In a classification model, a desirable situation is to have classification classes evenly represented in the training dataset. Datasets that satisfy this property are called balanced datasets.
However, in a Naive Bayes classification model, the classifier is defined as an optimization problem that maximizes the posterior probability:
argmax_C P(C|F1,...,Fn) = P(C) Sum_i(P(F_i|C))
F_i are features and
C are classes (in this equation the Naive assumption has already been applied).
But, if we try to get balanced datasets with evenly represented categories, then the estimation of
P(C) (the prior) would be the same for all
C and, thus, we could get rid of
P(C) when we maximize because it'd be the same for all categories.
Further, by considering evenly represented categories we would be altering the real distribution of the class.
My question is: are we really interested in doing that, or do we want to capture the fact that some classes are more likely than others, in our classification model (keeping the dataset unbalanced)?