A Pairwise Naïve Bayes Approach to Bayesian Classification

Despite the relatively high accuracy of the naïve Bayes (NB) classifier, there may be several instances where it is not optimal, i.e. does not have the same classification performance as the Bayes classifier utilizing the joint distribution of the examined attributes. However, the Bayes classifier can be computationally intractable due to its required knowledge of the joint distribution. Therefore, we introduce a "pairwise naïve" Bayes (PNB) classifier that incorporates all pairwise relationships among the examined attributes, but does not require specification of the joint distribution. In this paper, we first describe the necessary and sufficient conditions under which the PNB classifier is optimal. We then discuss sufficient conditions for which the PNB classifier, and not NB, is optimal for normal attributes. Through simulation and actual studies, we evaluate the performance of our proposed classifier relative to the Bayes and NB classifiers, along with the HNB, AODE, LBR and TAN classifiers, using normal density and empirical estimation methods. Our applications show that the PNB classifier using normal density estimation yields the highest accuracy for data sets containing continuous attributes. We conclude that it offers a useful compromise between the Bayes and NB classifiers.