  Bayesian network classifiers are used in many fields, and one common class of
classifiers are naive Bayes classifiers. In this paper, we introduce an
approach for reasoning about Bayesian network classifiers in which we
explicitly convert them into Ordered Decision Diagrams (ODDs), which are then
used to reason about the properties of these classifiers. Specifically, we
present an algorithm for converting any naive Bayes classifier into an ODD, and
we show theoretically and experimentally that this algorithm can give us an ODD
that is tractable in size even given an intractable number of instances. Since
ODDs are tractable representations of classifiers, our algorithm allows us to
efficiently test the equivalence of two naive Bayes classifiers and
characterize discrepancies between them. We also show a number of additional
results including a count of distinct classifiers that can be induced by
changing some CPT in a naive Bayes classifier, and the range of allowable
changes to a CPT which keeps the current classifier unchanged.
