Universality of approximate message passing algorithms

Wei Kuo Chen, Wai Kit Lam

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Article number36
JournalElectronic Journal of Probability
StatePublished - 2021

Bibliographical note

Funding Information:
*University of Minnesota. Partially supported by NSF grant DMS-17-52184. E-mail: wkchen@umn.edu †University of Minnesota. E-mail: wlam@umn.edu

Publisher Copyright:
© 2021, Institute of Mathematical Statistics. All rights reserved.


  • Message passing
  • Spike recovery
  • Spiked random matrix
  • Universality


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