Editing Naive Bayes classifier (section)

===Bernoulli naive Bayes===
In the multivariate [[Bernoulli distribution|Bernoulli]] event model, features are independent [[Boolean data type|Boolean variables]] ([[binary data|binary variables]]) describing inputs. Like the multinomial model, this model is popular for document classification tasks,<ref name="mccallum"/> where binary term occurrence features are used rather than term frequencies. If <math>x_i</math> is a Boolean expressing the occurrence or absence of the {{mvar|i}}'th term from the vocabulary, then the likelihood of a document given a class <math>C_k</math> is given by:<ref name="mccallum"/>
<math display="block">
p(\mathbf{x} \mid C_k) = \prod_{i=1}^n p_{ki}^{x_i} (1 - p_{ki})^{(1-x_i)}
</math>
where <math>p_{ki}</math> is the probability of class <math>C_k</math> generating the term <math>x_i</math>. This event model is especially popular for classifying short texts. It has the benefit of explicitly modelling the absence of terms. Note that a naive Bayes classifier with a Bernoulli event model is not the same as a multinomial NB classifier with frequency counts truncated to one.