How is Naïve Bayes derived from the principle of maximum a posteriori (MAP) classification?

Naïve Bayes classification is equivalent to selecting the class that maximizes posterior probability under MAP decision rule.

MAP classification selects argmax_C P(C|X). Using Bayes theorem, this becomes argmax_C P(X|C)P(C). Naïve Bayes introduces conditional independence, factorizing P(X|C) into Π P(xi|C). This transforms an intractable joint probability estimation problem into a product of independent marginal likelihoods, making MAP computation efficient in high-dimensional spaces.