When learning naive bayesian classifiers preserves monotonicity

Authors:
Barbara F. I. Pieters;Linda C. Van Der Gaag;Ad Feelders
Affiliations:
Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands;Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands;Department of Information and Computing Sciences, Utrecht University, Utrecht, The Netherlands
Venue:
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Year:
2011

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Abstract

Naive Bayesian classifiers are used in a large range of application domains. These models generally show good performance despite their strong underlying assumptions. In this paper, we demonstrate however, by means of an example probability distribution, that a data set of instances can give rise to a classifier with counterintuitive behaviour. We will argue that such behaviour can be attributed to the learning algorithm having constructed incorrect directions of monotonicity for some of the feature variables involved. We will further show that conditions can be derived for the learning algorithm to retrieve the correct directions.