What is the mathematical formulation of Multinomial Naïve Bayes and where is it used?

Multinomial Naïve Bayes models class probabilities using word counts or frequency features under a multinomial distribution assumption.

Multinomial Naïve Bayes computes P(C|X) ∝ P(C) * Π P(x_i|C), where x_i represents feature counts. It assumes features are generated from a multinomial distribution conditioned on class labels. It is widely used in text classification where each feature corresponds to word frequency in a document. The model estimates likelihood using normalized counts with smoothing.