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I have a question about generative and discriminative models. As I understand it generative models aim to model the joint distribution p(x,y) of the input x and output y and the discriminative approach estimates the conditional distribution p(y|x). I understand that the generative approach is more complex but I have a small niggle...

Applying Bayes rule, we have the conditional distribution

p(y|x) = p(x|y) p(y)/p(x)

which is equal to:

P(y|x) = p(x, y)/p(x)

So it seems when we want to model discriminative modelling, we have to estimate this joint distribution (in he numerator) as well. I am sure this is wrong and I have a flaw in my understanding but I cannot seem to figure it out. Is there something about this modelling process that I am not understanding. Perhaps we do not estimate it in this way?

Also, a markov random field defined over an undirected graph, is it a joint distribution?

I would really appreciate any help anyone can give me on this.

Thanks,

Luc

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# Generative vs discriminative model

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