Selective Regression Under Fairness Criteria

TL;DR

This paper addresses fairness issues in selective regression, proposing new criteria to ensure subgroup performance improves with reduced coverage and introducing methods to mitigate disparities, validated on synthetic and real data.

Contribution

It introduces fairness criteria for selective regression ensuring subgroup performance improvement and proposes regularization methods to reduce disparities.

Findings

Fairness criteria ensure subgroup performance improves with coverage reduction.

Regularization methods effectively mitigate performance disparities.

Validated approaches on synthetic and real-world datasets.

Abstract

Selective regression allows abstention from prediction if the confidence to make an accurate prediction is not sufficient. In general, by allowing a reject option, one expects the performance of a regression model to increase at the cost of reducing coverage (i.e., by predicting on fewer samples). However, as we show, in some cases, the performance of a minority subgroup can decrease while we reduce the coverage, and thus selective regression can magnify disparities between different sensitive subgroups. Motivated by these disparities, we propose new fairness criteria for selective regression requiring the performance of every subgroup to improve with a decrease in coverage. We prove that if a feature representation satisfies the sufficiency criterion or is calibrated for mean and variance, than the proposed fairness criteria is met. Further, we introduce two approaches to mitigate the performance disparity across subgroups: (a) by regularizing an upper bound of conditional mutual information under a Gaussian assumption and (b) by regularizing a contrastive loss for conditional mean and conditional variance prediction. The effectiveness of these approaches is demonstrated on synthetic and real-world datasets.