Stable Causal Estimation with Optimal Transport
Abstract
In observational studies, the overlap assumption, also called positivity, is frequently strained in practice. Limited overlap destabilizes widely used estimators such as inverse propensity weighting (IPW), whose variance depends on density ratios that explode as propensity scores approach zero or one. To address this challenge, we propose the Stable Transport Estimator (STE), an optimal transport-based approach for estimating average causal effects when overlap holds but strict overlap fails. Unlike IPW, the variance of STE contains no density-ratio factor; it is governed by the transport map itself and stays finite under bounded moments, even when density ratios diverge. By replacing reweighting with a geometry-aware transport map, STE constructs stable counterfactual comparisons without requiring density estimation or propensity score modeling. STE further extends to settings where the overlap condition is violated: when covariate supports overlap only partially, a linear interpolation transport map enables principled extrapolation with explicit bias-variance trade-offs. We establish consistency, asymptotic normality, and a variance characterization that makes explicit the contribution of the estimated transport map to the asymptotic variance. Across synthetic and real datasets, STE demonstrates improved robustness, reduced bias, and markedly more stable variance compared to existing estimators.
Related
- Stability, discretization, and optimality of continuous-time causal optimal transport
- PLOT: Progressive Localization via Optimal Transport in Neural Causal Abstraction
- Structurally stable singularities and Lipschitz stable optimal transport metrics for the compressible Euler equations
- Sieve Estimation of Optimal Transport Maps from Paired Data in Gaussian Spaces
- Deep Barycentric Regression for Optimal Transport Map Estimation and its Statistical Optimality
BibTeX
@misc{xu2026stable,
title = {{Stable Causal Estimation with Optimal Transport}},
author = {Yidan Xu and Yixin Wang and XuanLong Nguyen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15212},
eprint = {2610.15212},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15212},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Stable Causal Estimation with Optimal Transport
AU - Yidan Xu
AU - Yixin Wang
AU - XuanLong Nguyen
PY - 2026
DA - 2026/10/14
PB - arXiv
DO - 10.48550/arxiv.2610.15212
UR - https://arxiv.org/abs/2610.15212
AB - In observational studies, the overlap assumption, also called positivity, is frequently strained in practice. Limited overlap destabilizes widely used estimators such as inverse propensity weighting (IPW), whose variance depends on density ratios that explode as propensity scores approach zero or one. To address this challenge, we propose the Stable Transport Estimator (STE), an optimal transport-based approach for estimating average causal effects when overlap holds but strict overlap fails. Unlike IPW, the variance of STE contains no density-ratio factor; it is governed by the transport map itself and stays finite under bounded moments, even when density ratios diverge. By replacing reweighting with a geometry-aware transport map, STE constructs stable counterfactual comparisons without requiring density estimation or propensity score modeling. STE further extends to settings where the overlap condition is violated: when covariate supports overlap only partially, a linear interpolation transport map enables principled extrapolation with explicit bias-variance trade-offs. We establish consistency, asymptotic normality, and a variance characterization that makes explicit the contribution of the estimated transport map to the asymptotic variance. Across synthetic and real datasets, STE demonstrates improved robustness, reduced bias, and markedly more stable variance compared to existing estimators.
ER -