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MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com Understanding Belief Propagation and its Generalizations Jonathan S. Yedidia, William T. Freeman, and Yair Weiss TR2001-22 November 2001 Abstract ”Inference” problems arise in statistical physics, computer vision, error-correcting coding the- ory, and AI. We explain the principles behind the belief propagation (BP) algorithm, which is an efficient way to solve inference problems based on passing local messages. We develop a unified approach with examples, notation, and graphical models borrowed from the relevant dis- ciplines.We explain the close connection between the BP algorithm and the Bethe approximation of statistical physics. In particular, we show that BP can only converge to a fixed point that is also a stationary point of the Bethe approximation to the free energy. This result helps explain the successes of the BP algorithm and enables connections to be made with variational approaches to approximate inference. Delivered in the the ’Destinguished Lecture’ track at the 2001 International Joint Conference on Artificial Intelligence in August 2001. To be published in a book collecting those lectures. This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c Mitsubishi Electric Research Laboratories, Inc., 2001 201 Broadway, Cambridge, Massachusetts 02139
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Page 1: TR2001-22 November 2001 - Mitsubishi Electric Research … · 2011-10-21 · Delivered in the “Distinguished Lecture” track at the 2001 International Joint Conference on Arti-ficial

MITSUBISHI ELECTRIC RESEARCH LABORATORIEShttp://www.merl.com

Understanding Belief Propagation and itsGeneralizations

Jonathan S. Yedidia, William T. Freeman, and Yair Weiss

TR2001-22 November 2001

Abstract

”Inference” problems arise in statistical physics, computer vision, error-correcting coding the-ory, and AI. We explain the principles behind the belief propagation (BP) algorithm, which isan efficient way to solve inference problems based on passing local messages. We develop aunified approach with examples, notation, and graphical models borrowed from the relevant dis-ciplines.We explain the close connection between the BP algorithm and the Bethe approximationof statistical physics. In particular, we show that BP can only converge to a fixed point that is alsoa stationary point of the Bethe approximation to the free energy. This result helps explain thesuccesses of the BP algorithm and enables connections to be made with variational approachesto approximate inference.

Delivered in the the ’Destinguished Lecture’ track at the 2001 International Joint Conference onArtificial Intelligence in August 2001. To be published in a book collecting those lectures.

This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in partwithout payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies includethe following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment ofthe authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, orrepublishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. Allrights reserved.

Copyright c©Mitsubishi Electric Research Laboratories, Inc., 2001201 Broadway, Cambridge, Massachusetts 02139

Page 2: TR2001-22 November 2001 - Mitsubishi Electric Research … · 2011-10-21 · Delivered in the “Distinguished Lecture” track at the 2001 International Joint Conference on Arti-ficial

MERLCoverPageSide2

Page 3: TR2001-22 November 2001 - Mitsubishi Electric Research … · 2011-10-21 · Delivered in the “Distinguished Lecture” track at the 2001 International Joint Conference on Arti-ficial

Deliveredin the“DistinguishedLecture” trackat the2001InternationalJointConferenceon Arti-ficial Intelligencein August2001. To bepublishedin a bookcollectingthoselectures.First DraftAugust2001.Final Draft January2002.

Page 4: TR2001-22 November 2001 - Mitsubishi Electric Research … · 2011-10-21 · Delivered in the “Distinguished Lecture” track at the 2001 International Joint Conference on Arti-ficial

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Page 36: TR2001-22 November 2001 - Mitsubishi Electric Research … · 2011-10-21 · Delivered in the “Distinguished Lecture” track at the 2001 International Joint Conference on Arti-ficial

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