Bayes-Optimal Fair Classification with Multiple Sensitive Features
This addresses fairness in classification for individuals with multiple sensitive attributes, though it is incremental as it builds on prior single-feature theory.
The paper tackles the problem of extending Bayes-optimal fair classification to handle multiple sensitive features, showing that optimal classifiers become instance-dependent thresholding rules based on weighted sums of group probabilities, and proposes algorithms that empirically outperform existing methods.
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.