Appliance for improving the efficiency of numerical methods of structure learning algorithms for dynamic bayesian networks

Abstract

Dynamic Bayesian network models are used to describe processes in the conditions of risk and uncertainty, the random nature have not only the vertices of the network, but communication between nodes. To determine the presence of causal relationships and their orientation, special expert and statistical methods of the network structure and learning are used. When using expert methods for constructing Bayesian networks, the graph structure is set by the expert on the basis of his experience in the research area, and then only the network parameters corresponding to the conditional probability distributions of the network vertices are trained. It is not always possible for the expert to correctly determine causal relationships between the vertices of the network and their direction. Formalized procedures for the network structure and parameters learning are quite effective. Formalized methods of learning network structure include the stage of determining the relationship between the vertices of the network and the stage of determining the direction of relations. The stage of determining the direction of learning is local in nature and involves the solution of a number of optimization problems. As a rule, numerical optimization algorithms are used as learning algorithms for dynamic Bayesian networks. Due to the large dimension of solving problems, the efficiency of dynamic Bayesian network learning procedures depends on the efficiency of the numerical algorithms. Numerical algorithms based on the Newtonian approach are often used. This article describes the use of various tools to improve the efficiency of Newtonian algorithms for solving problems of learning the structure of dynamic Bayesian networks. The use of the methods of Broyden, Davidon-Fletcher-Powell and Broyden-Fletcher-Goldfarb-Shanno can significantly improve the efficiency of the algorithms, as well as makes it possible to use the parallelization of individual blocks.