Data Mining: Foundations and Intelligent Paradigms

Volume 23 of the series Intelligent Systems Reference Library pp 49-93

Bayesian Networks with Imprecise Probabilities: Theory and Application to Classification

  • G. CoraniAffiliated withIDSIA
  • , A. AntonucciAffiliated withIDSIA
  • , M. ZaffalonAffiliated withIDSIA

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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.


Credal sets credal networks Bayesian networks classification credal classifiers naive Bayes classifier naive credal classifier tree-augmented naive Bayes classifier tree-augmented naive credal classifier