Approximate inference techniques with expectation constraints
tom heskes, Manfred Opper, Wim Wiegerinck, ole winther and Onno Zoeter
Journal of Statistical Mechanics: Theory and Experiment Number P11015, 2005.

Abstract

This paper discusses inference problems in probabilistic graphical models that often occur in a machine learning setting. In particular it presents a unified view of several recently proposed approximation schemes. Expectation consistent approximations and expectation propagation are both shown to be related to Bethe free energies with weak consistency constraints, i.e. free energies where local approximations are only required to agree on certain statistics instead of full marginals.

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