Tightening Causal Bounds via Covariate-Aware Optimal Transport

Sirui Lin, Zijun Gao, Jose Blanchet, Peter Glynn
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:37815-37845, 2025.

Abstract

Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates can substantially tighten these bounds, but requires determining the range of PI over probability models consistent with the joint distributions of observed covariates and outcomes in treatment and control groups. This problem is known to be equivalent to a conditional optimal transport (COT) optimization task, which is more challenging than standard optimal transport (OT) due to the additional conditioning constraints. In this work, we study a tight relaxation of COT that effectively reduces it to standard OT, leveraging its well-established computational and theoretical foundations. Our relaxation incorporates covariate information and ensures narrower PI intervals for any value of the penalty parameter, while becoming asymptotically exact as a penalty increases to infinity. This approach preserves the benefits of covariate adjustment in PI and results in a data-driven estimator for the PI set that is easy to implement using existing OT packages. We analyze the convergence rate of our estimator and demonstrate the effectiveness of our approach through extensive simulations, highlighting its practical use and superior performance compared to existing methods.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-lin25f, title = {Tightening Causal Bounds via Covariate-Aware Optimal Transport}, author = {Lin, Sirui and Gao, Zijun and Blanchet, Jose and Glynn, Peter}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {37815--37845}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/lin25f/lin25f.pdf}, url = {https://proceedings.mlr.press/v267/lin25f.html}, abstract = {Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates can substantially tighten these bounds, but requires determining the range of PI over probability models consistent with the joint distributions of observed covariates and outcomes in treatment and control groups. This problem is known to be equivalent to a conditional optimal transport (COT) optimization task, which is more challenging than standard optimal transport (OT) due to the additional conditioning constraints. In this work, we study a tight relaxation of COT that effectively reduces it to standard OT, leveraging its well-established computational and theoretical foundations. Our relaxation incorporates covariate information and ensures narrower PI intervals for any value of the penalty parameter, while becoming asymptotically exact as a penalty increases to infinity. This approach preserves the benefits of covariate adjustment in PI and results in a data-driven estimator for the PI set that is easy to implement using existing OT packages. We analyze the convergence rate of our estimator and demonstrate the effectiveness of our approach through extensive simulations, highlighting its practical use and superior performance compared to existing methods.} }
Endnote
%0 Conference Paper %T Tightening Causal Bounds via Covariate-Aware Optimal Transport %A Sirui Lin %A Zijun Gao %A Jose Blanchet %A Peter Glynn %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-lin25f %I PMLR %P 37815--37845 %U https://proceedings.mlr.press/v267/lin25f.html %V 267 %X Causal estimands can vary significantly depending on the relationship between outcomes in treatment and control groups, leading to wide partial identification (PI) intervals that impede decision making. Incorporating covariates can substantially tighten these bounds, but requires determining the range of PI over probability models consistent with the joint distributions of observed covariates and outcomes in treatment and control groups. This problem is known to be equivalent to a conditional optimal transport (COT) optimization task, which is more challenging than standard optimal transport (OT) due to the additional conditioning constraints. In this work, we study a tight relaxation of COT that effectively reduces it to standard OT, leveraging its well-established computational and theoretical foundations. Our relaxation incorporates covariate information and ensures narrower PI intervals for any value of the penalty parameter, while becoming asymptotically exact as a penalty increases to infinity. This approach preserves the benefits of covariate adjustment in PI and results in a data-driven estimator for the PI set that is easy to implement using existing OT packages. We analyze the convergence rate of our estimator and demonstrate the effectiveness of our approach through extensive simulations, highlighting its practical use and superior performance compared to existing methods.
APA
Lin, S., Gao, Z., Blanchet, J. & Glynn, P.. (2025). Tightening Causal Bounds via Covariate-Aware Optimal Transport. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:37815-37845 Available from https://proceedings.mlr.press/v267/lin25f.html.

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