-form solutions for the optimal fair discretized predictor. Experiments on synthetic and real datasets illustrate an interpretable fairness-accuracy trade-off, enabling targeted corrections at decision-relevant quantiles or thresholds while preserving predictive performance.

Problem

• fair regression
• demographic parity
• group fairness
• quantile constraints
• distributional fairness

Innovation

• localized demographic parity
• fair regression
• quantile-based fairness
• CDF matching
• model-agnostic post-processing