  It has been argued that in supervised classification tasks, in practice it
may be more sensible to perform model selection with respect to some more
focused model selection score, like the supervised (conditional) marginal
likelihood, than with respect to the standard marginal likelihood criterion.
However, for most Bayesian network models, computing the supervised marginal
likelihood score takes exponential time with respect to the amount of observed
data. In this paper, we consider diagnostic Bayesian network classifiers where
the significant model parameters represent conditional distributions for the
class variable, given the values of the predictor variables, in which case the
supervised marginal likelihood can be computed in linear time with respect to
the data. As the number of model parameters grows in this case exponentially
with respect to the number of predictors, we focus on simple diagnostic models
where the number of relevant predictors is small, and suggest two approaches
for applying this type of models in classification. The first approach is based
on mixtures of simple diagnostic models, while in the second approach we apply
the small predictor sets of the simple diagnostic models for augmenting the
Naive Bayes classifier.
