Generative classification obtains the posterior probability of a class given a data point by applying Bayes' rule to a class-conditional density and a class prior, with the evidence term recovered by marginalizing over classes rather than modeled separately. The particular classifier that results is determined entirely by the assumed form of the class-conditional density: a single multivariate Gaussian per class yields linear discriminant analysis (and quadratic discriminant analysis under a weaker covariance assumption), a weighted mixture of simpler densities yields mixture-model classifiers capable of representing multimodal classes, and a factorization of the density across input dimensions conditional on the class yields the naive Bayes assumption. This situates linear discriminant analysis in supervised statistical machine learning alongside logistic regression and regression on indicator variables as one of the linear discriminant-based classifiers, distinguished by modeling the data-generating densities rather than the decision boundary directly.
Generative classification obtains the posterior probability of a class given a data point by applying Bayes' rule to a class-conditional density and a class prior, with the evidence term recovered by…