Naive Bayes
Also: Naïve Bayes, naive Bayes classifier, multinomial naive Bayes
It picks the class maximizing P(c)·Πᵢ P(xᵢ | c), estimated by counting, usually computed as a sum of logs for stability with Laplace smoothing to avoid zero probabilities. The independence assumption is rarely true, yet it is a strong text-classification baseline.
ŷ = argmax_c P(c) Πᵢ P(xᵢ | c)
Example
With P(spam) = 0.4, P("free" | spam) = 0.2 and P("free" | ham) = 0.01, a message containing "free" scores 0.4 · 0.2 = 0.08 for spam versus 0.6 · 0.01 = 0.006 for ham, so it is labeled spam.