What is the role of independence assumption in feature space factorization?

Independence allows factorization of joint likelihood into a product of marginal likelihoods.

Naïve Bayes assumes P(X1, X2, ..., Xn | C) = Π P(Xi | C), reducing exponential joint modeling complexity to linear complexity. This assumption is rarely true but enables tractable inference in high-dimensional spaces. It is the core reason NB scales efficiently.