I am a computer science master student. In a statistical learning theory course

Question

I am a computer science master student. In a statistical learning theory course I am taking, mean field approximation was introduced to approximately solve non-factorizable Gibbs distributions that were derived using maximum entropy inference. Our professor has a strong background in physics and often uses terms from statistical physics. Unfortunately, I lack that background. So,

Are there any resources explaining mean field approximations from a non-physical/computer science perspective? I couldn't find any.

Or alternatively, are there "crash course"-like resources that would allow me to understand one of the more physically motivated explanations without looking up tons of terms?

Explanation / Answer

A concise 16 page exposition (starting essentially from scratch) is given in Sections 8.1-8.3 of my book

Classical and Quantum Mechanics via Lie algebras http://lanl.arxiv.org/pdf/0810.1019v2.pdf

The mean field theory (and corrections to it) appears at the very end of Section 8.3.

In your case, the algebra is commutative, so you don't need to understand all the fine points related to noncommutative observables in the quantum case, and the mean field will simply be a high-dimensional Gaussian, where the cumulant generating function W(f) is just the exponential of a quadratic form.

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