Learning extended tree augmented naive structures

Abstract

This work proposes an extended version of the well-known tree-augmented naive Bayes (TAN) classifier where the structure learning step is performed without requiring features to be connected to the class. Based on a modification of Edmonds' algorithm, our structure learning procedure explores a superset of the structures that are considered by TAN, yet achieves global optimality of the learning score function in a very efficient way (quadratic in the number of features, the same complexity as learning TANs). We enhance our procedure with a new score function that only takes into account arcs that are relevant to predict the class, as well as an optimization over the equivalent sample size during learning. These ideas may be useful for structure learning of Bayesian networks in general. A range of experiments shows that we obtain models with better prediction accuracy than naive Bayes and TAN, and comparable to the accuracy of the state-of-the-art classifier averaged one-dependence estimator (AODE). We release our implementation of ETAN so that it can be easily installed and run within Weka. • New Bayesian network structure learning approach to extend the Tree Augmented Naive (TAN) classifier. • Efficient implementation of TAN and Extended-TAN using the Edmonds algorithm for directed weighted spanning trees. • Alternative approach to well-known classifiers such as TAN and AODE. • Missing data can be treated without the need of data imputation. • Easy-to-install Weka plugin.