The Naive Hierarchical Credal Classifier
Authors: Alessandro Antonucci, Marco Cattaneo and Giorgio Corani
Abstract: The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substituting the uniform prior by the imprecise Dirichlet model. As an alternative to the naive credal classifier, we present a hierarchical likelihood-based approach, which extends in a novel way the naive Bayes towards imprecise probabilities; in particular, it considers any possible quantification (each one defining a naive Bayes classifier) apart from those assigning to the available data a probability below a given threshold level. Besides the available supervised data, in the likelihood evaluation we also consider the instance to be classified, for which the value of the class variable is assumed missing-at-random. We obtain a closed formula to compute the dominance according to the maximality criterion for any threshold level. As there are currently no well-established metrics for comparing credal classifiers which have considerably different determinacy, we compare the two classifiers when they have comparable determinacy, finding that in those cases they generate almost equivalent classifications.
Details: In ISIPTA '11: Proceedings of the seventh International Symposium on Imprecise Probability: Theories and Applications. SIPTA, pp. 21-30.
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