Fixed points of generalized approximate message passing with arbitrary matrices

Sundeep Rangan, Philip Schniter, Erwin Riegler, Alyson Fletcher, Volkan Cevher

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The estimation of a random vector with independent components passed through a linear transform followed by a componentwise (possibly nonlinear) output map arises in a range of applications. Approximate message passing (AMP) methods, based on Gaussian approximations of loopy belief propagation, have recently attracted considerable attention for such problems. For large random transforms, these methods exhibit fast convergence and admit precise analytic characterizations with testable conditions for optimality, even for certain non-convex problem instances. However, the behavior of AMP under general transforms is not fully understood. In this paper, we consider the generalized AMP (GAMP) algorithm and relate the method to more common optimization techniques. This analysis enables a precise characterization of the GAMP algorithm fixed-points that applies to arbitrary transforms. In particular, we show that the fixed points of the so-called max-sum GAMP algorithm for MAP estimation are critical points of a constrained maximization of the posterior density. The fixed-points of the sum-product GAMP algorithm for estimation of the posterior marginals can be interpreted as critical points of a certain mean-field variational optimization.

Original languageEnglish (US)
Title of host publication2013 IEEE International Symposium on Information Theory, ISIT 2013
Pages664-668
Number of pages5
DOIs
StatePublished - Dec 19 2013
Event2013 IEEE International Symposium on Information Theory, ISIT 2013 - Istanbul, Turkey
Duration: Jul 7 2013Jul 12 2013

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Other

Other2013 IEEE International Symposium on Information Theory, ISIT 2013
CountryTurkey
CityIstanbul
Period7/7/137/12/13

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Keywords

  • ADMM
  • Belief propagation
  • message passing
  • variational optimization

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Cite this

Rangan, S., Schniter, P., Riegler, E., Fletcher, A., & Cevher, V. (2013). Fixed points of generalized approximate message passing with arbitrary matrices. In 2013 IEEE International Symposium on Information Theory, ISIT 2013 (pp. 664-668). [6620309] (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2013.6620309