Gaussian Discriminant Analysis an example of Generative Learning Algorithms

Generative Learning Algorithms: In Linear Regression and Logistic Regression both we modelled conditional distribution of y given x, as follow. Algorithms that model p(y x) directly from the training set are called discriminative algorithms. There can be a different approach to the same problem, consider the same binary classification problem where we want learn to distinguish between two classes, class A (y 1) and class B (y 0) based on some features. Now we take all the examples of label A and try to learn the features and build a model for class A. Then we take all the examples labeled B and try to learn it's features and build a separate model for class B. Finally to classify a new element, we match it against each model and see which one fits better (generate high value for probability). In this approach we try to model p(x y) and p(y) as oppose to p(y x) we did earlier, it's called Generative Learning Algorithms.