Markov Property in Generative Classifiers
This work addresses theoretical foundations for generative classifiers, offering incremental insights into their expressive power and integration with discriminative methods.
The paper demonstrates that conditional independence in generative classifiers corresponds to linear constraints on discrimination functions, enabling characterization of undirected Markov network classifiers and a method to combine discriminative and generative approaches.
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.