Markov processes in Bayesian network computation

Abstract

The article examines the influence of Markov processes on computations in Bayesian networks (BN), an important area of research within probabilistic graphical models. The concept of Bayesian Markov networks (BMN) is introduced, an extension of traditional Bayesian networks with the addition of a Markov constraint, according to which the probability in a node can only depend on the state of neighboring nodes. This constraint makes the model more realistic for many practical tasks, as most graphical models that reflect real-world processes possess the Markov property. The article also discusses that Bayesian networks, in the absence of evidence, actually exhibit the Markov property. However, when evidence (additional information) is introduced into the model, challenges arise that require more complex computational methods. In response, the article proposes algorithms adapted for working with Bayesian Markov networks in the presence of evidence. These algorithms are aimed at optimizing computations and reducing computational complexity. Additionally, a comparative analysis of calculations in Bayesian networks without Markov constraints and with them is conducted, highlighting the advantages and disadvantages of each approach. Special attention is paid to the practical applications of the proposed methods and their effectiveness in various scenarios.