## The Naïve Bayes classifier

The name Naïve Bayes comes from the basic assumption in the model that the probability of a particular feature is independent of any other feature given the class label . This implies the following:

Using this assumption and the Bayes rule, one can show that the probability of class , given features , is given by:

Here, is the normalization term obtained by summing the numerator on all the values of *k*. It is also called Bayesian evidence or partition function Z. The classifier selects a class label as the target class that maximizes the posterior class probability :

The Naïve Bayes classifier is a baseline classifier for document classification. One reason for this is that the underlying assumption that each feature (words or m-grams) is independent of others, given the class label typically holds good for text. Another reason is that the Naïve Bayes classifier scales well when there is a large number of documents.

There are two implementations of Naïve Bayes. In...