As machine learning powered decision-making becomes increasingly important in our daily lives, it is imperative to strive for fairness in the underlying data processing. We propose a pre-processing algorithm for fair data representation via which supervised learning results in estimations of the Pareto frontier between prediction error and statistical disparity. Particularly, the present work applies the optimal affine transport to approach the post-processing Wasserstein-2 barycenter characterization of the optimal fair $L^2$-objective supervised learning via a pre-processing data deformation. Furthermore, we show that the Wasserstein-2 geodesics from the conditional (on sensitive information) distributions of the learning outcome to their barycenter characterizes the Pareto frontier between $L^2$-loss and the average pairwise Wasserstein-2 distance among sensitive groups on the learning outcome. Numerical simulations underscore the advantages: (1) the pre-processing step is compositive with arbitrary conditional expectation estimation supervised learning methods and unseen data; (2) the fair representation protects the sensitive information by limiting the inference capability of the remaining data with respect to the sensitive data; (3) the optimal affine maps are computationally efficient even for high-dimensional data.

翻译：随着机器学习驱动的决策在我们日常生活中日益重要，确保底层数据处理的公平性势在必行。我们提出了一种用于公平数据表示的预处理算法，通过该算法，监督学习能够估计预测误差与统计差异之间的帕累托前沿。具体而言，本研究应用最优仿射传输来逼近后处理Wasserstein-2重心表征，该表征对应于通过预处理数据变形实现的最优公平$L^2$目标监督学习。此外，我们证明从学习结果的条件分布（基于敏感信息）到其重心的Wasserstein-2测地线，能够刻画学习结果在敏感群体间的$L^2$损失与平均成对Wasserstein-2距离之间的帕累托前沿。数值模拟突显了以下优势：(1) 该预处理步骤可与任意基于条件期望估计的监督学习方法及未见数据兼容；(2) 公平表示通过限制剩余数据对敏感数据的推理能力来保护敏感信息；(3) 即使对于高维数据，最优仿射映射仍具有计算高效性。