Reasoning about Bayesian Network Classifiers

TL;DR

This paper introduces a method to convert naive Bayes classifiers into Ordered Decision Diagrams (ODDs) for efficient reasoning, enabling comparison and analysis of classifiers even with large datasets.

Contribution

The paper presents an algorithm for converting naive Bayes classifiers into tractable ODD representations, facilitating efficient reasoning and comparison of classifiers.

Findings

Conversion algorithm produces tractable ODDs for large datasets

Enables efficient testing of classifier equivalence

Characterizes the impact of CPT modifications on classifiers

Abstract

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.