What is conditional independence violation and its mathematical impact on Naïve Bayes?

Violating conditional independence causes Naïve Bayes to overcount evidence and distort probability estimates.

Naïve Bayes assumes P(X1, X2|C) = P(X1|C)P(X2|C). If features are dependent, this factorization becomes incorrect, leading to double counting of correlated evidence. This inflates likelihood ratios and can bias posterior probabilities. However, classification may still remain correct if distortion is uniform across classes.