NDLI: On the convergence of approximate message passing with arbitrary matrices

Content Provider	IEEE Xplore Digital Library
Author	Rangan, S. Schniter, P. Fletcher, A.
Copyright Year	2014
Description	Author affiliation: Elec. Eng., U.C. Santa Cruz, Santa Cruz, CA, USA (Fletcher, A.) \|\| Elec. & Comp. Eng., Ohio State Univ., Columbus, OH, USA (Schniter, P.) \|\| Elec. & Comp. Eng., NYU-Poly, New York, NY, USA (Rangan, S.)
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.
Starting Page	236
Ending Page	240
File Size	409286
Page Count	5
File Format	PDF
ISBN	9781479951864
ISSN	21578117
DOI	10.1109/ISIT.2014.6874830
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Convergence Damping Estimation Message passing Algorithm design and analysis Vectors Transforms primal-dual methods Belief propagation message passing
Content Type	Text
Resource Type	Article

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