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Gaussian Discriminant Analysis and Naive Bayes: Model Each Class First, Then Classify with Bayes' Rule | Stanford CS229 Lecture 5

Lecture 5 turns classification around: instead of learning p(y|x) directly, it learns p(x|y) and p(y). GDA assumes the two classes are Gaussians with a shared covariance. Maximum likelihood then takes nothing more than counting proportions and averaging, the decision boundary comes out as a straight line, and the posterior is exactly a sigmoid. Naive Bayes uses conditional independence to squeeze 2^d parameters down to 2d+1.

Probabilistic Generative Models, Naive Bayes and Gaussian Discriminant Analysis | CMU 07-380 Lecture 9

Lecture 9 stops learning p(y|x) directly. Instead it learns the class prior p(y) and the class-conditional p(x|y), then inverts them with Bayes rule. The price is stronger assumptions; the payoff is the ability to generate new data and more stability with little data. Naive Bayes uses conditional independence to make the parameters estimable, GDA uses multivariate Gaussians for continuous features, and whether the covariances match decides a linear or a curved boundary.