In this paper, we link two existing approaches to derive counterfactuals: adaptations based on a causal graph, as suggested in Ple\v{c}ko and Meinshausen (2020) and optimal transport, as in De Lara et al. (2024). We extend "Knothe's rearrangement" Bonnotte (2013) and "triangular transport" Zech and Marzouk (2022a) 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.

翻译：本文融合了两种现有的反事实推导方法：基于因果图的适应性方法（如Plečko和Meinshausen（2020）所提出）与最优传输方法（如De Lara等人（2024）所提出）。我们将Bonnotte（2013）的“Knothe重排”与Zech和Marzouk（2022a）的“三角传输”扩展至概率图模型，并利用这种被称为顺序传输的反事实方法来探讨个体公平性问题。在建立所提出方法的理论基础后，我们通过在合成数据集和真实数据集上的数值实验展示了其应用效果。