Hybrid Approximate Message Passing

Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framewo...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 65; no. 17; pp. 4577 - 4592
Main Authors: Rangan, Sundeep, Fletcher, Alyson K., Goyal, Vivek K., Byrne, Evan, Schniter, Philip
Format: Journal Article
Language:English
Published: IEEE 01.09.2017
Subjects:
Approximate message passing
Approximation algorithms
belief propagation
Graphical models
group sparsity
Inference algorithms
max-sum algorithm
Message passing
multinomial logistic regression
Optimization
Signal processing algorithms
sum-product algorithm
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable recent attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper presents a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with the weak edges representing small, linearizable couplings of variables. AMP approximations based on the central limit theorem can be readily applied to aggregates of many weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (HyGAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition of strong and weak edges, a performance-complexity tradeoff can be achieved. Group sparsity and multinomial logistic regression problems are studied as examples of the proposed methodology.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2017.2713759