Fair Regression under Approximate Demographic Parity
Abstract
Exact demographic parity requires the same prediction distribution across sensitive groups. In regression, this can be too restrictive and reduce predictive accuracy. We instead bound every pairwise Wasserstein distance between group-specific prediction distributions by a chosen tolerance, allowing the groups to differ while keeping fairness tunable. On the real line, the prediction and constrained transport problems have the same infimum. If the transport problem attains this value and suitable Monge maps exist, a deterministic transport-form predictor realizes it. Under a standard one-dimensional condition, the problem becomes a bounded quantile optimization that is convex when the conditional expected loss is convex in prediction. Under squared loss with two positively weighted groups, the W1, W2, and W∞ constraints yield soft-thresholding, shrinkage, and clipping. Under the stated conditions, we establish rates for the known-cost plug-in estimator. When the cost is unavailable, we describe an observed-loss computational proxy. Synthetic and California 2018 ACS studies illustrate the tunable fairness-accuracy trade-off and distinguish calibration feasibility from held-out fairness and accuracy.
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BibTeX
@misc{wang2026fair,
title = {{Fair Regression under Approximate Demographic Parity}},
author = {Weiwei Wang and Xianyang Zhang and Raymond K. W. Wong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.25796},
eprint = {2610.25796},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.25796},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Fair Regression under Approximate Demographic Parity
AU - Weiwei Wang
AU - Xianyang Zhang
AU - Raymond K. W. Wong
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.25796
UR - https://arxiv.org/abs/2610.25796
AB - Exact demographic parity requires the same prediction distribution across sensitive groups. In regression, this can be too restrictive and reduce predictive accuracy. We instead bound every pairwise Wasserstein distance between group-specific prediction distributions by a chosen tolerance, allowing the groups to differ while keeping fairness tunable. On the real line, the prediction and constrained transport problems have the same infimum. If the transport problem attains this value and suitable Monge maps exist, a deterministic transport-form predictor realizes it. Under a standard one-dimensional condition, the problem becomes a bounded quantile optimization that is convex when the conditional expected loss is convex in prediction. Under squared loss with two positively weighted groups, the W_1, W_2, and W_∞ constraints yield soft-thresholding, shrinkage, and clipping. Under the stated conditions, we establish rates for the known-cost plug-in estimator. When the cost is unavailable, we describe an observed-loss computational proxy. Synthetic and California 2018 ACS studies illustrate the tunable fairness-accuracy trade-off and distinguish calibration feasibility from held-out fairness and accuracy.
ER -