Sequential Transport for Causal Mediation Analysis

2026-03-16

AI Summary

This study addresses the challenge in traditional causal mediation analysis that relies on unverifiable cross-world counterfactual assumptions, particularly when dealing with mixed-type mediators where constructing structurally coherent individual-level counterfactuals is difficult. The authors propose a Sequential Transport (ST) framework that, for the first time, integrates optimal transport with the directed acyclic graph (DAG) structure of mediators to generate deterministic counterfactuals satisfying causal constraints through minimal perturbation—without invoking cross-world assumptions. The method employs conditional CDF/quantile mappings for continuous mediators and extends to discrete mediators via simplex transport, rigorously preserving causal consistency under DAG constraints. Theoretical results establish the consistency between transport maps and effect decomposition; the approach recovers classical results in Gaussian models, demonstrates superior performance in nonlinear and mixed-type settings through simulations, and enables fine-grained disparity attribution in the COMPAS dataset.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

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.

Problem

• causal mediation analysis
• counterfactuals
• optimal transport
• direct and indirect effects
• mediator

Innovation

• Sequential Transport
• Optimal Transport
• Causal Mediation Analysis
• Directed Acyclic Graph
• Counterfactual Mediation