Although undirected cycles in directed graphs of Bayesian belief networks have been thoroughly studied, little attention has so far been given to a systematic analysis of directed (feedback) cycles. In this paper we propose a way of looking at those cycles; namely, we suggest that a feedback cycle represents a family of probabilistic distributions rather than a single distribution (as a regular Bayesian belief network does). A non-empty family of distributions can be explicitly represented by an ideal of conjunctions with interval estimates on the probabilities of its elements. This ideal can serve as a probabilistic model of an experts uncertain knowledge pattern; such models are studied in the theory of algebraic Bayesian networks. The family of probabilistic distributions may also be empty; in this case, the probabilistic assignment over cycle nodes is inconsistent. We propose a simple way of explicating the probabilistic relationships an isolated directed cycle contains, give an algorithm (based on linear programming) of its consistency checking, and establish a lower bound of the complexity of this checking. © Springer-Verlag Berlin Heidelberg 2005.
CITATION STYLE
Tulupyev, A. L., & Nikolenko, S. I. (2005). Directed cycles in bayesian belief networks: Probabilistic semantics and consistency checking complexity. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 3789 LNAI, pp. 214–223). https://doi.org/10.1007/11579427_22
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