Accounting for Data Uncertainty in Counterfactual Reasoning

Rafael Cabañas, Helge Langseth, Thomas D. Nielsen, Antonio Salmerón
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:153-166, 2026.

Abstract

Structural causal models with discrete variables are a class of probabilistic graphical models used for causal and counterfactual reasoning. In the presence of observational (i.e., non-experimental) data, some queries in such models are non-identifiable and therefore cannot be computed exactly. Instead, several methods derive bounds on non-identifiable queries by solving linear programming problems. However, these methods usually assume a precise specification of the data distribution. In this work, we consider a more realistic scenario in which uncertainty in the data is represented through an interval-valued specification of the data distribution. We formulate the corresponding linear programming problem under this setting, which covers both identifiable and non-identifiable counterfactual queries under data uncertainty. We show how a recently proposed divide-and-conquer algorithm for bounding counterfactual probabilities (Bj{ø}ru et al., 2025) can be adapted to such imprecise specifications of the data distribution without a substantial increase in computational complexity.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-cabanas26a, title = {Accounting for Data Uncertainty in Counterfactual Reasoning}, author = {{Caba\~{n}as}, Rafael and Langseth, Helge and Nielsen, Thomas D. and {Salmer\'{o}n}, Antonio}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {153--166}, year = {2026}, editor = {Camps-Valls, Gustau and Leonelli, Manuele and Varando, Gherardo}, volume = {343}, series = {Proceedings of Machine Learning Research}, month = {09--11 Sep}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v343/main/assets/cabanas26a/cabanas26a.pdf}, url = {https://proceedings.mlr.press/v343/cabanas26a.html}, abstract = {Structural causal models with discrete variables are a class of probabilistic graphical models used for causal and counterfactual reasoning. In the presence of observational (i.e., non-experimental) data, some queries in such models are non-identifiable and therefore cannot be computed exactly. Instead, several methods derive bounds on non-identifiable queries by solving linear programming problems. However, these methods usually assume a precise specification of the data distribution. In this work, we consider a more realistic scenario in which uncertainty in the data is represented through an interval-valued specification of the data distribution. We formulate the corresponding linear programming problem under this setting, which covers both identifiable and non-identifiable counterfactual queries under data uncertainty. We show how a recently proposed divide-and-conquer algorithm for bounding counterfactual probabilities (Bj{ø}ru et al., 2025) can be adapted to such imprecise specifications of the data distribution without a substantial increase in computational complexity.} }
Endnote
%0 Conference Paper %T Accounting for Data Uncertainty in Counterfactual Reasoning %A Rafael Cabañas %A Helge Langseth %A Thomas D. Nielsen %A Antonio Salmerón %B Proceedings of the 13th International Conference on Probabilistic Graphical Models %C Proceedings of Machine Learning Research %D 2026 %E Gustau Camps-Valls %E Manuele Leonelli %E Gherardo Varando %F pmlr-v343-cabanas26a %I PMLR %P 153--166 %U https://proceedings.mlr.press/v343/cabanas26a.html %V 343 %X Structural causal models with discrete variables are a class of probabilistic graphical models used for causal and counterfactual reasoning. In the presence of observational (i.e., non-experimental) data, some queries in such models are non-identifiable and therefore cannot be computed exactly. Instead, several methods derive bounds on non-identifiable queries by solving linear programming problems. However, these methods usually assume a precise specification of the data distribution. In this work, we consider a more realistic scenario in which uncertainty in the data is represented through an interval-valued specification of the data distribution. We formulate the corresponding linear programming problem under this setting, which covers both identifiable and non-identifiable counterfactual queries under data uncertainty. We show how a recently proposed divide-and-conquer algorithm for bounding counterfactual probabilities (Bj{ø}ru et al., 2025) can be adapted to such imprecise specifications of the data distribution without a substantial increase in computational complexity.
APA
Cabañas, R., Langseth, H., Nielsen, T.D. & Salmerón, A.. (2026). Accounting for Data Uncertainty in Counterfactual Reasoning. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:153-166 Available from https://proceedings.mlr.press/v343/cabanas26a.html.

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