We consider a binary classification problem under group fairness constraints, which can be one of Demographic Parity (DP), Equalized Opportunity (EOp), or Equalized Odds (EO). We propose an explicit characterization of Bayes optimal classifier under the fairness constraints, which turns out to be a simple modification rule of the unconstrained classifier. Namely, we introduce a novel instance-level measure of bias, which we call bias score, and the modification rule is a simple linear rule on top of the finite amount of bias scores. Based on this characterization, we develop a post-hoc approach that allows us to adapt to fairness constraints while maintaining high accuracy. In the case of DP and EOp constraints, the modification rule is thresholding a single bias score, while in the case of EO constraints we are required to fit a linear modification rule with 2 parameters. The method can also be applied for composite group-fairness criteria, such as ones involving several sensitive attributes. We achieve competitive or better performance compared to both in-processing and post-processing methods across three datasets: Adult, COMPAS, and CelebA. Unlike most post-processing methods, we do not require access to sensitive attributes during the inference time.

翻译：我们考虑在群体公平约束下的二分类问题，公平约束可以是人口统计均等（DP）、机会均等（EOp）或几率均等（EO）之一。我们提出了在公平约束下贝叶斯最优分类器的显式刻画，它实际上是对无约束分类器的一种简单修改规则。具体而言，我们引入了一种新颖的实例级偏差度量，称为偏差评分，而修改规则是基于有限数量偏差评分的简单线性规则。基于这一刻画，我们开发了一种事后方法，能够在保持高精度的同时适应公平约束。在DP和EOp约束的情况下，修改规则是对单个偏差评分进行阈值化处理；而在EO约束的情况下，我们需要拟合一个包含2个参数的线性修改规则。该方法也可应用于复合群体公平性准则，例如涉及多个敏感属性的准则。在Adult、COMPAS和CelebA三个数据集上，我们的方法相比处理中和处理后方法均取得了有竞争力或更优的性能。与大多数后处理方法不同，我们在推理过程中无需访问敏感属性。