Development of the hybrid algorithm of tutoring of structure of dynamic Bayesian networkon the basis of the Levenberg-Markvardt method

Dynamic Bayesian networks are used quite effectively for modeling complex stochastic processes of modern multi-user information and communication systems. Dynamic Bayesian networks are graphical probabilistic models that reflect topology and stochastic cause and effect relationships between elements of the handled simulated information processes. The construction of topologies of dynamic Bayesian networks that appropriately reflect the probabilistic and functional relationships between the elements of such processes is a main factor in the simulation using this tool. Network topology usually built either by expert means or be means of training. Training mechanisms allow to get spanning tree of the network, as well as to determine the conditional connections and their direction between the individual vertices of the network. In this article regard the usage of mathematical apparatus for testing statistical hypotheses based on conditional independency tests between random variables with the Pearson criteria, Schwartz, Akaike and Bayes-Dirichlet metrics. Unlike static Bayesian networks, when determining the structure of dynamic Bayesian networks, it is necessary to determine variables and relations between them not only within one slice, but also between variables of different slices, which implement transitive connections between the time slices that reflect functioning of a certain process or object. The construction of structure of transitive links between slices is a rather complex and problematic step in almost all existing algorithms. This article presents an algorithm for learning the structure of a dynamic Bayesian network based on the Levenberg-Marquardt method within the optimization of algorithms for constructing dynamic Bayesian networks with transitive links between slices.