A Bayesian Lasso based sparse learning model

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 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 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, the Bayesian 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.