An Efficient Sparse Bayesian Learning Algorithm Based on Gaussian-Scale Mixtures

doi:10.1109/TNNLS.2020.3049056

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An Efficient Sparse Bayesian Learning Algorithm Based on Gaussian-Scale Mixtures

2022-07-01

PRE

Wei Zhou

Hai‐Tao Zhang *

王娟 (Jun Wang) *

DOI：10.1109/TNNLS.2020.3049056

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Abstract

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Sparse Bayesian learning (SBL) is a popular machine learning approach with a superior generalization capability due to the sparsity of its adopted model. However, it entails a matrix inversion at each iteration, hindering its practical applications with large-scale data sets. To overcome this bottleneck, we propose an efficient SBL algorithm with O(n(2)) computational complexity per iteration based on a Gaussian-scale mixture prior model. By specifying two different hyperpriors, the proposed efficient SBL algorithm can meet two different requirements, such as high efficiency and high sparsity. A surrogate function is introduced herein to approximate the posterior density of model parameters and thereby to avoid matrix inversions. Using a data-dependent term, a joint cost function with separate penalty terms is reformulated in a joint space of model parameters and hyperparameters. The resulting nonconvex optimization problem is solved using a block coordinate descent method in a majorization-minimization framework. Finally, the results of extensive experiments for sparse signal recovery and sparse image reconstruction on benchmark problems are elaborated to substantiate the effectiveness and superiority of the proposed approach in terms of computational time and estimation error.

Keywords:

Bayes methods

Computational modeling

GSM

Kernel

Gamma distribution

Covariance matrices

Approximation algorithms

Gaussian scale mixture

iterative algorithms

optimization methods

regression

sparse Bayesian learning (SBL)

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