Universality of approximate message passing algorithms
Copyright policy )Universality of approximate message passing algorithms
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.
43 pages, minor revision in the introduction
- University of Minnesota United States
- University of Minnesota Morris United States
Signal theory (characterization, reconstruction, filtering, etc.), FOS: Computer and information sciences, Random matrices (algebraic aspects), message passing, Computer Science - Information Theory, Information Theory (cs.IT), Probability (math.PR), FOS: Physical sciences, Mathematics - Statistics Theory, Mathematical Physics (math-ph), Statistics Theory (math.ST), spiked random matrix, Random matrices (probabilistic aspects), Optimization and Control (math.OC), FOS: Mathematics, spike recovery, universality, Mathematics - Optimization and Control, Mathematics - Probability, Mathematical Physics
Signal theory (characterization, reconstruction, filtering, etc.), FOS: Computer and information sciences, Random matrices (algebraic aspects), message passing, Computer Science - Information Theory, Information Theory (cs.IT), Probability (math.PR), FOS: Physical sciences, Mathematics - Statistics Theory, Mathematical Physics (math-ph), Statistics Theory (math.ST), spiked random matrix, Random matrices (probabilistic aspects), Optimization and Control (math.OC), FOS: Mathematics, spike recovery, universality, Mathematics - Optimization and Control, Mathematics - Probability, Mathematical Physics
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