Application of junction tree clustering methods for solving dynamic Bayesian networks probabilistic inference tasks

Abstract

The article covers clustering algorithms for dynamic Bayesian networks based on the construction of join tree. Investigated problems associated with simplifying the topology of dynamic Bayesian networks using clustering methods and consider various semantic approaches of junction trees construction. The paper presents a junction tree constructing algorithm for the dynamic Bayesian network that takes into account the transition and perception models applied to the process of network formation. Analyzed The relationship between the complete joint probability distribution for the dynamic Bayesian network and the complete joint distribution obtained for the junction tree. It is shown that the required complete joint distribution of the junction tree for the dynamic Bayesian network can be obtained as a product of local probability distributions for each node associated with the resulting junction tree, and proved that this distribution will be equivalent to the probability distribution of the original dynamic Bayesian network. Introduced the main structural approaches to the construction of junction tree for the discrete dynamic Bayesian network and inspected the use of junction tree for solving similar problems for continuous dynamic Bayesian networks with Gaussian and exponential distribution functions of network variables.