Universality of Approximate Message Passing Algorithms

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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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