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 calculate efficiently the maximum
a posterior TAN model. Furthermore, we prove that it is also possible
to 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.
Keywords: Bayesian networks, Bayesian network classifiers, Naive
Bayes, decomposable distributions, Bayesian model averaging.