n this paper both weak points are addressed. A computationally more
efficient alternative to the first weak point is introduced and a well founded
softening alternative is proposed that solves the second weak point. More concretely,
we show that under the assumption of decomposable distributions over
TANs, we can efficiently compute the TAN model with a maximum a posteriori
(MAP) probability. This result allows the construction of maptan, a classifier
that provides a well founded alternative to the softening proposed in [7] and
improves its error rate and the accuracy of the predicted class probabilities.
Furthermore, we will also prove that under this assumption we can efficiently
compute the k most probable TAN models and their relative probabilities. This
result allows the construction of maptan+bma, a classifier that takes into consideration
model uncertainty to some extent and improves in time complexity
and accuracy over its equivalent presented in [3]. Furthermore, established TAN
classifiers do not easily allow the introduction of prior knowledge into the learning
process. Being able to compute MAP TAN structures means that we can
easily do that, whenever our prior knowledge can be represented as a decomposable
distribution over TANs.