Universality of Approximate Message Passing Algorithms
March 23, 2020 Β· Declared Dead Β· π Electronic Journal of Probability
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Authors
Wei-Kuo Chen, Wai-Kit Lam
arXiv ID
2003.10431
Category
math.PR
Cross-listed
cs.IT,
math-ph,
math.OC,
math.ST
Citations
42
Venue
Electronic Journal of Probability
Last Checked
6 months ago
Abstract
We consider a broad class of Approximate Message Passing (AMP) algorithms defined as a Lipschitzian functional iteration in terms of an $n\times n$ 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.
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