Causal Fair Metric: Bridging Causality, Individual Fairness, and Adversarial Robustness

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.