# Linking generative, discriminative models to supervised and unsupervised learning

Definitions that I am considering: A generative model learns p(x,y) whereas a discriminative model learns p(y|x=x).

I would like to verify if my understanding is correct by sharing the following claims. Please let me know if my claims are right or wrong (do provide counter-examples).

Claim 1: All generative models are learnt using unsupervised learning.

Claim 2: Not every unsupervised learning algorithm is a generative model. For example, clustering algorithm is not a generative model.

Claim 3: All discriminative models are learnt using supervised learning.

Claim 4: Every supervised learning algorithm is a discriminative model.

Well first I would nitpick your definition. Consider a conditional GAN which given a category $$x$$ generates a realistic image $$y$$ in category $$x$$ -- that is, it models $$P(y|x)$$. This is arguably not a discriminative model, but it is according to your definition.