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[D] Why is it difficult to sample from Energy Based Models?

I have very little experience with generative models, so apologies if that is a trivial question.

My understanding of an energy based model (EBM) is that it is an undiredted graph defining the joint distribution over the vector X as p(X)=exp(-E(X)) such that E(x) is a sum of potentials defined over clicks.

The well-known Deep learning book by Goodfellow et al. claims that sampling from an EBM is difficult:

To understand why drawing samples from an energy-based model (EBM) is difficult, consider the EBM over just two variables, defining a distribution p(a,b). In order to sample a, we must draw from p(a|b), and in order to sample b, we must draw it from p(b|a). It seems to be an intractable chicken-and-egg problem.

I really find that perplexing. We already know p(a,b), so why can’t we just compute the marginal p(a), sample from it, and then sample from p(b|a)?

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Toronto AI is a social and collaborative hub to unite AI innovators of Toronto and surrounding areas. We explore AI technologies in digital art and music, healthcare, marketing, fintech, vr, robotics and more. Toronto AI was founded by Dave MacDonald and Patrick O'Mara.