Bayesian network equivalence analysis via bayesian — dirichlet asymptotic score

Abstract

Dynamic and static Bayesian networks are an effective tool for modeling stochastic processes. The areas of practical implementation of these models have significantly expanded recently. The quality of their application in solving practical problems is largely determined by the capabilities of algorithms for learning the structure and probabilistic parameters of models that allow the network to be configured to solve the range of applied problems under consideration. Tools based on equivalence principles play an important role in the algorithms for determining the optimal structure of Bayesian networks and the modification of algorithms for setting their parameters. On the basis of the equivalence principle, asymptotic estimates of transformations obtained in the process of adding, changing or deleting individual nodes of the Bayesian network graph are formed and an apparatus for obtaining a local a priori distribution for each of the network parameters is created. In this paper, we study tools for estimating the equivalence of Bayesian networks based on the Bayes-Dirichlet metric, the Hamming and Kullbak-Leibler structural distance. These tools can also be applied to dynamic Bayesian networks, for working with which it is additionally necessary to determine the structure of the transition model between time slices. In the framework of the study, the issues of equivalence of a priori probability distributions formed in the process of parameter learning are also considered. In the final part of the paper, a computational experiment is presented that reflects the effectiveness of using various learning algorithms from the point of view of comparing their results with equivalent reference Bayesian networks. The tools proposed in the work allow adapting static and dynamic Bayesian models to solve practical problems, optimizing the learning processes of these models by equivalence principle of graphical probabilistic models.