Proximal Identification and Estimation in Front-Door Causal Structures with Unobserved Confounding of the Mediator

Helen Guo, Beatrix Yaxin Wen, Ilya Shpitser
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:1857-1881, 2026.

Abstract

Unobserved confounding is a fundamental obstacle in causal inference problems. In the graphical modeling literature, a general theory has been developed that allows identification in the presence of hidden variables, with some limitations. In particular, {Pearl}’s celebrated front-door criterion allows nonparametric identification in the presence of unobserved common causes of the treatment and the outcome, however it requires the presence of an unconfounded variable that mediates all causal influence from the treatment to the outcome. This stringent requirement limits the applicability of the front-door criterion. We propose proximal generalizations of the front-door criterion, allowing both arbitrary treatment/outcome confounding, and unobserved confounders of the mediator, provided informative proxies for the latter type of confounders are observed. In addition to deriving three new identification strategies in this setting, we provide plug-in and influence function-based estimation strategies for the resulting functionals, and evaluate their performance through simulations.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-guo26c, title = {Proximal Identification and Estimation in Front-Door Causal Structures with Unobserved Confounding of the Mediator}, author = {Guo, Helen and Wen, Beatrix Yaxin and Shpitser, Ilya}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {1857--1881}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/guo26c/guo26c.pdf}, url = {https://proceedings.mlr.press/v337/guo26c.html}, abstract = {Unobserved confounding is a fundamental obstacle in causal inference problems. In the graphical modeling literature, a general theory has been developed that allows identification in the presence of hidden variables, with some limitations. In particular, {Pearl}’s celebrated front-door criterion allows nonparametric identification in the presence of unobserved common causes of the treatment and the outcome, however it requires the presence of an unconfounded variable that mediates all causal influence from the treatment to the outcome. This stringent requirement limits the applicability of the front-door criterion. We propose proximal generalizations of the front-door criterion, allowing both arbitrary treatment/outcome confounding, and unobserved confounders of the mediator, provided informative proxies for the latter type of confounders are observed. In addition to deriving three new identification strategies in this setting, we provide plug-in and influence function-based estimation strategies for the resulting functionals, and evaluate their performance through simulations.} }
Endnote
%0 Conference Paper %T Proximal Identification and Estimation in Front-Door Causal Structures with Unobserved Confounding of the Mediator %A Helen Guo %A Beatrix Yaxin Wen %A Ilya Shpitser %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-guo26c %I PMLR %P 1857--1881 %U https://proceedings.mlr.press/v337/guo26c.html %V 337 %X Unobserved confounding is a fundamental obstacle in causal inference problems. In the graphical modeling literature, a general theory has been developed that allows identification in the presence of hidden variables, with some limitations. In particular, {Pearl}’s celebrated front-door criterion allows nonparametric identification in the presence of unobserved common causes of the treatment and the outcome, however it requires the presence of an unconfounded variable that mediates all causal influence from the treatment to the outcome. This stringent requirement limits the applicability of the front-door criterion. We propose proximal generalizations of the front-door criterion, allowing both arbitrary treatment/outcome confounding, and unobserved confounders of the mediator, provided informative proxies for the latter type of confounders are observed. In addition to deriving three new identification strategies in this setting, we provide plug-in and influence function-based estimation strategies for the resulting functionals, and evaluate their performance through simulations.
APA
Guo, H., Wen, B.Y. & Shpitser, I.. (2026). Proximal Identification and Estimation in Front-Door Causal Structures with Unobserved Confounding of the Mediator. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:1857-1881 Available from https://proceedings.mlr.press/v337/guo26c.html.

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