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Expectation Propagation (Minka, 2001) is a widely successful algorithm forvariational inference. EP is an iterative algorithm used to approximatecomplicated distributions, typically to find a Gaussian approximation ofposterior distributions. In many applications of this type, EP performsextremely well. Surprisingly, despite its widespread use, there are very fewtheoretical guarantees on Gaussian EP, and it is quite poorly understood.  In order to analyze EP, we first introduce a variant of EP: averaged-EP(aEP), which operates on a smaller parameter space. We then consider aEP and EPin the limit of infinite data, where the overall contribution of eachlikelihood term is small and where posteriors are almost Gaussian. In thislimit, we prove that the iterations of both aEP and EP are simple: they behavelike iterations of Newton's algorithm for finding the mode of a function. Weuse this limit behavior to prove that EP is asymptotically exact, and to obtainother insights into the dynamic behavior of EP: for example, that it maydiverge under poor initialization exactly like Newton's method. EP is a simplealgorithm to state, but a difficult one to study. Our results should facilitatefurther research into the theoretical properties of this important method.

Expectation Propagation in the large-data limit