Reasoning about Bayesian Network Classifiers
This provides a method for analyzing and verifying naive Bayes classifiers, which is incremental as it builds on existing ODD techniques for a specific domain.
The paper tackles the problem of reasoning about Bayesian network classifiers by converting naive Bayes classifiers into Ordered Decision Diagrams (ODDs), enabling efficient equivalence testing and discrepancy characterization with tractable size even for intractable instance numbers.
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.