An expectation-maximization approach to tuning generalized vector approximate message passing

Christopher A. Metzler, Philip Schniter, Richard G. Baraniuk

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

Abstract

Generalized Vector Approximate Message Passing (GVAMP) is an efficient iterative algorithm for approximately minimum-mean-squared-error estimation of a random vector x~px(x) from generalized linear measurements, i.e., measurements of the form y=Q(z) where z = Ax with known A, and Q(·) is a noisy, potentially nonlinear, componentwise function. Problems of this form show up in numerous applications, including robust regression, binary classification, quantized compressive sensing, and phase retrieval. In some cases, the prior p(x) and/or channel Q(·) depend on unknown deterministic parameters θ, which prevents a direct application of GVAMP. In this paper we propose a way to combine expectation maximization (EM) with GVAMP to jointly estimate x and θ. We then demonstrate how EM-GVAMP can solve the phase retrieval problem with unknown measurement-noise variance.

Original languageEnglish (US)
Title of host publicationLatent Variable Analysis and Signal Separation - 14th International Conference, LVA/ICA 2018, Proceedings
EditorsSharon Gannot, Yannick Deville, Russell Mason, Mark D. Plumbley, Dominic Ward
PublisherSpringer-Verlag
Pages395-406
Number of pages12
ISBN (Print)9783319937632
DOIs
StatePublished - 2018
Event14th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2018 - Guildford, United Kingdom
Duration: Jul 2 2018Jul 5 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10891 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other14th International Conference on Latent Variable Analysis and Signal Separation, LVA/ICA 2018
CountryUnited Kingdom
CityGuildford
Period7/2/187/5/18

Keywords

  • Compressive sensing
  • Expectation maximization
  • Generalized linear model
  • Phase retrieval

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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