Convex sets of probability distributions are also called credal sets. They generalize probability theory with special regard to the relaxation of the precision requirement about the probability values. Classification, i.e., assigning class labels to instances described by a set of attributes, is a typical domain of application of Bayesian methods, where the naive Bayesian classifier is considered among the best tools. This paper explores the classification model obtained when the naive Bayesian classifier is extended to credal sets. Exact and effective solution procedures for classification are derived, and the related dominance criteria are discussed. A methodology to induce the classifier from data is proposed.
Keywords. Imprecise probabilities, credal sets, classication, naive Bayesian classification, Bayesian networks
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