Counterfactual Fairness with Imperfect Causal Graphs

Fairness-aware machine learning aims to build predictive models that comply with fairness requirements, particularly concerning sensitive attributes such as race, gender, and age. Among causality-based fairness notions, counterfactual fairness is widely adopted for its individual-level guarantees, requiring that an individual's predicted outcome remains unchanged in a counterfactual world where its sensitive attribute is altered. However, existing methods critically assume that the true causal graph is fully known, which is rarely the case in practice. Moreover, counterfactual fairness suffers from inherent identifiability limitations, as counterfactual quantities cannot always be uniquely estimated from observational data, especially under incomplete causal knowledge. To address these challenges, we propose a principled framework (CF-ICG) for counterfactual fairness under imperfectly known causal graphs, e.g., Completed Partially Directed Acyclic Graphs (CPDAGs). We first introduce a criterion to determine the identifiability, and bound the counterfactual quantities under CPDAGs. Building upon this, we develop an efficient local algorithm that avoids the exhaustive enumeration of all DAGs, ensuring robustness against worst-case fairness violations. Experimental results on synthetic and real-world datasets demonstrate the practical effectiveness and theoretical soundness of CF-ICG.