Maximum a posteriori tree augmented naive Bayes classifiers

Bayesian classifiers such as Naive Bayes or Tree Augmented Naive Bayes (TAN) have shown excellent performance given their simplicity and heavy underlying independence assumptions. In this paper we prove that under suitable conditions it is possible to efficiently compute the maximum a posterior TAN model. Furthermore, we prove that it is also possible to efficiently calculate a weighted set with the k maximum a posteriori TAN models. This allows efficient TAN ensemble learning and accounting for model uncertainty. These results can be used to construct two classifiers. Both classifiers have the advantage of allowing the introduction of prior knowledge about structure or parameters into the learning process. Empirical results show that both classifiers lead to an improvement in error rate and accuracy of the predicted class probabilities over established TAN based classifiers with equivalent complexity.