### Alessandro Antonucci, Marco Cattaneo, Giorgio Corani

## Likelihood-Based Naive Credal Classifier

### Abstract

The naive credal classifier extends the classical naive Bayes classifier to imprecise probabilities, substituting the imprecise Dirichlet model for the uniform prior. As an alternative to the naive credal classifier, we present a likelihood-based approach, which extends in a novel way the naive Bayes towards imprecise probabilities, by considering 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.

### Keywords

Classification, naive credal classifier, naive Bayes classifier, likelihood-based learning.

### Download area

The paper is available in the following formats:

Plenary talk:
file

Poster:
file

### Authors’ addresses

**Alessandro Antonucci**

c/o IDSIA

Galleria 2

CH-6928 Manno (Lugano)

**Marco Cattaneo**

Institut fuer Statistik

Ludwig-Maximilians-Universitaet Muenchen

Ludwigstrasse 33

80539 Muenchen

**Giorgio Corani**

IDSIA

CH-6928 Manno

Lugano

Switzerland

### E-mail addresses