Constrained Naïve Bayes with application to unbalanced data classification

The Naïve Bayes is a tractable and efficient approach for statistical classification. In general classification problems, the consequences of misclassifications may be rather different in different classes, making it crucial to control misclassification rates in the most critical and, in many realworld problems, minority cases, possibly at the expense of higher misclassification rates in less problematic classes. One traditional approach to address this problem consists of assigning misclassification costs to the different classes and applying the Bayes rule, by optimizing a loss function. However, fixing precise values for such misclassification costs may be problematic in realworld applications. In this paper we address the issue of misclassification for the Naïve Bayes classifier. Instead of requesting precise values of misclassification costs, threshold values are used for different performance measures. This is done by adding constraints to the optimization problem underlying the estimation process. Our findings show that, under a reasonable computational cost, indeed, the performance measures under consideration achieve the desired levels yielding a user-friendly constrained classification procedure.