Histogram distance-based Bayesian Network structure learning: A supervised classification specific approach

In this work we introduce a methodology based on histogram distances for the automatic induction of Bayesian Networks (BN) from a file containing cases and variables related to a supervised classification problem. The main idea consists of learning the Bayesian Network structure for classification purposes taking into account the classification itself, by comparing the class distribution histogram distances obtained by the Bayesian Network after classifying each case. The structure is learned by applying eight different measures or metrics: the Cooper and Herskovits metric for a general Bayesian Network and seven different statistical distances between pairs of histograms.The results obtained confirm the hypothesis of the authors about the convenience of having a BN structure learning method which takes into account the existence of the special variable (the one corresponding to the class) in supervised classification problems.