On the Asymptotic Optimality of Maximum Margin Bayesian Networks

Maximum margin Bayesian networks (MMBNs) are Bayesian networks with dis-criminatively optimized parameters. They have shown good classification performance in various applications. However, there has not been any theoretic analysis of their asymptotic performance, e.g. their Bayes consistency. For specific classes of MMBNs, i.e. MMBNs with fully connected graphs and discrete-valued nodes, we show Bayes consistency for binary-class problems and a sufficient condition for Bayes consistency in the multi-class case. We provide simple examples showing that MMBNs in their current formulation are not Bayes consistent in general. These examples are especially in-teresting, as the model used for the MMBNs can represent the assumed true distributions. This indicates that the current formulations of MMBNs may be deficient. Furthermore, experimental results on the generalization performance are presented.