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Information, Physics, and Computation$
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Marc Mézard and Andrea Montanari

Print publication date: 2009

Print ISBN-13: 9780198570837

Published to Oxford Scholarship Online: September 2009

DOI: 10.1093/acprof:oso/9780198570837.001.0001

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Belief propogation

Belief propogation

(p.291) 14 Belief propogation
Information, Physics, and Computation

Marc Mézard

Andrea Montanari

Oxford University Press

This chapter discusses a general method for approximating marginals of large graphical models. This powerful technique has been discovered independently in various fields: statistical physics (under the name ‘Bethe Peierls approximation’), coding theory (‘sum-product’ and ‘min-sum’ algorithms), and artificial intelligence (‘belief propagation’). It is based on an exchange of messages between variables and factors, along the edges of the factor graph. These messages are interpreted as probability distributions for the variable in a graph where a cavity has been dug. The chapter also discusses the statistical analysis of these messages in large random graphical models: density evolution and the replica symmetric cavity method.

Keywords:   belief propagation, sum-product, min-sum, Bethe Peierls, message passing, cavity method, replica symmetric, density evolution

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