Directed Cycles in Bayesian Belief Networks: Probabilistic Semantics and Consistency Checking Complexity

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 al...

• Type: Conference
• Year: 2005
• Where: MICAI
• Authors: Alexander L. Tulupyev, Sergey I. Nikolenko
• Keywords: Artificial Intelligence, Bayesian Belief Network, MICAI 2005, Probabilistic, Probabilistic Distributions