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. https://resolver.caltech.edu/CaltechAUTHORS:20200204-144202684
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Abstract
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. | ||||||||||
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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 | ||||||||||
DOI: | 10.1007/978-0-387-21696-6_10 | ||||||||||
Record Number: | CaltechAUTHORS:20200204-144202684 | ||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20200204-144202684 | ||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||
ID Code: | 101117 | ||||||||||
Collection: | CaltechAUTHORS | ||||||||||
Deposited By: | Tony Diaz | ||||||||||
Deposited On: | 04 Feb 2020 22:56 | ||||||||||
Last Modified: | 16 Nov 2021 17:59 |
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