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/
Bapst, Victor ;
Coja-Oghlan, Amin
Harnessing the Bethe Free Energy
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: |
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Belief Propagation, free energy, Gibbs measure, partition function |
Collection: |
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015) |
Issue Date: |
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2015 |
Date of publication: |
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13.08.2015 |