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JAIR
2011

Properties of Bethe Free Energies and Message Passing in Gaussian Models

12 years 6 months ago
Properties of Bethe Free Energies and Message Passing in Gaussian Models
We address the problem of computing approximate marginals in Gaussian probabilistic models by using mean field and fractional Bethe approximations. We define the Gaussian fractional Bethe free energy in terms of the moment parameters of the approximate marginals, derive a lower and an upper bound on the fractional Bethe free energy and establish a necessary condition for the lower bound to be bounded from below. It turns out that the condition is identical to the pairwise normalizability condition, which is known to be a sufficient condition for the convergence of the message passing algorithm. We show that stable fixed points of the Gaussian message passing algorithm are local minima of the Gaussian Bethe free energy. By a counterexample, we disprove the conjecture stating that the unboundedness of the free energy implies the divergence of the message passing algorithm.
Botond Cseke, Tom Heskes
Added 15 Sep 2011
Updated 15 Sep 2011
Type Journal
Year 2011
Where JAIR
Authors Botond Cseke, Tom Heskes
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