Fair Bayes-Optimal Classifiers Under Predictive Parity

TL;DR

This paper studies fair classifiers under predictive parity, proving conditions for optimality, revealing potential within-group unfairness when group performances vary widely, and proposing an adaptive algorithm to achieve fairness and accuracy.

Contribution

It characterizes the structure of fair Bayes-optimal classifiers under predictive parity and introduces the FairBayes-DPP algorithm for practical fairness enforcement.

Findings

Optimal classifiers are group-wise thresholding under moderate performance variation.

Predictive parity may cause within-group unfairness with large performance disparities.

FairBayes-DPP effectively achieves predictive parity and high accuracy in experiments.

Abstract

Increasing concerns about disparate effects of AI have motivated a great deal of work on fair machine learning. Existing works mainly focus on independence- and separation-based measures (e.g., demographic parity, equality of opportunity, equalized odds), while sufficiency-based measures such as predictive parity are much less studied. This paper considers predictive parity, which requires equalizing the probability of success given a positive prediction among different protected groups. We prove that, if the overall performances of different groups vary only moderately, all fair Bayes-optimal classifiers under predictive parity are group-wise thresholding rules. Perhaps surprisingly, this may not hold if group performance levels vary widely; in this case we find that predictive parity among protected groups may lead to within-group unfairness. We then propose an algorithm we call FairBayes-DPP, aiming to ensure predictive parity when our condition is satisfied. FairBayes-DPP is an adaptive thresholding algorithm that aims to achieve predictive parity, while also seeking to maximize test accuracy. We provide supporting experiments conducted on synthetic and empirical data.