The post-processing approaches are becoming prominent techniques to enhance machine learning models' fairness because of their intuitiveness, low computational cost, and excellent scalability. However, most existing post-processing methods are designed for task-specific fairness measures and are limited to single-output models. In this paper, we introduce a post-processing method for multi-output models, such as the ones used for multi-task/multi-class classification and representation learning, to enhance a model's distributional parity, a task-agnostic fairness measure. Existing techniques to achieve distributional parity are based on the (inverse) cumulative density function of a model's output, which is limited to single-output models. Extending previous works, our method employs an optimal transport mapping to move a model's outputs across different groups towards their empirical Wasserstein barycenter. An approximation technique is applied to reduce the complexity of computing the exact barycenter and a kernel regression method is proposed for extending this process to out-of-sample data. Our empirical studies, which compare our method to current existing post-processing baselines on multi-task/multi-class classification and representation learning tasks, demonstrate the effectiveness of the proposed approach.

Combining the concepts of individual and group fairness, we search for discrimination by matching individuals in different protected groups to each other, and comparing their classifier outcomes. Specifically, we formulate a GAN-based approximation of the optimal transport mapping, and use it to translate the distribution of one protected group to that of another, returning pairs of in-distribution samples that statistically correspond to one another. We then define the flipset: the set of individuals whose classifier output changes post-translation, which intuitively corresponds to the set of people who were harmed because of their protected group membership. To shed light on why the model treats a given subgroup differently, we introduce the transparency report: a ranking of features that are most associated with the model's behavior on the flipset. We show that this provides a computationally inexpensive way to identify subgroups that are harmed by model discrimination, including in cases where the model satisfies population-level group fairness criteria.