A Semi-Algebraic Description of Naive Bayes Models with Two Hidden Classes

Discrete Bayesian network models with hidden variables de ne an important class of statistical models. These models are usually de ned parametrically, but can also be described semi-algebraically as the solutions in the probability simplex of a nite set of polynomial equations and inequations. In this paper we present a semi-algebraic description of discrete Naive Bayes models with two hidden classes and a nite number of observable variables. The identi ability of the parameters is also studied. Our derivations are based on an alternative parametrization of the Naive Bayes models with an arbitrary number of hidden classes.