Finite Mixture Model of Bounded Semi-naive Bayesian Networks Classifier

Abstract

The Semi-Naive Bayesian network (SNB) classifier, a probabilistic model with an assumption of conditional independence among the combined attributes, shows a good performance in classification tasks. However, the traditional SNBs can only combine two attributes into a combined attribute. This inflexibility together with its strong independency assumption may generate inaccurate distributions for some datasets and thus may greatly restrict the classification performance of SNBs. In this paper we develop a Bounded Semi-Naive Bayesian network (B-SNB) model based on direct combinatorial optimization. Our model can join any number of attributes within a given bound and maintains a polynomial time cost at the same time. This improvement expands the expressive ability of the SNB and thus provide potentials to increase accuracy in classification tasks. Further, aiming at relax the strong independency assumption of the SNB, we then propose an algorithm to extend the B-SNB into a finite mixture structure, named Mixture of Bounded Semi-Naive Bayesian network (MBSNB). We give theoretical derivations, outline of the algorithm, analysis of the algorithm and a set of experiments to demonstrate the usefulness of MBSNB in classification tasks. The novel finite MBSNB network shows a better classification performance in comparison with than other types of classifiers in this paper.