We study the problem of post-processing a supervised machine-learned regressor to maximize fair binary classification at all decision thresholds. By decreasing the statistical distance between each group's score distributions, we show that we can increase fair performance across all thresholds at once, and that we can do so without a large decrease in accuracy. To this end, we introduce a formal measure of Distributional Parity, which captures the degree of similarity in the distributions of classifications for different protected groups. Our main result is to put forward a novel post-processing algorithm based on optimal transport, which provably maximizes Distributional Parity, thereby attaining common notions of group fairness like Equalized Odds or Equal Opportunity at all thresholds. We demonstrate on two fairness benchmarks that our technique works well empirically, while also outperforming and generalizing similar techniques from related work.

翻译：我们研究了后处理监督机器学习回归器的问题，旨在最大化所有决策阈值下的公平二元分类。通过降低各组别评分分布之间的统计距离，我们证明可以同时提升所有阈值下的公平性能，且不会导致准确率大幅下降。为此，我们引入了分布公平性的形式化度量，用于捕捉不同受保护群体分类分布的相似程度。我们的主要成果是提出了一种基于最优传输的新型后处理算法，该算法可证明最大化分布公平性，从而在任意阈值下实现如等概率机会或平等机会等常见的群体公平性概念。我们通过两个公平性基准实验证明，该技术在实际中表现良好，同时优于并泛化了相关工作中的类似方法。