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The Naive-Bayes classifier is widely used due to its simplicity, speed andaccuracy. However this approach fails when, for at least one attribute value ina test sample, there are no corresponding training samples with that attributevalue. This is known as the zero frequency problem and is typically addressedusing Laplace Smoothing. However, Laplace Smoothing does not take into accountthe statistical characteristics of the neighbourhood of the attribute values ofthe test sample. Gaussian Naive Bayes addresses this but the resulting Gaussianmodel is formed from global information. We instead propose an approach thatestimates conditional probabilities using information in the neighbourhood ofthe test sample. In this case we no longer need to make the assumption ofindependence of attribute values and hence consider the joint probabilitydistribution conditioned on the given class which means our approach (unlikethe Gaussian and Laplace approaches) takes into consideration dependenciesamong the attribute values. We illustrate the performance of the proposedapproach on a wide range of datasets taken from the University of California atIrvine (UCI) Machine Learning Repository. We also include results for the$k$-NN classifier and demonstrate that the proposed approach is simple, robustand outperforms standard approaches.

Bayes Classification using an approximation to the Joint Probability Distribution of the Attributes