Implementation of Continuous Bayesian Networks Using Sums of Weighted Gaussians

TL;DR

This paper extends Bayesian networks to continuous variables by approximating probability densities with sums of weighted Gaussians, enabling density propagation and analysis of approximation errors.

Contribution

It introduces a method to compute continuous variable densities in Bayesian networks using Gaussian sums, including propagation rules and an illustrative example.

Findings

Effective approximation of densities with Gaussian sums

Propagation rules for continuous Bayesian networks

Impact of network structure and approximation errors

Abstract

Bayesian networks provide a method of representing conditional independence between random variables and computing the probability distributions associated with these random variables. In this paper, we extend Bayesian network structures to compute probability density functions for continuous random variables. We make this extension by approximating prior and conditional densities using sums of weighted Gaussian distributions and then finding the propagation rules for updating the densities in terms of these weights. We present a simple example that illustrates the Bayesian network for continuous variables; this example shows the effect of the network structure and approximation errors on the computation of densities for variables in the network.