How does Naïve Bayes behave under class-conditional feature dependency violations?

Violating conditional independence assumptions introduces multiplicative bias in likelihood estimation.

Naïve Bayes assumes P(X1,...,Xn|C) factorizes. When dependencies exist, likelihoods are double-counted or undercounted, distorting posterior probabilities. Interestingly, even with violated assumptions, NB can still perform well in classification tasks because ranking of posterior probabilities may remain stable.