A General Framework for Fair and Robust Regression

Wenhai Cui, Xiaoting Ji, Wen Su, Xingqiu Zhao
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:21864-21884, 2026.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-cui26d, title = {A General Framework for Fair and Robust Regression}, author = {Cui, Wenhai and Ji, Xiaoting and Su, Wen and Zhao, Xingqiu}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {21864--21884}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/cui26d/cui26d.pdf}, url = {https://proceedings.mlr.press/v306/cui26d.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T A General Framework for Fair and Robust Regression %A Wenhai Cui %A Xiaoting Ji %A Wen Su %A Xingqiu Zhao %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-cui26d %I PMLR %P 21864--21884 %U https://proceedings.mlr.press/v306/cui26d.html %V 306 %X 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.
APA
Cui, W., Ji, X., Su, W. & Zhao, X.. (2026). A General Framework for Fair and Robust Regression. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:21864-21884 Available from https://proceedings.mlr.press/v306/cui26d.html.

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