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 methods for achieving distributional parity rely on the (inverse) cumulative density function of a model's output, restricting their applicability to single-output models. Extending previous works, we propose to employ optimal transport mappings 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 to extend this process to out-of-sample data. Our empirical studies evaluate the proposed approach against various baselines on multi-task/multi-class classification and representation learning tasks, demonstrating the effectiveness of the proposed approach.

翻译：后处理方法因其直观性、低计算成本和优异的可扩展性，正成为提升机器学习模型公平性的重要技术。然而，现有后处理方法大多针对特定任务的公平性度量设计，且仅限于单输出模型。本文提出一种适用于多输出模型（如多任务/多分类和表示学习模型）的后处理方法，以提升模型的分布均衡性——一种与任务无关的公平性度量。现有实现分布均衡性的方法依赖于模型输出的（逆）累积分布函数，限制了其在单输出模型中的应用。基于先前研究，我们提出采用最优传输映射，将不同群体间的模型输出向经验Wasserstein重心移动。通过近似技术降低精确重心计算复杂度，并采用核回归方法将该过程扩展至样本外数据。实证研究在多任务/多分类及表示学习任务中，将所提方法与多种基线方法进行比较，验证了其有效性。