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.

翻译：我们考虑在群体公平约束下的二分类问题，该约束可表现为人口均等（DP）、机会均等（EOp）或均等优势（EO）三种形式。我们提出了公平约束下贝叶斯最优分类器的显式表征，该表征本质上是对无约束分类器的简单修正规则。具体而言，我们引入一种新颖的实例级偏差度量——称为偏差评分，修正规则即为基于有限数量偏差评分的简单线性规则。基于这一表征，我们开发了一种后验方法，能够在保持高准确率的同时适应公平约束。在DP和EOp约束下，修正规则为对单一偏差评分设置阈值；在EO约束下，则需要拟合包含两个参数的线性修正规则。该方法还可适用于复合群体公平准则，例如涉及多个敏感属性的情形。