Generalized Memory Approximate Message Passing
Abstract
Generalized approximate message passing (GAMP) is a promising technique for unknown signal reconstruction of generalized linear models (GLM). However, it requires that the transformation matrix has independent and identically distributed (IID) entries. In this context, generalized vector AMP (GVAMP) is proposed for general unitarily-invariant transformation matrices but it has a high-complexity matrix inverse. To this end, we propose a universal generalized memory AMP (GMAMP) framework including the existing orthogonal AMP/VAMP, GVAMP, and memory AMP (MAMP) as special instances. Due to the characteristics that local processors are all memory, GMAMP requires stricter orthogonality to guarantee the asymptotic IID Gaussianity and state evolution. To satisfy such orthogonality, local orthogonal memory estimators are established. The GMAMP framework provides a principle toward building new advanced AMP-type algorithms. As an example, we construct a Bayes-optimal GMAMP (BO-GMAMP), which uses a low-complexity memory linear estimator to suppress the linear interference, and thus its complexity is comparable to GAMP. Furthermore, we prove that for unitarily-invariant transformation matrices, BO-GMAMP achieves the replica minimum (i.e., Bayes-optimal) MSE if it has a unique fixed point.
Cite
@article{arxiv.2110.06069,
title = {Generalized Memory Approximate Message Passing},
author = {Feiyan Tian and Lei Liu and Xiaoming Chen},
journal= {arXiv preprint arXiv:2110.06069},
year = {2021}
}
Comments
This article provides a universal GMAMP framework including the existing OAMP/VAMP, GVAMP, and MAMP as instances. It gives new directions to construct low-complexity AMP algorithms for unitarily-invariant systems. BO-GMAMP is an example that overcomes the IID-matrix limitation of GAMP and avoids the high-complexity matrix inverse in GVAMP