A variety of fairness constraints have been proposed in the literature to
mitigate group-level statistical bias. Their impacts have been largely
evaluated for different groups of populations corresponding to a set of
sensitive attributes, such as race or gender. Nonetheless, the community has
not observed sufficient explorations for how imposing fairness constraints fare
at an instance level. Building on the concept of influence function, a measure
that characterizes the impact of a training example on the target model and its
predictive performance, this work studies the influence of training examples
when fairness constraints are imposed. We find out that under certain
assumptions, the influence function with respect to fairness constraints can be
decomposed into a kernelized combination of training examples. One promising
application of the proposed fairness influence function is to identify
suspicious training examples that may cause model discrimination by ranking
their influence scores. We demonstrate with extensive experiments that training
on a subset of weighty data examples leads to lower fairness violations with a
trade-off of accuracy.

本研究使用影响函数（influence function）的概念研究了在实例级别强制公平约束时，训练示例的影响，提出了一种公平性影响函数。通过排名它们的影响分数，确定可能导致模型歧视的可疑培训示例，进行了大量实验并得出结论，仅在重要数据示例的子集上训练可以在准确性与公平性之间进行权衡。