Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness

Agathe Fernandes Machado, Arthur Charpentier, Ewen Gallic

Abstract: In this paper, we link two existing approaches to derive counterfactuals: adaptations based on a causal graph, and optimal transport. We extend "Knothe's rearrangement" and "triangular transport" to probabilistic graphical models, and use this counterfactual approach, referred to as sequential transport, to discuss individual fairness. After establishing the theoretical foundations of the proposed method, we demonstrate its application through numerical experiments on both synthetic and real datasets.