We propose sequential transport (ST), a distributional framework for mediation analysis that combines optimal transport (OT) with a mediator directed acyclic graph (DAG). Instead of relying on cross-world counterfactual assumptions, ST constructs unit-level mediator counterfactuals by minimally transporting each mediator, either marginally or conditionally, toward its distribution under an alternative treatment while preserving the causal dependencies encoded by the DAG. For numerical mediators, ST uses monotone (conditional) OT maps based on conditional CDF/quantile estimators; for categorical mediators, it extends naturally via simplex-based transport. We establish consistency of the estimated transport maps and of the induced unit-level decompositions into mutatis mutandis direct and indirect effects under standard regularity and support conditions. When the treatment is randomized or ignorable (possibly conditional on covariates), these decompositions admit a causal interpretation; otherwise, they provide a principled distributional attribution of differences between groups aligned with the mediator structure. Gaussian examples show that ST recovers classical mediation formulas, while additional simulations confirm good performance in nonlinear and mixed-type settings. An application to the COMPAS dataset illustrates how ST yields deterministic, DAG-consistent counterfactual mediators and a fine-grained mediator-level attribution of disparities.

翻译：我们提出序列传输（ST），一种结合最优传输（OT）与中介有向无环图（DAG）的中介分析分布框架。ST不依赖于跨世界反事实假设，而是通过将每个中介变量（边际地或条件地）最小化地传输至替代处理下的分布，同时保留DAG编码的因果依赖关系，从而构建单元级中介反事实。对于数值型中介变量，ST使用基于条件CDF/分位数估计的单调（条件）OT映射；对于类别型中介变量，则通过基于单纯形的传输自然扩展。我们在标准正则性和支撑条件下，建立了估计传输映射的一致性，以及由此诱导的单元级分解为相应直接效应和间接效应的一致性。当处理是随机化或可忽略时（可能以协变量为条件），这些分解具有因果解释；否则，它们提供一种与中介结构对齐的、原则性的组间差异分布归因。高斯示例表明ST恢复了经典中介公式，而额外模拟证实了其在非线性和混合类型设置中的良好性能。在COMPAS数据集上的应用展示了ST如何生成确定性的、DAG一致的反事实中介变量，并提供差异的细粒度中介级归因。