Likelihood-Based Naive Credal Classifier
Alessandro Antonucci, Marco Cattaneo, Giorgio Corani · 2011
The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substitut-ing the imprecise Dirichlet model for the uniform prior. As an alternative to the naive credal classi-fier, we present a likelihood-based approach, which extends in a novel way the naive Bayes towards impre-cise probabilities, by considering any possible quan-tification (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 classi-fiers which have considerably different determinacy, we compare the two classifiers when they have com-parable determinacy, finding that in those cases they generate almost equivalent classifications.