  We present a growing dimension asymptotic formalism. The perspective in this
paper is classification theory and we show that it can accommodate
probabilistic networks classifiers, including naive Bayes model and its
augmented version. When represented as a Bayesian network these classifiers
have an important advantage: The corresponding discriminant function turns out
to be a specialized case of a generalized additive model, which makes it
possible to get closed form expressions for the asymptotic misclassification
probabilities used here as a measure of classification accuracy. Moreover, in
this paper we propose a new quantity for assessing the discriminative power of
a set of features which is then used to elaborate the augmented naive Bayes
classifier. The result is a weighted form of the augmented naive Bayes that
distributes weights among the sets of features according to their
discriminative power. We derive the asymptotic distribution of the sample based
discriminative power and show that it is seriously overestimated in a high
dimensional case. We then apply this result to find the optimal, in a sense of
minimum misclassification probability, type of weighting.
