Bayes-Optimal Fair Classification with Multiple Sensitive Features

TL;DR

This paper extends the theory of Bayes-optimal fair classifiers to multiple sensitive features, providing a comprehensive framework and practical algorithms for fair classification under various fairness measures.

Contribution

It characterizes the Bayes-optimal fair classifier for multiple sensitive features and proposes practical algorithms for in-processing and post-processing.

Findings

Methods outperform existing approaches in empirical tests.

Framework applies to multiple fairness notions including Equalized Odds.

Characterizes classifiers as instance-dependent thresholding rules.

Abstract

Existing theoretical work on Bayes-optimal fair classifiers usually considers a single (binary) sensitive feature. In practice, individuals are often defined by multiple sensitive features. In this paper, we characterize the Bayes-optimal fair classifier for multiple sensitive features under general approximate fairness measures, including mean difference and mean ratio. We show that these approximate measures for existing group fairness notions, including Demographic Parity, Equal Opportunity, Predictive Equality, and Accuracy Parity, are linear transformations of selection rates for specific groups defined by both labels and sensitive features. We then characterize that Bayes-optimal fair classifiers for multiple sensitive features become instance-dependent thresholding rules that rely on a weighted sum of these group membership probabilities. Our framework applies to both attribute-aware and attribute-blind settings and can accommodate composite fairness notions like Equalized Odds. Building on this, we propose two practical algorithms for Bayes-optimal fair classification via in-processing and post-processing. We show empirically that our methods compare favorably to existing methods.