Because it assumes the features are independent of each other given the class, so an example's likelihood is simply the product of each feature's likelihood.
Card 1 of 259. Answer: Because it assumes the features are independent of each other given the class, so an example's likelihood is simply the product of each feature's likelihood.
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Naive Bayes is called naive because it assumes the features are conditionally independent given the class: once the class is known, one feature says nothing more about another. The likelihood then factors into one-feature terms: P(y | x) ∝ P(y) × P(x₁ | y) × … × P(xₙ | y).
Example: 30% of mail is spam; 'free' appears in 40% of spam and 5% of normal mail, 'winner' in 20% and 1%. With just these two features, an email containing both scores 0.3 × 0.4 × 0.2 = 0.024 for spam and 0.7 × 0.05 × 0.01 = 0.00035 for normal, so P(spam) ≈ 0.986. Words that usually appear together get counted twice.
Why does it work at all? Classification only needs the right class to score highest, and Domingos and Pazzani showed in 1997 that naive Bayes can be optimal under zero-one loss despite strong dependence, though its probabilities are often too extreme. Textbooks that call the features equally important mean no feature gets a learned weight.
