Statistical fairness seeks to ensure an equitable distribution of predictions or algorithmic decisions across different sensitive groups. Among the fairness criteria under consideration, demographic parity is arguably the most conceptually straightforward: it simply requires that the distribution of outcomes is identical across all sensitive groups. In this talk, we explore the relationship between classification and regression problems under this constraint.
We provide several fundamental characterizations of the optimal classification function under the demographic parity constraint. In the awareness framework, analogous to the classical unconstrained classification scenario, we demonstrate that maximizing accuracy under this fairness constraint is equivalent to solving a fair regression problem followed by thresholding at level 1/2. We extend this result to linear-fractional classification measures (e.g., 𝐹-score, AM measure, balanced accuracy, etc.), emphasizing the pivotal role played by regression in this framework. Our findings leverage the recently developed connection between the demographic parity constraint and the multi-marginal optimal transport formulation. Informally, our result shows that the transition between the unconstrained problem and the fair one is achieved by replacing the conditional expectation of the label by the solution of the fair regression problem. Leveraging our analysis, we also demonstrate an equivalence between the awareness and the unawareness setups for two sensitive groups.[-]