Learning Bayesian network classifiers for multidimensional supervised classification problems by means of a multiobjective approach

A classical supervised classification task tries to predict a single class variable based on a data set composed of a set of labeled examples. However, in many real domains more than one variable could be considered as a class variable, so a generalization of the single-class classification problem to the simultaneous prediction of a set of class variables should be developed. This problem is called multi-dimensional supervised classification. In this paper, we deal with the problem of learning Bayesian net work classifiers for multi-dimensional supervised classification problems. In order to do that, we have generalized the classical single-class Bayesian network classifier to the prediction of several class variables. In addition, we have defined new classification rules for probabilistic classifiers in multi-dimensional problems. We present a learning approach following a multi-objective strategy which considers the accuracy of each class variable separately as the functions to optimize. The solution of the learning approach is a Pareto set of non-dominated multi-dimensional Bayesian network classifiers and their accuracies for the different class variables, so a decision maker can easily choose by hand the classifier that best suits the particular problem and domain