Vector approximate message passing for the generalized linear model

Philip Schniter, Sundeep Rangan, Alyson K. Fletcher

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

The generalized linear model (GLM), where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform output z = Ax, arises in a range of applications such as robust regression, binary classification, quantized compressed sensing, phase retrieval, photon-limited imaging, and inference from neural spike trains. When A is large and i.i.d. Gaussian, the generalized approximate message passing (GAMP) algorithm is an efficient means of MAP or marginal inference, and its performance can be rigorously characterized by a scalar state evolution. For general A, though, GAMP can misbehave. Damping and sequential-updating help to robustify GAMP, but their effects are limited. Recently, a 'vector AMP' (VAMP) algorithm was proposed for additive white Gaussian noise channels. VAMP extends AMP's guarantees from i.i.d. Gaussian A to the larger class of rotationally invariant A. In this paper, we show how VAMP can be extended to the GLM. Numerical experiments show that the proposed GLM-VAMP is much more robust to ill-conditioning in A than damped GAMP.

Original languageEnglish (US)
Title of host publicationConference Record of the 50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
EditorsMichael B. Matthews
PublisherIEEE Computer Society
Pages1525-1529
Number of pages5
ISBN (Electronic)9781538639542
DOIs
StatePublished - Mar 1 2017
Event50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016 - Pacific Grove, United States
Duration: Nov 6 2016Nov 9 2016

Publication series

NameConference Record - Asilomar Conference on Signals, Systems and Computers
ISSN (Print)1058-6393

Other

Other50th Asilomar Conference on Signals, Systems and Computers, ACSSC 2016
CountryUnited States
CityPacific Grove
Period11/6/1611/9/16

ASJC Scopus subject areas

  • Signal Processing
  • Computer Networks and Communications

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