[UAI] Attribute relevance in Naive Bayes models.

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Hi all,

I was inspired by the recent discussion on degree of relevance in
Bayesian models. Is there any work on deciding on attribute
relevance/irrelevance for clustering via Naive Bayes models?
As an example consider two competing Naive Bayes models
model 1: on nodes H (hidden) and A1, A2, A3
     H
    /|\
  |/ V \|
 A1 A2 A3
and model 2: same nodes, with distribution of A3 being independent of H
     H
    /|
  |/ V
 A1 A2 A3

Now, if by some model selection mechanism (e.g. BIC) we prefer model 2
over model 1 then
attribute A3 is irrelevant.
Is there any work in this direction?

Another question: What are the common methods for deciding the number of
classes (hidden states) in Naive Bayes models? Had someone tried to do
it by the model selection procedures (e.g. compare two models with
different number of hidden states)?

Thank you in advance,
Dmitry.

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