A General Framework for Fair and Robust Regression

Fair regression methods typically rely on squared error loss, making them fragile under heavy tailed noise. We propose a general framework for robust regression under demographic parity (DP) that applies to a wide class of M-estimators, including Cauchy, Huber, least absolute deviation, quantile, and Tukey losses. We propose an optimal fair transformation that guarantees DP while achieving the minimum population risk among all rank preserving fair predictors. We also establish convergence rates for the resulting estimators. To balance fairness and predictive accuracy, we develop an interpolation scheme whose risk decreases while unfairness grows linearly with the interpolation parameter. The proposed framework can be further extended to conditional DP to account for legitimate covariates. Extensive simulation studies and real data applications show clear improvements over existing fair regression approaches in both robustness and predictive performance.