[2603.25224] Fair regression under localized demographic parity constraints

Statistics > Machine Learning arXiv:2603.25224 (stat) [Submitted on 26 Mar 2026] Title:Fair regression under localized demographic parity constraints Authors:Arthur Charpentier (UQAM), Christophe Denis (SAMM), Romuald Elie (LAMA), Mohamed Hebiri (LAMA), François HU (UdeM) View a PDF of the paper titled Fair regression under localized demographic parity constraints, by Arthur Charpentier (UQAM) and 4 other authors View PDF 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 cons...