Covariance-Free Sparse Bayesian Learning

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. The most popular inference algorithms for SBL exhibit prohibitively large computational costs for high-dimensional problems due to the need to maintain a lar...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 70; pp. 3818 - 3831
Main Authors: Lin, Alexander, Song, Andrew H., Bilgic, Berkin, Ba, Demba
Format: Journal Article
Language:English
Published: New York IEEE 2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithms
Bayes methods
Bayesian analysis
Coding
compressed sensing
computational efficiency
Computational modeling
Covariance matrices
Covariance matrix
Encoding
expectation-maximization algorithms
Inference
Inference algorithms
Linear algebra
Linear systems
Machine learning
Mathematical analysis
Signal processing algorithms
Sparse Bayesian learning (SBL)
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary:Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. The most popular inference algorithms for SBL exhibit prohibitively large computational costs for high-dimensional problems due to the need to maintain a large covariance matrix. To resolve this issue, we introduce a new method for accelerating SBL inference - named covariance-free expectation maximization (CoFEM) - that avoids explicit computation of the covariance matrix. CoFEM solves multiple linear systems to obtain unbiased estimates of the posterior statistics needed by SBL. This is accomplished by exploiting innovations from numerical linear algebra such as preconditioned conjugate gradient and a little-known diagonal estimation rule. For a large class of compressed sensing matrices, we provide theoretical justifications for why our method scales well in high-dimensional settings. Through simulations, we show that CoFEM can be up to thousands of times faster than existing baselines without sacrificing coding accuracy. Through applications to calcium imaging deconvolution and multi-contrast MRI reconstruction, we show that CoFEM enables SBL to tractably tackle high-dimensional sparse coding problems of practical interest.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2022.3186185