Interventional Processes For Causal Uncertainty Quantification

Hugh Dance, Peter Orbanz, Arthur Gretton
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:22758-22807, 2026.

Abstract

Reliable uncertainty quantification for causal effects is crucial in high-stakes applications, but remains challenging when the target is an entire function rather than a scalar estimand. In this work, we introduce a GP-based approach for uncertainty quantification of interventional functions. The central idea is to build on recent work representing interventional functions as an inner-product of observational functions in a reproducing kernel Hilbert space (RKHS), by constructing appropriate GP priors for such functions and inferring posteriors from observational data. Our approach yields closed-form posterior moments and tractable training and inference, while avoiding pathologies of previous GP prior constructions for RKHS functions. We further derive a practical procedure for posterior coverage calibration. Across synthetic benchmarks, causal Bayesian optimization tasks, and a large-scale real dataset, our method improves uncertainty quantification while remaining competitive in causal effect estimation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-dance26a, title = {Interventional Processes For Causal Uncertainty Quantification}, author = {Dance, Hugh and Orbanz, Peter and Gretton, Arthur}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {22758--22807}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/dance26a/dance26a.pdf}, url = {https://proceedings.mlr.press/v306/dance26a.html}, abstract = {Reliable uncertainty quantification for causal effects is crucial in high-stakes applications, but remains challenging when the target is an entire function rather than a scalar estimand. In this work, we introduce a GP-based approach for uncertainty quantification of interventional functions. The central idea is to build on recent work representing interventional functions as an inner-product of observational functions in a reproducing kernel Hilbert space (RKHS), by constructing appropriate GP priors for such functions and inferring posteriors from observational data. Our approach yields closed-form posterior moments and tractable training and inference, while avoiding pathologies of previous GP prior constructions for RKHS functions. We further derive a practical procedure for posterior coverage calibration. Across synthetic benchmarks, causal Bayesian optimization tasks, and a large-scale real dataset, our method improves uncertainty quantification while remaining competitive in causal effect estimation.} }
Endnote
%0 Conference Paper %T Interventional Processes For Causal Uncertainty Quantification %A Hugh Dance %A Peter Orbanz %A Arthur Gretton %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-dance26a %I PMLR %P 22758--22807 %U https://proceedings.mlr.press/v306/dance26a.html %V 306 %X Reliable uncertainty quantification for causal effects is crucial in high-stakes applications, but remains challenging when the target is an entire function rather than a scalar estimand. In this work, we introduce a GP-based approach for uncertainty quantification of interventional functions. The central idea is to build on recent work representing interventional functions as an inner-product of observational functions in a reproducing kernel Hilbert space (RKHS), by constructing appropriate GP priors for such functions and inferring posteriors from observational data. Our approach yields closed-form posterior moments and tractable training and inference, while avoiding pathologies of previous GP prior constructions for RKHS functions. We further derive a practical procedure for posterior coverage calibration. Across synthetic benchmarks, causal Bayesian optimization tasks, and a large-scale real dataset, our method improves uncertainty quantification while remaining competitive in causal effect estimation.
APA
Dance, H., Orbanz, P. & Gretton, A.. (2026). Interventional Processes For Causal Uncertainty Quantification. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:22758-22807 Available from https://proceedings.mlr.press/v306/dance26a.html.

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