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Belief Propagation on Partially Ordered Sets

McEliece, Robert J. and Yildirim, Muhammed (2003) Belief Propagation on Partially Ordered Sets. In: Mathematical Systems Theory in Biology, Communications, Computation, and Finance. IMA Volumes in Mathematics and its Applications. No.134. Springer , New York, NY, pp. 275-299. ISBN 978-1-4419-2326-4.

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In this paper, which is based on the important recent work of Yedidia, Freeman, and Weiss, we present a generalized form of belief propagation, viz. belief propagation on a partially ordered set (PBP). PBP is an iterative message-passing algorithm for solving, either exactly or approximately, the marginalized product density problem, which is a general computational problem of wide applicability. We will show that PBP can be thought of as an algorithm for minimizing a certain “free energy” function, and by exploiting this interpretation, we will exhibit a one-to-one correspondence between the fixed points of PBP and the stationary points of the free energy.

Item Type:Book Section
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Additional Information:© 2003 Springer-Verlag New York, Inc. This research was supported by NSF grant no. CCR-0118670, and grants from Sony, Qualcomm, and Caltech’s Lee Center for Advanced Networking.
Funding AgencyGrant Number
Sony CorporationUNSPECIFIED
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
Subject Keywords:Free Energy; Belief Propagation; Helmholtz Free Energy; Hasse Diagram; Cluster Variation Method
Series Name:IMA Volumes in Mathematics and its Applications
Issue or Number:134
Record Number:CaltechAUTHORS:20200204-144202684
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101117
Deposited By: Tony Diaz
Deposited On:04 Feb 2020 22:56
Last Modified:16 Nov 2021 17:59

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