Expectation propagation

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Expectation propagation (EP) is a technique in Bayesian machine learning.[1]

EP finds approximations to a probability distribution.[1] It uses an iterative approach that uses the factorization structure of the target distribution.[1] It differs from other Bayesian approximation approaches such as variational Bayesian methods.[1]

More specifically, suppose we wish to approximate an intractable probability distribution with a tractable distribution . Expectation propagation achieves this approximation by minimizing the Kullback-Leibler divergence .[1] Variational Bayesian methods minimize instead.[1]

If is a Gaussian , then is minimized with and being equal to the mean of and the covariance of , respectively; this is called moment matching.[1]


Expectation propagation via moment matching plays a vital role in approximation for indicator functions that appear when deriving the message passing equations for TrueSkill.


  1. ^ a b c d e f g Bishop, Christopher (2007). Pattern Recognition and Machine Learning. New York: Springer-Verlag New York Inc. ISBN 978-0387310732.

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