Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. However, the most popular inference algorithms for SBL become too expensive for high-dimensional problems due to the need to maintain a large covariance matrix. To resolve this issue, we introduce a new SBL inference algorithm that avoids explicit computation of the covariance matrix, thereby saving significant time and space. Instead of performing costly matrix
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