Unifying Message Passing Algorithms Under the Framework of Constrained Bethe Free Energy Minimization

Variational message passing (VMP), belief propagation (BP) and expectation propagation (EP) have found their wide applications in complex statistical signal processing problems. In addition to viewing them as a class of algorithms operating on graphical models, this article unifies them under an opt...

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Bibliographic Details
Published in:IEEE transactions on wireless communications Vol. 20; no. 7; pp. 4144 - 4158
Main Authors: Zhang, Dan, Song, Xiaohang, Wang, Wenjin, Fettweis, Gerhard, Gao, Xiqi
Format: Journal Article
Language:English
Published: New York IEEE 01.07.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Bayes methods
Bethe free energy
Channel estimation
constrained optimization
Constraints
Free energy
Machine learning
Message passing
message passing algorithms
Minimization
Optimization
Propagation
Signal processing
Signal processing algorithms
Signal reconstruction
Statistical inference
Statistical models
Task complexity
Wireless communication
ISSN:1536-1276, 1558-2248
Online Access:Get full text
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Summary:Variational message passing (VMP), belief propagation (BP) and expectation propagation (EP) have found their wide applications in complex statistical signal processing problems. In addition to viewing them as a class of algorithms operating on graphical models, this article unifies them under an optimization framework, namely, Bethe free energy minimization with differently and appropriately imposed constraints. This new perspective in terms of constraint manipulation can offer additional insights on the connection between different message passing algorithms and is valid for a generic statistical model. It also founds a theoretical framework to systematically derive message passing variants. Taking the sparse signal recovery (SSR) problem as an example, a low-complexity EP variant can be obtained by simple constraint reformulation, delivering better estimation performance with lower complexity than the standard EP algorithm. Furthermore, we can resort to the framework for the systematic derivation of hybrid message passing for complex inference tasks. Notably, a hybrid message passing algorithm is exemplarily derived for joint SSR and statistical model learning with near-optimal inference performance and scalable complexity.
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ISSN:1536-1276
1558-2248
DOI:10.1109/TWC.2021.3056193