Sparse Bayesian learning with automatic-weighting Laplace priors for sparse signal recovery

Zonglong Bai () and Jinwei Sun
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Zonglong Bai: North China Electric Power University
Jinwei Sun: Harbin Institute of Technology

Computational Statistics, 2023, vol. 38, issue 4, No 20, 2053-2074

Abstract: Abstract The least absolute shrinkage and selection operator (LASSO) and its variants are widely used for sparse signal recovery. However, the determination of the regularization factor requires cross-validation strategy, which may obtain a sub-optimal solution. Motivated by the self-regularization nature of sparse Bayesian learning (SBL) approach and the framework of generalized LASSO, we propose a new hierarchical Bayesian model using automatic-weighting Laplace priors in this paper. In the proposed hierarchical Bayesian model, the posterior distributions of all the parameters can be approximated using variational Bayesian inference, resulting in closed-form solutions for all parameters updating. Moreover, the space alternating variational estimation strategy is used to avoid matrix inversion, and a fast algorithm (SAVE-WLap-SBL) is proposed. Comparing to existed SBL methods, the proposed method encourages the sparsity of signals more efficiently. Numerical experiments on synthetic and real data illustrate the benefit of these advances.

Keywords: Sparse signal recovery; Sparse Bayesian leaning; Space alternative variational estimation (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00180-023-01354-4

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