We study the fair regression problem under the notion of Mean Parity (MP) fairness, which requires the conditional mean of the learned function output to be constant with respect to the sensitive attributes. We address this problem by leveraging reproducing kernel Hilbert space (RKHS) to construct the functional space whose members are guaranteed to satisfy the fairness constraints. The proposed functional space suggests a closed-form solution for the fair regression problem that is naturally compatible with multiple sensitive attributes. Furthermore, by formulating the fairness-accuracy tradeoff as a relaxed fair regression problem, we derive a corresponding regression function that can be implemented efficiently and provides interpretable tradeoffs. More importantly, under some mild assumptions, the proposed method can be applied to regression problems with a covariance-based notion of fairness. Experimental results on benchmark datasets show the proposed methods achieve competitive and even superior performance compared with several state-of-the-art methods.

翻译：我们研究在均值奇偶（MP）公平性概念下的公平回归问题，该概念要求学习所得函数输出的条件均值关于敏感属性保持恒定。我们通过利用再生核希尔伯特空间（RKHS）构建满足公平性约束的函数空间来解决该问题。所提出的函数空间为公平回归问题提供了闭式解，且该解天然适用于多个敏感属性的场景。此外，通过将公平-准确性权衡建模为松弛的公平回归问题，我们推导出相应的回归函数，该函数可实现高效计算并提供可解释的权衡关系。更重要的是，在温和假设下，所提方法可应用于基于协方差公平性概念的回归问题。基准数据集上的实验结果表明，与多种现有最优方法相比，所提方法实现了具有竞争力乃至更优的性能。