Journal article

Margins of discrete Bayesian networks

RJ Evans

Annals of Statistics | Published : 2018

Abstract

Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper, we provide a complete algebraic characterization of these models when the observed variables are discrete and no assumption is made about the state-space of the latent variables. We show that it is algebraically equivalent to the so-called nested Markov model, meaning that the two are the same up to inequality constraints on the joint probabilities. In particular, these two models have the same dimension, differing only by inequality constraints for which there is no general description. The nested Markov model is therefore the closest possible description of the latent variable m..

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