The Expectation Propagation Algorithm for use in Approximate Bayesian Analysis of Latent Gaussian Models

Abstract

Analyzing latent Gaussian models by using approximate Bayesian inference methods has proven to be a fast and accurate alternative to running time consuming Markov chain Monte Carlo simulations. A crucial part of these methods is the use of a Gaussian approximation, which is commonly found using an asymptotic expansion approximation. This study considered an alternative method for making a Gaussian approximation, the expectation propagation (EP) algorithm, which is known to be more accurate, but also more computationally demanding. By assuming that the latent field is a Gaussian Markov random field, specialized algorithms for factorizing sparse matrices was used to speed up the EP algorithm. The approximation methods were then compared both with regards to computational complexity and accuracy in the approximations. The expectation propagation algorithm was shown to provide some improvements in accuracy compared to the asymptotic expansion approximation when tested on a binary logistic regression model. However, tests of computational time requirement for computing approximations in simple examples show that the EP algorithm is as much as 15-20 times slower than the alternative method.