Vector Approximate Message Passing

By Sundeep Rangan, Philip Schniter, Alyson K. Fletcher. IEEE Transactions on Information Theory, 2019

455 citations recorded by the source corpus.

The standard linear regression (SLR) problem is to recover a vector $\mathrm {x}^{0}$ from noisy linear observations $\mathrm {y}=\mathrm {Ax}^{0}+\mathrm {w}$ . The approximate message passing (AMP) algorithm 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 A, 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 A: those that are right-orthogonally invariant. After performing an initial singular value decomposition (SVD) of A, the per-iteration complexity of VAMP is similar to that of AMP. In addition, the fixed points of VAMP’s state evolution are consistent with the replica prediction of the minimum mean-squared error derived by Tulino, Caire, Verdú, and Shamai. Numerical experiments are used to confirm the effectiveness of VAMP and its consistency with state-evolution predictions.

Subfields: Artificial Intelligence, Computer Networks and Communications, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/fee0b2bb08dffef6cbd76c6a8fb94b96313fa00e

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Citations in the corpus

Learned D-AMP: Principled Neural Network based Compressive Image Recovery (2017, methodology): “To solve this convex problem, researchers often use linear programming [18] or iterative algorithms, e.g. ISTA [15], AMP [16], and VAMP [17].”
Channel Estimation for RIS-Empowered Multi-User MISO Wireless Communications (2020, methodology): “In this paper, motivated by the PARAFAC decomposition [43], [44], we leverage ALS and the Vector Approximate Message Passing (VAMP) algorithm [45] to iteratively recover signals from noisy observations.”