Implementation of Continuous Bayesian Networks Using Sums of Weighted Gaussians
This work addresses a domain-specific challenge in probabilistic modeling for researchers and practitioners, but it appears incremental as it builds on existing Bayesian network frameworks.
The paper tackles the problem of extending Bayesian networks to handle continuous random variables by approximating probability densities with sums of weighted Gaussians and deriving propagation rules, resulting in a method demonstrated through a simple example that shows the impact of network structure and approximation errors on density computations.
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.