Expectation-Propagation with Low-Rank Constraints for Linear Inverse Problems

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Abstract

In this work, we address the problem of scalable approximate inference and covariance estimation for linear inverse problems using Expectation-Propagation (EP). Traditional EP methods rely on Gaussian approximations with either diagonal or full covariance structures. Full covariance matrices can capture correlation but do not scale as the dimensions of the problem increases, while diagonal matrices scale better but omit potentially important correlations. For the first time to the best of our knowledge, we propose to investigate low-rank decompositions within EP for linear regression. The potential benefits of such covariance structures are illustrated thorough simulations results obtained on sparse linear regression problems and a more challenging spectral unmixing problem where the sparse mixing coefficients are, in addition, subject to positivity constraints.
Original languageEnglish
Title of host publication31st European Signal Processing Conference (EUSIPCO 2023)
PublisherIEEE
Pages1828-1832
Number of pages5
ISBN (Electronic)9789464593600
DOIs
Publication statusPublished - 1 Nov 2023
Event31st European Signal Processing Conference 2023 - Helsinki, Finland
Duration: 4 Sept 20238 Sept 2023
https://eusipco2023.org/
http://eusipco2023.org/

Conference

Conference31st European Signal Processing Conference 2023
Abbreviated titleEUSIPCO 2023
Country/TerritoryFinland
CityHelsinki
Period4/09/238/09/23
Internet address

Keywords

  • Expectation-Propagation
  • Variational inference
  • low-rank representation
  • sparse regression
  • spectral unmixing

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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