On the optimality of Naïve Bayes with dependent binary features

Authors:
Ludmila I. Kuncheva
Affiliations:
School of Informatics, University of Wales, Dean Street, Bangor, Gwynedd LL57 1UT, UK
Venue:
Pattern Recognition Letters
Year:
2006

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Abstract

While Naive Bayes classifier (NB) is Bayes-optimal for independent features, we prove that it is also optimal for two equiprobable classes and two features with equal class-conditional covariances. Although strict optimality does not extend for three features, equal covariances are expected to be beneficial in higher-dimensional spaces.