Abstract

We consider the problem of signal estimation in generalized linear models (GLM), a class of models which includes canonical problems such as linear regression, logistic regression, and phase retrieval. Recent work has precisely characterized the asymptotic minimum mean-squared error (MMSE) for GLMs with i.i.d. Gaussian measurement matrices. However, in many models there is a significant gap between the MMSE and the performance of the best known feasible estimators. To address this, we consider GLMs defined via spatially coupled measurement matrices. We propose an efficient approximate message passing (AMP) algorithm for estimation and prove that the error of a carefully tuned AMP estimator approaches the asymptotic MMSE .

The talk will not assume any background on message passing or spatial coupling. Joint work with Pablo Pascual Cobo and Kuan Hsieh.