Counterfactual Graphical Models: Constraints and Inference

Juan D. Correa, Elias Bareinboim
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:11245-11254, 2025.

Abstract

Graphical models have been widely used as parsimonious encoders of constraints of the underlying probability models. When organized in a structured way, these models can facilitate the derivation of non-trivial constraints, the inference of quantities of interest, and the optimization of their estimands. In particular, causal diagrams allow for the efficient representation of structural constraints of the underlying causal system. In this paper, we introduce an efficient graphical construction called Ancestral Multi-world Networks that is sound and complete for reading counterfactual independences from a causal diagram using d-separation. Moreover, we introduce the counterfactual (ctf-) calculus, which can be used to transform counterfactual quantities using three rules licensed by the constraints encoded in the diagram. This result generalizes Pearl’s celebrated do-calculus from interventional to counterfactual reasoning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-correa25a, title = {Counterfactual Graphical Models: Constraints and Inference}, author = {Correa, Juan D. and Bareinboim, Elias}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {11245--11254}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/correa25a/correa25a.pdf}, url = {https://proceedings.mlr.press/v267/correa25a.html}, abstract = {Graphical models have been widely used as parsimonious encoders of constraints of the underlying probability models. When organized in a structured way, these models can facilitate the derivation of non-trivial constraints, the inference of quantities of interest, and the optimization of their estimands. In particular, causal diagrams allow for the efficient representation of structural constraints of the underlying causal system. In this paper, we introduce an efficient graphical construction called Ancestral Multi-world Networks that is sound and complete for reading counterfactual independences from a causal diagram using d-separation. Moreover, we introduce the counterfactual (ctf-) calculus, which can be used to transform counterfactual quantities using three rules licensed by the constraints encoded in the diagram. This result generalizes Pearl’s celebrated do-calculus from interventional to counterfactual reasoning.} }
Endnote
%0 Conference Paper %T Counterfactual Graphical Models: Constraints and Inference %A Juan D. Correa %A Elias Bareinboim %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-correa25a %I PMLR %P 11245--11254 %U https://proceedings.mlr.press/v267/correa25a.html %V 267 %X Graphical models have been widely used as parsimonious encoders of constraints of the underlying probability models. When organized in a structured way, these models can facilitate the derivation of non-trivial constraints, the inference of quantities of interest, and the optimization of their estimands. In particular, causal diagrams allow for the efficient representation of structural constraints of the underlying causal system. In this paper, we introduce an efficient graphical construction called Ancestral Multi-world Networks that is sound and complete for reading counterfactual independences from a causal diagram using d-separation. Moreover, we introduce the counterfactual (ctf-) calculus, which can be used to transform counterfactual quantities using three rules licensed by the constraints encoded in the diagram. This result generalizes Pearl’s celebrated do-calculus from interventional to counterfactual reasoning.
APA
Correa, J.D. & Bareinboim, E.. (2025). Counterfactual Graphical Models: Constraints and Inference. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:11245-11254 Available from https://proceedings.mlr.press/v267/correa25a.html.

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