Dealing with cycles in graph-based probabilistic models: the case of Logical Credal Networks

Fabio G. Cozman, Radu Marinescu, Junkyu Lee, Alexander Gray, Denis D. Mauá
Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, PMLR 290:93-102, 2025.

Abstract

We examine the consequences of directed cycles in graph-based representations of joint distributions, investigating the effect of cycles on Markov conditions and on Gibbs factorizations. We focus on Logical Credal Networks, a flexible and general formalism, showing that Koster’s theory of Directed-Undirected Mixed Graphs (DUMGs) leads to an interesting Gibbs factorization. We show that inferences with DUMGs lead to multilinear programs. We also study the failure of global Markov conditions in cyclic structural equation models, connecting that failure to probabilistic imprecision under interventions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v290-cozman25a, title = {Dealing with cycles in graph-based probabilistic models: the case of Logical Credal Networks}, author = {Cozman, Fabio G. and Marinescu, Radu and Lee, Junkyu and Gray, Alexander and Mau\'a, Denis D.}, booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications}, pages = {93--102}, year = {2025}, editor = {Destercke, Sébastien and Erreygers, Alexander and Nendel, Max and Riedel, Frank and Troffaes, Matthias C. M.}, volume = {290}, series = {Proceedings of Machine Learning Research}, month = {15--18 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v290/main/assets/cozman25a/cozman25a.pdf}, url = {https://proceedings.mlr.press/v290/cozman25a.html}, abstract = {We examine the consequences of directed cycles in graph-based representations of joint distributions, investigating the effect of cycles on Markov conditions and on Gibbs factorizations. We focus on Logical Credal Networks, a flexible and general formalism, showing that Koster’s theory of Directed-Undirected Mixed Graphs (DUMGs) leads to an interesting Gibbs factorization. We show that inferences with DUMGs lead to multilinear programs. We also study the failure of global Markov conditions in cyclic structural equation models, connecting that failure to probabilistic imprecision under interventions.} }
Endnote
%0 Conference Paper %T Dealing with cycles in graph-based probabilistic models: the case of Logical Credal Networks %A Fabio G. Cozman %A Radu Marinescu %A Junkyu Lee %A Alexander Gray %A Denis D. Mauá %B Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications %C Proceedings of Machine Learning Research %D 2025 %E Sébastien Destercke %E Alexander Erreygers %E Max Nendel %E Frank Riedel %E Matthias C. M. Troffaes %F pmlr-v290-cozman25a %I PMLR %P 93--102 %U https://proceedings.mlr.press/v290/cozman25a.html %V 290 %X We examine the consequences of directed cycles in graph-based representations of joint distributions, investigating the effect of cycles on Markov conditions and on Gibbs factorizations. We focus on Logical Credal Networks, a flexible and general formalism, showing that Koster’s theory of Directed-Undirected Mixed Graphs (DUMGs) leads to an interesting Gibbs factorization. We show that inferences with DUMGs lead to multilinear programs. We also study the failure of global Markov conditions in cyclic structural equation models, connecting that failure to probabilistic imprecision under interventions.
APA
Cozman, F.G., Marinescu, R., Lee, J., Gray, A. & Mauá, D.D.. (2025). Dealing with cycles in graph-based probabilistic models: the case of Logical Credal Networks. Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications, in Proceedings of Machine Learning Research 290:93-102 Available from https://proceedings.mlr.press/v290/cozman25a.html.

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