Machine learning algorithms are becoming integrated into more and more high-stakes decision-making processes, such as in social welfare issues. Due to the need of mitigating the potentially disparate impacts from algorithmic predictions, many approaches have been proposed in the emerging area of fair machine learning. However, the fundamental problem of characterizing Bayes-optimal classifiers under various group fairness constraints has only been investigated in some special cases. Based on the classical Neyman-Pearson argument (Neyman and Pearson, 1933; Shao, 2003) for optimal hypothesis testing, this paper provides a unified framework for deriving Bayes-optimal classifiers under group fairness. This enables us to propose a group-based thresholding method we call FairBayes, that can directly control disparity, and achieve an essentially optimal fairness-accuracy tradeoff. These advantages are supported by thorough experiments.

翻译：机器学习算法正越来越多地融入社会福利等高风险决策过程中。为减轻算法预测可能带来的差异化影响，公平机器学习这一新兴领域已提出诸多方法。然而，关于在各类群体公平约束下刻画贝叶斯最优分类器的基本问题，目前仅在若干特例中有所研究。本文基于经典奈曼-皮尔逊假设检验框架（Neyman and Pearson, 1933; Shao, 2003），提出了统一推导群体公平下贝叶斯最优分类器的理论框架。据此我们提出基于群体阈值化的方法FairBayes，该方法能直接控制差异性，并实现本质上最优的公平-准确率权衡。充分的实验验证了上述优势。