Vector Approximate Message Passing
Sundeep Rangan, Philip Schniter, and Alyson K. Fletcher

TL;DR
This paper introduces the Vector AMP (VAMP) algorithm, which extends the applicability of approximate message passing to a broader class of matrices, providing rigorous state-evolution analysis and matching theoretical MMSE predictions.
Contribution
The paper develops VAMP with a rigorous state-evolution for right-orthogonally invariant matrices, broadening AMP's scope and confirming its fixed points align with replica predictions.
Findings
VAMP's state evolution is valid for right-orthogonally invariant matrices.
VAMP's fixed points match the replica minimum mean-squared error predictions.
Numerical results confirm VAMP's effectiveness and theoretical predictions.
Abstract
The standard linear regression (SLR) problem is to recover a vector from noisy linear observations . The approximate message passing (AMP) algorithm recently proposed by Donoho, Maleki, and Montanari is a computationally efficient iterative approach to SLR that has a remarkable property: for large i.i.d.\ sub-Gaussian matrices , its per-iteration behavior is rigorously characterized by a scalar state-evolution whose fixed points, when unique, are Bayes optimal. The AMP algorithm, however, is fragile in that even small deviations from the i.i.d.\ sub-Gaussian model can cause the algorithm to diverge. This paper considers a "vector AMP" (VAMP) algorithm and shows that VAMP has a rigorous scalar state-evolution that holds under a much broader class of large random matrices : those that are right-orthogonally…
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Taxonomy
TopicsDistributed Sensor Networks and Detection Algorithms · Sparse and Compressive Sensing Techniques · Blind Source Separation Techniques
