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Abstract: We extend recent work on the connection between loopy belief propagation and the Bethe free energy. Constrained minimization of the Bethe free energy can be turned into an unconstrained saddle-point problem. Both converging double-loop algorithms and standard loopy belief propagation can be interpreted as attempts to solve this saddle-point problem. Stability analysis then leads us to conclude that stable fixed points of loopy belief propagation must be (local) minima of the Bethe free energy.... (Update)
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BibTeX entry: (Update)
T. Heskes. Stable fixed points of loopy belief propagation are minima of the bethe free energy. In Advances in Neural Information Processing Systems, volume 15, Vancouver, CA, 2003. http://citeseer.ist.psu.edu/heskes02stable.html More
@misc{ heskes03stable,
author = "T. Heskes",
title = "Stable fixed points of loopy belief propagation are minima of the bethe
free energy",
text = "T. Heskes. Stable fixed points of loopy belief propagation are minima of
the bethe free energy. In Advances in Neural Information Processing Systems,
volume 15, Vancouver, CA, 2003.",
year = "2003",
url = "citeseer.ist.psu.edu/heskes02stable.html" }
Citations (may not include all citations):1543 Probabilistic Reasoning in Intelligent systems: Networks of .. (context) - Pearl - 1988
142 Factor graphs and the sum-product algorithm - Kschischang, Frey et al. - 2001
82 Generalized belief propagation - Yedidia, Freeman et al. - 2001
74 Loopy belief propagation for approximate inference: An empir.. - Murphy, Weiss et al. - 1999
14 CCCP algorithms to minimize the Bethe and Kikuchi free energ.. (context) - Yuille - 2002
13 Expectation propagation for approximate inference in dynamic.. - Heskes, Zoeter - 2002
11 Tree-based reparameterization for approximate estimation on .. - Wainwright, Jaakola et al. - 2002
7 The uni ed propagation and scaling algorithm (context) - Teh, Welling - 2002
4 The EP energy function and minimization schemes (context) - Minka - 2001
2 Minimax and Hamiltonian dynamics of excitatory-inhibitory ne.. - Seung, Richardson et al. - 1998
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