论文标题
与Wasserstein Barycenters进行公平学习，以实现不可兼容的性能指标
Fair learning with Wasserstein barycenters for non-decomposable performance measures
论文作者
论文摘要
这项工作提供了在人口统计学奇迹约束下的最佳分类功能的几种基本特征。在意识框架中，类似于经典的无约束分类案例，我们表明，在这种公平性约束下，最大化准确性等于解决相应的回归问题，然后在级别$ 1/2 $上进行阈值。我们将此结果扩展到线性分类分类度量（例如，$ {\ rm f} $ - 得分，AM测量，平衡准确性等），突出了回归问题在此框架中所起的基本作用。我们的结果利用了最近在人口统计学限制与多界限最佳运输配方之间建立了联系。非正式地，我们的结果表明，通过解决公平回归问题的解决方案来代替标签的有条件期望来实现无约束的问题与公平问题之间的过渡。最后，利用我们的分析，我们证明了在两个敏感群体的情况下，意识与不认识的设置之间的等效性。
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.
