This study proposes and evaluates a novel Bayesian network classifier which can asymptotically estimate the true probability distribution of the class variable with the fewest class variable parameters among all structures for which the class variable has no parent. Moreover, to search for an optimal structure of the proposed classifier, we propose (1) a depth-first search based method and (2) an integer programming based method. The proposed methods are guaranteed to obtain the true probability distribution asymptotically while minimizing the number of class variable parameters. Comparative experiments using benchmark datasets demonstrate the effectiveness of the proposed method.

This study proposes and evaluates a new Bayesian network classifier (BNC) having an I-map structure with the fewest class variable parameters among all structures for which the class variable has no parent. Moreover, a new learning algorithm to learn our proposed model is presented. The proposed method is guaranteed to obtain the true classification probability asymptotically. Moreover, the method has lower computational costs than those of exact learning BNC using marginal likelihood. Comparison experiments have demonstrated the superior performance of the proposed method.