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

We examine the consequences of directed cycles in raph-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.