Fair learning with Wasserstein barycenters for non-decomposable performance measures

This work provides several fundamental characterizations of the optimal function under the demographic parity constraint. In the framework, akin to the classical unconstrained classification case, show that maximizing accuracy under this fairness constraint is equivalent solving a corresponding 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.), highlighting the role played by the regression problem in this framework. Our leverage recently developed connection between the demographic parity and the multi-marginal optimal transport formulation. Informally, result shows that the transition between the unconstrained problems and the one is achieved by replacing the conditional expectation of the label by solution of the fair regression problem. Finally, leveraging our analysis, demonstrate an equivalence between the awareness and the unawareness setups the case of two sensitive groups.