Abstract

Convex sets of probability distributions are also called credal sets. They generalize probability theory by relaxing the requirement that probability values be precise. Classification, i.e. assigning class labels to instances described by a set of attributes, is an important domain of application of Bayesian methods, where the naive Bayes classifier has a surprisingly good performance. This paper proposes a new method of classification which involves extending the naive Bayes classifier to credal sets. Exact and effective solution procedures for naive credal classification are derived, and the related dominance criteria are discussed. Credal classification appears as a new method, based on more realistic assumptions and in the direction of more reliable inferences.

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