Dealing with Cycles in Graph-Based Probabilistic Models: The Case of Logical Credal Networks
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
Text
Cozman et al. "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, 2025.Markdown
[Cozman et al. "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, 2025.](https://mlanthology.org/isipta/2025/cozman2025isipta-dealing/)BibTeX
@inproceedings{cozman2025isipta-dealing,
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 Mauá, Denis D.},
booktitle = {Proceedings of the Fourteenth International Symposium on Imprecise Probabilities: Theories and Applications},
year = {2025},
pages = {93-102},
volume = {290},
url = {https://mlanthology.org/isipta/2025/cozman2025isipta-dealing/}
}