L1 regularization, or regularization with an L1 penalty, is a popular idea in statistics and
machine learning. This paper reviews the concept and application of L1 regularization for …

We study full Bayesian procedures for high-dimensional linear regression under sparsity
constraints. The prior is a mixture of point masses at zero and continuous distributions …

The Lasso estimate for linear regression parameters can be interpreted as a Bayesian
posterior mode estimate when the regression parameters have independent Laplace (ie …

Multivariable regression models are of fundamental importance in all areas of science in
which empirical data must be analyzed. This book proposes a systematic approach to …

Abstract Fan & Li (2001) propose a family of variable selection methods via penalized
likelihood using concave penalty functions. The nonconcave penalized likelihood estimators …

The lasso estimate for linear regression corresponds to a posterior mode when
independent, double-exponential prior distributions are placed on the regression …

Bayesian variable selection with shrinking and diffusing priors Page 1 The Annals of Statistics
2014, Vol. 42, No. 2, 789–817 DOI: 10.1214/14-AOS1207 © Institute of Mathematical Statistics …

We propose a generalized double Pareto prior for Bayesian shrinkage estimation and
inferences in linear models. The prior can be obtained via a scale mixture of Laplace or …

We provide a review of prior distributions for objective Bayesian analysis. We start by
examining some foundational issues and then organize our exposition into priors for: i) …

The paper revisits the Bayesian group lasso and uses spike and slab priors for group
variable selection. In the process, the connection of our model with penalized regression is …