What is the difference between a generative and a discriminative algorithm?

Question

What is the difference between a generative and a discriminative algorithm?

Answer 1

All previous answers are great, and I'd like to plug in one more point.

From generative algorithm models, we can derive any distribution; while we can only obtain the conditional distribution P(Y|X) from the discriminative algorithm models(or we can say they are only useful for discriminating Y’s label), and that's why it is called discriminative model. The discriminative model doesn't assume that the X's are independent given the Y($X_i \perp X_{-i} | Y$) and hence is usually more powerful for calculating that conditional distribution.