This article is my notes on generative model for Lecture 5 and 6 of Machine Learning by Andrew Ng. What we do in logistic regression using generalized linear model is that, we approximate \(P(y|x)\) using given data. This kind of learning algorithms is discriminative, in which we predict \(y\) based on the input features \(x\). On the contrary, generative model is to model \(P(x|y)\), the probability of the features \(x\) given class \(y\). In other words, we want to study how the features structure looks like given a class \(y\). If we also learn what \(P(y)\) is, we can easily recover \(P(y|x)\), for example, in the binary classification problem,
where \(P(x) = P(x|y=0)P(y=0) + P(x|y=1)P(y=1)\).
In this article, we are going to see a simple example of generative model on Gaussian discriminant analysis and Naive Bayes.