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

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 cap...

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Bibliographic Details
Published in2023 31st European Signal Processing Conference (EUSIPCO) pp. 1828 - 1832
Main Authors Shen, Dongrui, McLaughlin, Stephen, Altmann, Yoann
Format Conference Proceeding
LanguageEnglish
Published EURASIP 04.09.2023
Subjects
Correlation
Expectation-Propagation
Inverse problems
Linear regression
low-rank representation
Signal processing
Simulation
Sparse matrices
sparse regression
spectral unmixing
Stability analysis
Variational inference
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Summary: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.
ISSN:2076-1465
DOI:10.23919/EUSIPCO58844.2023.10289976