A Note on Bayesian Networks with Latent Root Variables

arXiv:2402.17087v1 Announce Type: cross
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 …

abstract arxiv bayesian call cs.ai cs.lg dataset distribution function likelihood manifest network networks nodes show stat.ml type variables