Fair learning with Wasserstein barycenters for non-decomposable performance measures
This work addresses fairness in machine learning for classification tasks, providing theoretical insights into demographic parity constraints, but it is incremental as it builds on existing frameworks and transport formulations.
The paper characterizes optimal classification functions under demographic parity constraints, showing that maximizing accuracy under fairness is equivalent to solving a regression problem followed by thresholding, and extends this to linear-fractional measures like F-score and balanced accuracy. It leverages connections to multi-marginal optimal transport and demonstrates equivalence between awareness and unawareness setups for two sensitive groups.
This work provides several fundamental characterizations of the optimal classification function under the demographic parity constraint. In the awareness framework, akin to the classical unconstrained classification case, we show that maximizing accuracy under this fairness constraint is equivalent to solving a corresponding regression problem followed by thresholding at level $1/2$. We extend this result to linear-fractional classification measures (e.g., ${\rm F}$-score, AM measure, balanced accuracy, etc.), highlighting the fundamental role played by the regression problem in this framework. Our results leverage 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 problems and the fair one is achieved by replacing the conditional expectation of the label by the solution of the fair regression problem. Finally, leveraging our analysis, we demonstrate an equivalence between the awareness and the unawareness setups in the case of two sensitive groups.