Gaussian mixture modeling of nodes in Bayesian network according to maximal parental cliques

TL;DR

This paper introduces a Gaussian mixture model approach for nodes in Bayesian networks, replacing linear Gaussian models, and proposes a double iteration algorithm combining EM and gradient descent for optimization, validated on real data.

Contribution

It presents a novel Gaussian mixture modeling approach for Bayesian network nodes and a new double iteration algorithm for effective optimization.

Findings

Gaussian mixture models outperform linear Gaussian models in fitting node distributions

The double iteration algorithm effectively optimizes mixture models in Bayesian networks

Experimental results demonstrate improved modeling on real-world datasets

Abstract

This paper uses Gaussian mixture model instead of linear Gaussian model to fit the distribution of every node in Bayesian network. We will explain why and how we use Gaussian mixture models in Bayesian network. Meanwhile we propose a new method, called double iteration algorithm, to optimize the mixture model, the double iteration algorithm combines the expectation maximization algorithm and gradient descent algorithm, and it performs perfectly on the Bayesian network with mixture models. In experiments we test the Gaussian mixture model and the optimization algorithm on different graphs which is generated by different structure learning algorithm on real data sets, and give the details of every experiment.