  As a consequence of the strong and usually violated conditional independence
assumption (CIA) of naive Bayes (NB) classifier, the performance of NB becomes
less and less favorable compared to sophisticated classifiers when the sample
size increases. We learn from this phenomenon that when the size of the
training data is large, we should either relax the assumption or apply NB to a
"reduced" data set, say for example use NB as a local model. The latter
approach trades the ignored information for the robustness to the model
assumption. In this paper, we consider using NB as a model for locally weighted
data. A special weighting function is designed so that if CIA holds for the
unweighted data, it also holds for the weighted data. The new method is
intuitive and capable of handling class imbalance. It is theoretically more
sound than the locally weighted learners of naive Bayes that base
classification only on the $k$ nearest neighbors. Empirical study shows that
the new method with appropriate choice of parameter outperforms seven existing
classifiers of similar nature.
