On the error probability of model selection for classification

We estimate a conditional probability P(y|x) of class y/spl isin/Y given attribute x/spl isin/X from training examples, where X and Y are respectively infinite and finite sets. The estimated conditional probability is used for classification in which a class y is guessed from an attribute x based on the conditional probability P(y|x). The procedure can be also applied to order identification of Markov models. We derive the asymptotically exact error probability in model selection for an arbitrary function d(/spl middot/) which determines the selection procedure as well as the information criterion.