# Optimal transport weights for causal inference

arXiv: https://arxiv.org/abs/2109.01991 · HTML: https://mlsanity.com/paper/2109.01991/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 77 references that are in the map.
- First posted on arXiv 5 Sep 2021.

## Builds on (most cited first, 18 of 18)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Learning Generative Models with Sinkhorn Divergences](https://mlsanity.com/paper/1706.00292/) (2017)
- [Near-linear time approximation algorithms for optimal transport via Sinkhorn iteration](https://mlsanity.com/paper/1705.09634/) (2017)
- [On Wasserstein Two Sample Testing and Related Families of Nonparametric Tests](https://mlsanity.com/paper/1509.02237/) (2015)
- [Computational Optimal Transport: Complexity by Accelerated Gradient Descent Is Better Than by Sinkhorn's Algorithm](https://mlsanity.com/paper/1802.04367/) (2018)
- [Statistical bounds for entropic optimal transport: sample complexity and the central limit theorem](https://mlsanity.com/paper/1905.11882/) (2019)
- [Smooth and Sparse Optimal Transport](https://mlsanity.com/paper/1710.06276/) (2017)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Generalized Optimal Matching Methods for Causal Inference](https://mlsanity.com/paper/1612.08321/) (2016)
- [Debiased Sinkhorn barycenters](https://mlsanity.com/paper/2006.02575/) (2020)
- [Inference for Empirical Wasserstein Distances on Finite Spaces](https://mlsanity.com/paper/1610.03287/) (2016)
- [Minimal Dispersion Approximately Balancing Weights: Asymptotic Properties and Practical Considerations](https://mlsanity.com/paper/1705.00998/) (2017)
- [Kernel Optimal Orthogonality Weighting: A Balancing Approach to Estimating Effects of Continuous Treatments](https://mlsanity.com/paper/1910.11972/) (2019)
- [Reweighting samples under covariate shift using a Wasserstein distance criterion](https://mlsanity.com/paper/2010.09267/) (2020)
- [Large Sample Properties of Matching for Balance](https://mlsanity.com/paper/1905.11386/) (2019)

## Built on by (most cited first, 7 of 7)

- [Optimal Transport for Treatment Effect Estimation](https://mlsanity.com/paper/2310.18286/) (2023)
- [Proximity Matters: Local Proximity Enhanced Balancing for Treatment Effect Estimation](https://mlsanity.com/paper/2407.01111/) (2024)
- [Matching for causal effects via multimarginal unbalanced optimal transport](https://mlsanity.com/paper/2112.04398/) (2021)
- [Revisiting Counterfactual Regression through the Lens of Gromov-Wasserstein Information Bottleneck](https://mlsanity.com/paper/2405.15505/) (2024)
- [Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights](https://mlsanity.com/paper/2406.19195/) (2024)
- [A Causal Inference Framework for Leveraging External Controls in Hybrid Trials](https://mlsanity.com/paper/2305.08969/) (2023)
- [Beyond Pooling: Matching for Robust Generalization under Data Heterogeneity](https://mlsanity.com/paper/2602.07154/) (2026)

## Abstract (arXiv)

Imbalance in covariate distributions leads to biased estimates of causal effects. Weighting methods attempt to correct this imbalance but rely on specifying models for the treatment assignment mechanism, which is unknown in observational studies. This leaves researchers to choose the proper weighting method and the appropriate covariate functions for these models without knowing the correct combination to achieve distributional balance. In response to these difficulties, we propose a nonparametric generalization of several other weighting schemes found in the literature: Causal Optimal Transport. This new method directly targets distributional balance by minimizing optimal transport distances between treatment and control groups or, more generally, between any source and target population. Our approach is semiparametrically efficient and model-free but can also incorporate moments or any other important functions of covariates that a researcher desires to balance. Moreover, our method can provide nonparametric estimate the conditional mean outcome function and we give rates for the convergence of this estimator. Moreover, we show how this method can provide nonparametric imputations of the missing potential outcomes and give rates of convergence for this estimator. We find that Causal Optimal Transport outperforms competitor methods when both the propensity score and outcome models are misspecified, indicating it is a robust alternative to common weighting methods. Finally, we demonstrate the utility of our method in an external control trial examining the effect of misoprostol versus oxytocin for the treatment of post-partum hemorrhage.