Adversarial perturbation is used to expose vulnerabilities in machine
learning models, while the concept of individual fairness aims to ensure
equitable treatment regardless of sensitive attributes. Despite their initial
differences, both concepts rely on metrics to generate similar input data
instances. These metrics should be designed to align with the data's
characteristics, especially when it is derived from causal structure and should
reflect counterfactuals proximity. Previous attempts to define such metrics
often lack general assumptions about data or structural causal models. In this
research, we introduce a causal fair metric formulated based on causal
structures that encompass sensitive attributes. For robustness analysis, the
concept of protected causal perturbation is presented. Additionally, we delve
into metric learning, proposing a method for metric estimation and deployment
in real-world problems. The introduced metric has applications in the fields
adversarial training, fair learning, algorithmic recourse, and causal
reinforcement learning.

通过引入基于因果结构的因果公平度量、保护性因果干扰以及度量学习的方法，本研究解决了机器学习模型漏洞暴露、公平性和度量估计等实际问题。