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I am trying to understand the difference between:

Wikipedia says:

Expectation Propagation differs from other Bayesian approximation approaches such as Variational Bayesian methods.

Why isn't EP considered a Variational Bayes method? Isn't EP Bayesian, and relies on message-passing to approximate the posterior? What makes a method Variational Bayes?

Also, what about the following methods. Can they be considered Variational Bayes?

  • Sum-product
  • Mean-field methods
  • Bethe-Kikuchi approximations
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To me VB just means we will approximate posterior by turning the problem into a minimization problem and then changing the solution space. In that sense, EP is a type of VB algorithm, because it does exactly that. When I think of VB, though, the first thing I think of is mean-field, and if I had to guess I would think that whoever wrote that EP is "different" from VB might have had mean-field algorithms in mind.

This source, which I take to be canonical, explicitly classifies all algorithms you mention as VB (i.e. Bethe-Kikuchi, sum-product, EP, and mean-field).

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