Evidence and scenario sensitivities in naive Bayesian classifiers

Authors:
Silja Renooij;Linda C. van der Gaag
Affiliations:
Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands;Department of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands
Venue:
International Journal of Approximate Reasoning
Year:
2008

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Abstract

Empirical evidence shows that naive Bayesian classifiers perform quite well compared to more sophisticated classifiers, even in view of inaccuracies in their parameters. In this paper, we study the effects of such parameter inaccuracies by investigating the sensitivity functions of a naive Bayesian network. We show that, as a consequence of the network's independence properties, these sensitivity functions are highly constrained. We further investigate whether the patterns of sensitivity that follow from these functions support the observed robustness of naive Bayesian classifiers. In addition to standard sensitivities given available evidence, we also study the effect of parameter inaccuracies in view of scenarios of additional evidence. We show that standard sensitivity functions suffice to describe such scenario sensitivities.