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 structures and should reflect counterfactual instances. Previous attempts to define such metrics often lack general assumptions about input data and structural causal models. In our research, we introduce the novel concept of a causal fair metric for data with unknown causal structures containing sensitive features. We introduce the concept of protected causal perturbation, revealing new properties of this novel definition. Additionally, we delve into metric learning and propose an efficient method for estimating and applying this metric in real-world applications. Our innovative metric definition has practical applications in adversarial training, fair learning, algorithmic recourse, and causal bandit problems.

Install the packages in requirements.txt, for instance using

python -m venv myenv/
source myenv/bin/activate
pip install -r requirements.txt

To run the experiments, execute the following commands:

#!/bin/bash

for i in {1..100}
do
   python main.py --seed $i
done

In the Numerical Study section, we endeavor to obtain empirical validation for the metric learning techniques. For a comprehensive comparison, we juxtapose our augmented deep learning methodologies, which incorporate causal structure and sensitive information, against other prevailing methods. To this end, we employ deep learning for the estimation of the embedding function and adopt the Siamese metric learning as the baseline. This can be stratified into three distinct scenarios relevant to the acquisition of a causal fair metric:

• Distance-based
• Label-based
• Triplet-based