License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2015.467
URN: urn:nbn:de:0030-drops-53180
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2015/5318/
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Bapst, Victor ; Coja-Oghlan, Amin

Harnessing the Bethe Free Energy

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Abstract

Gibbs measures induced by random factor graphs play a prominent role in computer science, combinatorics and physics. A key problem is to calculate the typical value of the partition function. According to the "replica symmetric cavity method", a heuristic that rests on non-rigorous considerations from statistical mechanics, in many cases this problem can be tackled by way of maximising a functional called the "Bethe free energy". In this paper we prove that the Bethe free energy upper-bounds the partition function in a broad class of models. Additionally, we provide a sufficient condition for this upper bound to be tight.

BibTeX - Entry

@InProceedings{bapst_et_al:LIPIcs:2015:5318,
  author =	{Victor Bapst and Amin Coja-Oghlan},
  title =	{{Harnessing the Bethe Free Energy}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)},
  pages =	{467--480},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-89-7},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{40},
  editor =	{Naveen Garg and Klaus Jansen and Anup Rao and Jos{\'e} D. P. Rolim},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2015/5318},
  URN =		{urn:nbn:de:0030-drops-53180},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2015.467},
  annote =	{Keywords: Belief Propagation, free energy, Gibbs measure, partition function}
}

Keywords: Belief Propagation, free energy, Gibbs measure, partition function
Collection: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)
Issue Date: 2015
Date of publication: 13.08.2015

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