Instrumental and Proximal Causal Inference with Gaussian Processes

Yuqi Zhang, Krikamol Muandet, Dino Sejdinovic, Edwin Fong, Siu Lun Chau
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:8130-8165, 2026.

Abstract

Instrumental variable (IV) and proximal causal learning (Proxy) methods are central frameworks for causal inference in the presence of unobserved confounding. Despite substantial methodological advances, existing approaches rarely provide reliable epistemic uncertainty (EU) quantification. We address this gap through a Deconditional {Gaussian} Process (GP) framework for uncertainty-aware causal learning. Our formulation recovers popular kernel estimators as the posterior mean, ensuring predictive precision, while the posterior variance yields principled and well-calibrated EU. Moreover, the probabilistic structure enables systematic model selection via marginal log-likelihood optimization. Empirical results demonstrate strong predictive performance alongside informative EU quantification, evaluated via empirical coverage frequencies and decision-aware accuracy–rejection curves. Together, our approach provides a unified, practical solution for causal inference under unobserved confounding with reliable uncertainty.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-zhang26f, title = {Instrumental and Proximal Causal Inference with {Gaussian} Processes}, author = {Zhang, Yuqi and Muandet, Krikamol and Sejdinovic, Dino and Fong, Edwin and Chau, Siu Lun}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {8130--8165}, 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/zhang26f/zhang26f.pdf}, url = {https://proceedings.mlr.press/v337/zhang26f.html}, abstract = {Instrumental variable (IV) and proximal causal learning (Proxy) methods are central frameworks for causal inference in the presence of unobserved confounding. Despite substantial methodological advances, existing approaches rarely provide reliable epistemic uncertainty (EU) quantification. We address this gap through a Deconditional {Gaussian} Process (GP) framework for uncertainty-aware causal learning. Our formulation recovers popular kernel estimators as the posterior mean, ensuring predictive precision, while the posterior variance yields principled and well-calibrated EU. Moreover, the probabilistic structure enables systematic model selection via marginal log-likelihood optimization. Empirical results demonstrate strong predictive performance alongside informative EU quantification, evaluated via empirical coverage frequencies and decision-aware accuracy–rejection curves. Together, our approach provides a unified, practical solution for causal inference under unobserved confounding with reliable uncertainty.} }
Endnote
%0 Conference Paper %T Instrumental and Proximal Causal Inference with Gaussian Processes %A Yuqi Zhang %A Krikamol Muandet %A Dino Sejdinovic %A Edwin Fong %A Siu Lun Chau %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-zhang26f %I PMLR %P 8130--8165 %U https://proceedings.mlr.press/v337/zhang26f.html %V 337 %X Instrumental variable (IV) and proximal causal learning (Proxy) methods are central frameworks for causal inference in the presence of unobserved confounding. Despite substantial methodological advances, existing approaches rarely provide reliable epistemic uncertainty (EU) quantification. We address this gap through a Deconditional {Gaussian} Process (GP) framework for uncertainty-aware causal learning. Our formulation recovers popular kernel estimators as the posterior mean, ensuring predictive precision, while the posterior variance yields principled and well-calibrated EU. Moreover, the probabilistic structure enables systematic model selection via marginal log-likelihood optimization. Empirical results demonstrate strong predictive performance alongside informative EU quantification, evaluated via empirical coverage frequencies and decision-aware accuracy–rejection curves. Together, our approach provides a unified, practical solution for causal inference under unobserved confounding with reliable uncertainty.
APA
Zhang, Y., Muandet, K., Sejdinovic, D., Fong, E. & Chau, S.L.. (2026). Instrumental and Proximal Causal Inference with Gaussian Processes. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:8130-8165 Available from https://proceedings.mlr.press/v337/zhang26f.html.

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