Canonical Domain Reduction for Partial Counterfactual Identification

Yesong Choe, Yeahoon Kwon, Min Woo Park, Sanghack Lee
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:1302-1326, 2026.

Abstract

Many counterfactual and causal queries are only partially identified from data, especially under unmeasured confounding. A common approach represents compatible nonparametric structural causal models (SCMs) on a finite canonical domain and computes sharp bounds via linear programming (LP) over the induced simplex. However, the canonical full counterfactual state space grows exponentially even for small graphs, making naive LP-based bounding computationally heavy. We propose a constraint-aware reduction that quotients out degrees of freedom irrelevant to the optimization problem. Because sharp bounds are determined jointly by the query functional and the data-implied information set, we aggregate full states into equivalence classes that are indistinguishable to every linear functional appearing in the LP objective and constraints. We show that optimizing over the induced push-forward distribution on the reduced domain preserves feasibility and yields the same sharp bounds as the full-domain.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-choe26a, title = {Canonical Domain Reduction for Partial Counterfactual Identification}, author = {Choe, Yesong and Kwon, Yeahoon and Park, Min Woo and Lee, Sanghack}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {1302--1326}, 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/choe26a/choe26a.pdf}, url = {https://proceedings.mlr.press/v337/choe26a.html}, abstract = {Many counterfactual and causal queries are only partially identified from data, especially under unmeasured confounding. A common approach represents compatible nonparametric structural causal models (SCMs) on a finite canonical domain and computes sharp bounds via linear programming (LP) over the induced simplex. However, the canonical full counterfactual state space grows exponentially even for small graphs, making naive LP-based bounding computationally heavy. We propose a constraint-aware reduction that quotients out degrees of freedom irrelevant to the optimization problem. Because sharp bounds are determined jointly by the query functional and the data-implied information set, we aggregate full states into equivalence classes that are indistinguishable to every linear functional appearing in the LP objective and constraints. We show that optimizing over the induced push-forward distribution on the reduced domain preserves feasibility and yields the same sharp bounds as the full-domain.} }
Endnote
%0 Conference Paper %T Canonical Domain Reduction for Partial Counterfactual Identification %A Yesong Choe %A Yeahoon Kwon %A Min Woo Park %A Sanghack Lee %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-choe26a %I PMLR %P 1302--1326 %U https://proceedings.mlr.press/v337/choe26a.html %V 337 %X Many counterfactual and causal queries are only partially identified from data, especially under unmeasured confounding. A common approach represents compatible nonparametric structural causal models (SCMs) on a finite canonical domain and computes sharp bounds via linear programming (LP) over the induced simplex. However, the canonical full counterfactual state space grows exponentially even for small graphs, making naive LP-based bounding computationally heavy. We propose a constraint-aware reduction that quotients out degrees of freedom irrelevant to the optimization problem. Because sharp bounds are determined jointly by the query functional and the data-implied information set, we aggregate full states into equivalence classes that are indistinguishable to every linear functional appearing in the LP objective and constraints. We show that optimizing over the induced push-forward distribution on the reduced domain preserves feasibility and yields the same sharp bounds as the full-domain.
APA
Choe, Y., Kwon, Y., Park, M.W. & Lee, S.. (2026). Canonical Domain Reduction for Partial Counterfactual Identification. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:1302-1326 Available from https://proceedings.mlr.press/v337/choe26a.html.

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