# Optimal transport and Wasserstein distances for causal models

arXiv: https://arxiv.org/abs/2303.14085 · HTML: https://mlsanity.com/paper/2303.14085/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Mar 2023.

## Built on by (most cited first, 9 of 9)

- [Neural Spacetimes for DAG Representation Learning](https://mlsanity.com/paper/2408.13885/) (2024)
- [Sequential Conditional Transport on Probabilistic Graphs for Interpretable Counterfactual Fairness](https://mlsanity.com/paper/2408.03425/) (2024)
- [Stochastic dynamics learning with state-space systems](https://mlsanity.com/paper/2508.07876/) (2025)
- [A primer on optimal transport for causal inference with observational data](https://mlsanity.com/paper/2503.07811/) (2025)
- [What is a good matching of probability measures? A counterfactual lens on transport maps](https://mlsanity.com/paper/2509.16027/) (2025)
- [Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairness](https://mlsanity.com/paper/2509.26275/) (2025)
- [Designing Ambiguity Sets for Distributionally Robust Optimization Using Structural Causal Optimal Transport](https://mlsanity.com/paper/2510.00599/) (2025)
- [Robust Optimization in Causal Models and G-Causal Normalizing Flows](https://mlsanity.com/paper/2510.15458/) (2025)
- [PLOT: Progressive Localization via Optimal Transport in Neural Causal Abstraction](https://mlsanity.com/paper/2605.06979/) (2026)

## Abstract (arXiv)

In this paper, we introduce a variant of optimal transport adapted to the causal structure given by an underlying directed graph G. Different graph structures lead to different specifications of the optimal transport problem. For instance, a fully connected graph yields standard optimal transport, a linear graph structure corresponds to causal optimal transport between the distributions of two discrete-time stochastic processes, and an empty graph leads to a notion of optimal transport related to CO-OT, Gromov-Wasserstein distances and factored OT. We derive different characterizations of G-causal transport plans and introduce Wasserstein distances between causal models that respect the underlying graph structure. We show that average treatment effects are continuous with respect to G-causal Wasserstein distances and small perturbations of structural causal models lead to small deviations in G-causal Wasserstein distance. We also introduce an interpolation between causal models based on G-causal Wasserstein distance and compare it to standard Wasserstein interpolation.