Flexible and tractable modeling of multivariate data using composite Bayesian networks

Abstract

The article presents a new approach to modeling nonlinear dependencies called composite Bayesian networks. The main emphasis is on integrating machine learning models into Bayesian networks while maintaining their fundamental principles. The novelty of the approach is that it allows us to solve the problem of data inconsistency with traditional assumptions about dependencies. The presented method consists in selecting a variety of machine learning models at the stage of training composite Bayesian networks. This allows you to flexibly customize the nature of the dependencies in accordance with the requirements and dictated characteristics of the modeled object. The software implementation is made in the form of a specialized framework that describes all the necessary functionality. The results of experiments to evaluate the effectiveness of modeling dependencies between features are presented. Data for the experiments was taken from the bnlearn repository for benchmarks and from the UCI repository for real data. The performance of composite Bayesian networks was validated by comparing the likelihood and F1 score with classical Bayesian networks trained with the Hill-Climbing algorithm, demonstrating high accuracy in representing multivariate distributions. The improvement in benchmarks is insignificant since they contain linear dependencies that are well modeled by the classical algorithm. An average 30 % improvement in likelihood was obtained on real UCI datasets. The obtained data can be applied in areas that require modeling complex dependencies between features, for example, in machine learning, statistics, data analysis, as well as in specific subject areas.