  Despite the essential need for comprehensive considerations in responsible
AI, factors like robustness, fairness, and causality are often studied in
isolation. Adversarial perturbation, used to identify vulnerabilities in
models, and individual fairness, aiming for equitable treatment of similar
individuals, despite initial differences, both depend on metrics to generate
comparable input data instances. Previous attempts to define such joint metrics
often lack general assumptions about data or structural causal models and were
unable to reflect counterfactual proximity. To address this, our paper
introduces a causal fair metric formulated based on causal structures
encompassing sensitive attributes and protected causal perturbation. To enhance
the practicality of our metric, we propose metric learning as a method for
metric estimation and deployment in real-world problems in the absence of
structural causal models. We also demonstrate the application of our novel
metric in classifiers. Empirical evaluation of real-world and synthetic
datasets illustrates the effectiveness of our proposed metric in achieving an
accurate classifier with fairness, resilience to adversarial perturbations, and
a nuanced understanding of causal relationships.
