Expectation Consistent Approximate Inference 
Manfred Opper, Ole Winther

Abstract  We propose a novel framework for approximations to intractable probabilistic models which is based on a free energy formulation. The approximation can be understood from replacing an average over the original intractable distribution with a tractable one. It requires two tractable probability distributions which are made consistent on a set of moments and encode different features of the original intractable distribution. In this way we are able to use Gaussian approximations for models with discrete or bounded variables which allow us to include nontrivial correlations which are neglected in many other methods.
We test the framework on toy benchmark problems for binary variables on fully connected graphs and 2D grids and compare with other methods, such as loopy belief propagation. Good performance is already achieved by using single nodes as tractable substructures. Significant improvements are obtained when a spanning tree is used instead. 
Type  Journal paper [With referee] 
Journal  Journal of Machine Learning Research 
Year  2005 Vol. 6 pp. 21772204 
Electronic version(s)  [pdf] [zip] 
BibTeX data  [bibtex] 
IMM Group(s)  Intelligent Signal Processing 