Surrogate Losses for Fairness-Aware Classification: Fisher Consistency and Calibration
Abstract
Fairness-aware classification seeks to balance predictive accuracy and fairness across demographic groups. Although surrogate losses facilitate the optimization of fairness-aware objectives, it remains unclear when minimizing these losses yields optimal decisions under the original fairness-aware risk. This paper investigates the statistical validity of surrogate-based fairness-aware classification under demographic parity and equal opportunity, considering both attribute-blind and attribute-aware settings. We introduce fairness-aware Fisher consistency and characterize it through conditions on the derivatives of the surrogate losses. The characterization shows that consistency depends not only on the individual loss functions but also on their interaction within the fairness-regularized objective. We further establish a calibration inequality that relates the excess fairness-aware risk to the excess surrogate risk, providing a quantitative connection between surrogate optimization and the original classification objective. Numerical experiments illustrate how deviations from the consistency conditions affect fairness-aware excess risk and how the regularization parameter influences the well-posedness of surrogate optimization. An application to consumer credit default prediction demonstrates that appropriately calibrated fairness regularization can substantially reduce demographic disparities while maintaining predictive performance.
Related
- Fairness in multi-class multi-group classification problems via contextial coherent risk measures
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- In-context classification: Calibration and noise in linear attention with softmax readout
- The Role of Uncertainty in Assessing the Fairness of Machine Learning Models
- Equality, Equity, and Causality in Fairness Research: A Commentary on Cheng (2026)
BibTeX
@misc{song2026surrogate,
title = {{Surrogate Losses for Fairness-Aware Classification: Fisher Consistency and Calibration}},
author = {Changcheng Song and Yi Yang and Xiangyu Chang and Xiaoling Lu and Yufeng Liu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01613},
eprint = {2611.01613},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01613},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Surrogate Losses for Fairness-Aware Classification: Fisher Consistency and Calibration
AU - Changcheng Song
AU - Yi Yang
AU - Xiangyu Chang
AU - Xiaoling Lu
AU - Yufeng Liu
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01613
UR - https://arxiv.org/abs/2611.01613
AB - Fairness-aware classification seeks to balance predictive accuracy and fairness across demographic groups. Although surrogate losses facilitate the optimization of fairness-aware objectives, it remains unclear when minimizing these losses yields optimal decisions under the original fairness-aware risk. This paper investigates the statistical validity of surrogate-based fairness-aware classification under demographic parity and equal opportunity, considering both attribute-blind and attribute-aware settings. We introduce fairness-aware Fisher consistency and characterize it through conditions on the derivatives of the surrogate losses. The characterization shows that consistency depends not only on the individual loss functions but also on their interaction within the fairness-regularized objective. We further establish a calibration inequality that relates the excess fairness-aware risk to the excess surrogate risk, providing a quantitative connection between surrogate optimization and the original classification objective. Numerical experiments illustrate how deviations from the consistency conditions affect fairness-aware excess risk and how the regularization parameter influences the well-posedness of surrogate optimization. An application to consumer credit default prediction demonstrates that appropriately calibrated fairness regularization can substantially reduce demographic disparities while maintaining predictive performance.
ER -