Bayesian network classifiers which perform well with continuous attributes: Flexible classifiers

When modelling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous works have solved the problem by discretizing them with the consequent loss of information. Another common alternative assumes that the data are generated by a Gaussian distribution (parametric approach), such as conditional Gaussian networks, with the consequent error in the estimation if the true density differs from it. In order to break with the strong parametric assumption, this work introduces the conditional flexible network paradigm for supervised classification. This paradigm is a Bayesian network which estimates the true density of the continuous variables using kernels. Moreover, some of the most popular Bayesian multinomial network based classifier induction algorithms (naive Bayes, tree-augmented naive Bayes, k-dependence Bayesian classifier and Bayesian network-augmented naive Bayes) are adapted to the conditional flexible network paradigm. Besides their thresholded versions are introduced in order to avoid the compulsory addition of arcs between low correlated variables. The conditional flexible network can be seen as a generalization of the conditional Gaussian network because it allows a more flexible and precise estimation of the true densities. From the point of view of modelling correlations between predictor variables, the classifiers presented in this work can be seen as the natural extension of the flexible naive Bayes classifier proposed by John and Langley (1995) breaking with the naive Bayes independence assumption allowing dependencies between variables. Flexible tree-augmented naive Bayes seems to have superior behavior for the supervised classification among the flexible classifiers. Besides, flexible classifiers obtain quite competitive errors compared with the stateof-the-art classifiers.