Application of uncertainty measures on credal sets on the naive Bayesian classifier

Abstract

The naive Bayes classifier is known to obtain good results with a simple procedure. The method is based on the independence of the attribute variables given the variable to be classified. In real databases, where this hypothesis is not verified, this classifier continues to give good results. In order to improve the accuracy of the method, various works have been carried out in an attempt to reconstruct the set of the attributes and to join them so that there is independence between the new sets although the elements within each set are dependent. These methods are included in the ones known as semi-naive Bayes classifiers. In this article, we present an application of uncertainty measures on closed and convex sets of probability distributions, also called credal sets, in classification. We represent the information obtained from a database by a set of probability intervals (a credal set) via the imprecise Dirichlet model and we use uncertainty measures on credal sets in order to reconstruct the set of attributes, such as those mentioned, which shall enable us to improve the result of the naive Bayes classifier in a satisfactory way.