Partially Ordering Graphical Models with Latent Confounders by their Equality Constraints

Thijs van Ommen, W. J. Merijn Roelfsema
Proceedings of the 13th International Conference on Probabilistic Graphical Models, PMLR 343:881-894, 2026.

Abstract

A linear structural equation model can represent causal relations and latent confounders between its variables by means of directed and bidirected edges. The set of distributions in such a graphical model can be difficult to describe: conditional independence constraints do not suffice in this case, so more general equality constraints are needed. We present an algorithm that can check whether two linear structural equation models differ by an equality constraint. Using this algorithm, we empirically study the partially ordered set of these models, for different subclasses of mixed graphs. We show that for some of these classes, a natural generalization of Meek’s conjecture does not hold. We also investigate what set of constraints is needed to distinguish the models for various classes of graphs.

Cite this Paper

BibTeX
@InProceedings{pmlr-v343-ommen26a, title = {Partially Ordering Graphical Models with Latent Confounders by their Equality Constraints}, author = {van Ommen, Thijs and Roelfsema, W. J. Merijn}, booktitle = {Proceedings of the 13th International Conference on Probabilistic Graphical Models}, pages = {881--894}, 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/ommen26a/ommen26a.pdf}, url = {https://proceedings.mlr.press/v343/ommen26a.html}, abstract = {A linear structural equation model can represent causal relations and latent confounders between its variables by means of directed and bidirected edges. The set of distributions in such a graphical model can be difficult to describe: conditional independence constraints do not suffice in this case, so more general equality constraints are needed. We present an algorithm that can check whether two linear structural equation models differ by an equality constraint. Using this algorithm, we empirically study the partially ordered set of these models, for different subclasses of mixed graphs. We show that for some of these classes, a natural generalization of Meek’s conjecture does not hold. We also investigate what set of constraints is needed to distinguish the models for various classes of graphs.} }
Endnote
%0 Conference Paper %T Partially Ordering Graphical Models with Latent Confounders by their Equality Constraints %A Thijs van Ommen %A W. J. Merijn Roelfsema %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-ommen26a %I PMLR %P 881--894 %U https://proceedings.mlr.press/v343/ommen26a.html %V 343 %X A linear structural equation model can represent causal relations and latent confounders between its variables by means of directed and bidirected edges. The set of distributions in such a graphical model can be difficult to describe: conditional independence constraints do not suffice in this case, so more general equality constraints are needed. We present an algorithm that can check whether two linear structural equation models differ by an equality constraint. Using this algorithm, we empirically study the partially ordered set of these models, for different subclasses of mixed graphs. We show that for some of these classes, a natural generalization of Meek’s conjecture does not hold. We also investigate what set of constraints is needed to distinguish the models for various classes of graphs.
APA
van Ommen, T. & Roelfsema, W.J.M.. (2026). Partially Ordering Graphical Models with Latent Confounders by their Equality Constraints. Proceedings of the 13th International Conference on Probabilistic Graphical Models, in Proceedings of Machine Learning Research 343:881-894 Available from https://proceedings.mlr.press/v343/ommen26a.html.

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