  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.
