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arXiv · 2402.17087

A Note on Bayesian Networks with Latent Root Variables

Marco Zaffalon·Alessandro Antonucci
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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.

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Marco Zaffalon, Alessandro Antonucci. 2024-02-26. A Note on Bayesian Networks with Latent Root Variables. https://arxiv.org/abs/2402.17087

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