We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an 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.
W-K. Chen was partially supported by NSF grant DMS-17-52184
"Universality of approximate message passing algorithms." Electron. J. Probab. 26 1 - 44, 2021. https://doi.org/10.1214/21-EJP604