Open Access
2021 Universality of approximate message passing algorithms
Wei-Kuo Chen, Wai-Kit Lam
Author Affiliations +
Electron. J. Probab. 26: 1-44 (2021). DOI: 10.1214/21-EJP604


We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an n×n random symmetric matrix A. We establish universality in noise for this AMP in the n-limit and validate this behavior in a number of AMPs popularly adapted in compressed sensing, statistical inferences, and optimizations in spin glasses.

Funding Statement

W-K. Chen was partially supported by NSF grant DMS-17-52184


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Wei-Kuo Chen. Wai-Kit Lam. "Universality of approximate message passing algorithms." Electron. J. Probab. 26 1 - 44, 2021.


Received: 1 June 2020; Accepted: 12 March 2021; Published: 2021
First available in Project Euclid: 23 March 2021

arXiv: 2003.10431
Digital Object Identifier: 10.1214/21-EJP604

Primary: 60F05
Secondary: 62E20 , 68W40

Keywords: message passing , spike recovery , spiked random matrix , Universality

Vol.26 • 2021
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