On the convergence of approximate message passing with arbitrary matrices

Sundeep Rangan, Philip Schniter, Alyson Fletcher

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

Abstract

Approximate message passing (AMP) methods and their variants have attracted considerable recent attention for the problem of estimating a random vector x observed through a linear transform A. In the case of large i.i.d. A, the methods exhibit fast convergence with precise analytic characterizations on the algorithm behavior. However, the convergence of AMP under general transforms is not fully understood. In this paper, we provide sufficient conditions for the convergence of a damped version of the generalized AMP (GAMP) algorithm in the case of Gaussian distributions. It is shown that, with sufficient damping the algorithm can be guaranteed to converge, but the amount of damping grows with peak-to-average ratio of the squared singular values of A. This condition explains the good performance of AMP methods on i.i.d. matrices, but also their difficulties with other classes of transforms. A related sufficient condition is then derived for the local stability of the damped GAMP method under more general (possibly non-Gaussian) distributions, assuming certain strict convexity conditions.

Original languageEnglish (US)
Title of host publication2014 IEEE International Symposium on Information Theory, ISIT 2014
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages236-240
Number of pages5
ISBN (Print)9781479951864
DOIs
StatePublished - Jan 1 2014
Event2014 IEEE International Symposium on Information Theory, ISIT 2014 - Honolulu, HI, United States
Duration: Jun 29 2014Jul 4 2014

Publication series

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

Other

Other2014 IEEE International Symposium on Information Theory, ISIT 2014
CountryUnited States
CityHonolulu, HI
Period6/29/147/4/14

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Keywords

  • Belief propagation
  • message passing
  • primal-dual methods

ASJC Scopus subject areas

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

Cite this

Rangan, S., Schniter, P., & Fletcher, A. (2014). On the convergence of approximate message passing with arbitrary matrices. In 2014 IEEE International Symposium on Information Theory, ISIT 2014 (pp. 236-240). [6874830] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2014.6874830