Development of optimal methods of logical inference in graphical probabilistic models based on Hamilton dynamics

Abstract

The research in different approaches to optimizing probabilistic inference in dynamic probabilistic models covers a wide range of tasks related to the search for effective methods of sample formation based on the Monte Carlo method. The use of Hamilton mechanics models makes it possible to evaluate stochastic distributions by solving the differential Hamilton equations. The study proposes to solve the problem of probabilistic inference in dynamic probability models, such as dynamic Bayesian networks, to use a hybrid approach based on a combination of Hamilton mechanics tools, Gibbs and Metropolis — Hastings’s algorithms. This approach, supplemented by computational parallelization tools, allows you to increase the efficiency of sampling and the accuracy of the posterior probability distribution. The article analyzes theoretical and practical issues related to the use of the Monte Carlo method, the Metropolis — Hastings algorithm, the Gibbs scheme and Hamilton dynamics models to form posterior distributions of static and dynamic Bayesian networks, reveals the features of generating consistent samples. The theoretical justification and computational experiment conducted on the basis of the developed software demonstrate the effectiveness of the proposed hybrid algorithm.