A Bayesian Lasso based Sparse Learning Model
This is an incremental improvement for researchers in sparse learning and regression, offering a new estimation method within an existing Bayesian framework.
The paper tackled the problem of sparse parameter estimation in regression by developing the Bayesian Lasso Sparse (BLS) model, which uses a type-II maximum likelihood procedure to provide sparse estimates and is extended to nonlinear problems with kernels, showing it is sparse and precise, especially on noisy and irregular datasets.
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that takes the hierarchical model formulation of the Bayesian Lasso. The main difference from the original Bayesian Lasso lies in the estimation procedure; the BLS method uses a learning algorithm based on the type-II maximum likelihood procedure. Opposed to the Bayesian Lasso, the BLS provides sparse estimates of the regression parameters. The BLS method is also derived for nonlinear supervised learning problems by introducing kernel functions. We compare the BLS model to the well known Relevance Vector Machine, the Fast Laplace method, the Byesian Lasso, and the Lasso, on both simulated and real data. The numerical results show that the BLS is sparse and precise, especially when dealing with noisy and irregular dataset.