Algebraic representation of generative classifier

We study the discrimination functions associated with classifiers induced by probabilistic graphical models and in particular Bayesian network classifiers. For every G -Markov probabilistic classifier we link the topology of the graph G with the class of discrimination functions induced, we prove that every conditional independence statement satisfied by the model implies linear constrains on the discrimination function. As an example we study the Naive Bayes model for two binary predictor variables and we formulate some questions for future work