Testing for Causal Fairness

Abstract: Causality is widely used in fairness analysis to prevent discrimination on sensitive attributes, such as genders in career recruitment and races in crime prediction. However, the current data-based Potential Outcomes Framework (POF) often leads to untrustworthy fairness analysis results when handling high-dimensional data. To address this, we introduce a distribution-based POF that transform fairness analysis into Distributional Closeness Testing (DCT) by intervening on sensitive attributes. We define counterfactual closeness fairness as the null hypothesis of DCT, where a sensitive attribute is considered fair if its factual and counterfactual potential outcome distributions are sufficiently close. We introduce the Norm-Adaptive Maximum Mean Discrepancy Treatment Effect (N-TE) as a statistic for measuring distributional closeness and apply DCT using the empirical estimator of NTE, referred to Counterfactual Fairness-CLOseness Testing ($\textrm{CF-CLOT}$). To ensure the trustworthiness of testing results, we establish the testing consistency of N-TE through rigorous theoretical analysis. $\textrm{CF-CLOT}$ demonstrates sensitivity in fairness analysis through the flexibility of the closeness parameter $\epsilon$. Unfair sensitive attributes have been successfully tested by $\textrm{CF-CLOT}$ in extensive experiments across various real-world scenarios, which validate the consistency of the testing.