  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.
