2016/01/22 by Alican Nalci, I. A. Fedorov, Nalci, Alican +7
Computer Science · Engineering · #Bayesian Methods and Mixture Models #Blind Source Separation Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1601.06207
openalex publication_date 2016/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we develop a Bayesian evidence maximization framework to solve\nthe sparse non-negative least squares (S-NNLS) problem. We introduce a family\nof probability densities referred to as the Rectified Gaussian Scale Mixture\n(R- GSM) to model the sparsity enforcing prior distribution for the solution.\nThe R-GSM prior encompasses a variety of heavy-tailed densities such as the\nrectified Laplacian and rectified Student- t distributions with a proper choice\nof the mixing density. We utilize the hierarchical representation induced by\nthe R-GSM prior and develop an evidence maximization framework based on the\nExpectation-Maximization (EM) algorithm. Using the EM based method, we estimate\nthe hyper-parameters and obtain a point estimate for the solution. We refer to\nthe proposed method as rectified sparse Bayesian learning (R-SBL). We provide\nfour R- SBL variants that offer a range of options for computational complexity\nand the quality of the E-step computation. These methods include the Markov\nchain Monte Carlo EM, linear minimum mean-square-error estimation, approximate\nmessage passing and a diagonal approximation. Using numerical experiments, we\nshow that the proposed R-SBL method outperforms existing S-NNLS solvers in\nterms of both signal and support recovery performance, and is also very robust\nagainst the structure of the design matrix.\n