  We show that, for generative classifiers, conditional independence
corresponds to linear constraints for the induced discrimination functions.
Discrimination functions of undirected Markov network classifiers can thus be
characterized by sets of linear constraints. These constraints are represented
by a second order finite difference operator over functions of categorical
variables. As an application we study the expressive power of generative
classifiers under the undirected Markov property and we present a general
method to combine discriminative and generative classifiers.
