A Note on Bayesian Networks with Latent Root Variables
Machine Learning
2024-02-28 v1 Artificial Intelligence
Machine Learning
Abstract
We characterise the likelihood function computed from a Bayesian network with latent variables as root nodes. We show that the marginal distribution over the remaining, manifest, variables also factorises as a Bayesian network, which we call empirical. A dataset of observations of the manifest variables allows us to quantify the parameters of the empirical Bayesian net. We prove that (i) the likelihood of such a dataset from the original Bayesian network is dominated by the global maximum of the likelihood from the empirical one; and that (ii) such a maximum is attained if and only if the parameters of the Bayesian network are consistent with those of the empirical model.
Cite
@article{arxiv.2402.17087,
title = {A Note on Bayesian Networks with Latent Root Variables},
author = {Marco Zaffalon and Alessandro Antonucci},
journal= {arXiv preprint arXiv:2402.17087},
year = {2024}
}