Bayesian networks with imprecise probabilities: theory and application to classification

Corani, Giorgio and Antonucci, Alessandro and Zaffalon, Marco (2012) Bayesian networks with imprecise probabilities: theory and application to classification. In: Data Mining: Foundations and Intelligent Paradigms. Intelligent Systems Reference Library, 23 . Springer, Berlin / Heidelberg, pp. 49-93. ISBN 978-3-642-23165-0

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Bayesian networks are powerful probabilistic graphical models for modelling uncertainty. Among others, classification represents an important application: some of the most used classifiers are based on Bayesian networks. Bayesian networks are precise models: exact numeric values should be provided for quantification. This requirement is sometimes too narrow. Sets instead of single distributions can provide a more realistic description in these cases. Bayesian networks can be generalized to cope with sets of distributions. This leads to a novel class of imprecise probabilistic graphical models, called credal networks. In particular, classifiers based on Bayesian networks are generalized to so-called credal classifiers. Unlike Bayesian classifiers, which always detect a single class as the one maximizing the posterior class probability, a credal classifier may eventually be unable to discriminate a single class. In other words, if the available information is not sufficient, credal classifiers allow for indecision between two or more classes, this providing a less informative but more robust conclusion than Bayesian classifiers.

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