Title:      Penalized Regression, Standard Errors, and Bayesian
Lassos

Authors:    Minjung Kyung, Jeff Gill, Malay Ghosh, George
Casella

Entrydate:  2009-01-23 08:24:45

Keywords:   model selection, lassos, Bayesian hierarchical
models, LARS algorithm, EM/Gibbs sampler

Abstract:   Penalized regression methods for simultaneous
variable selection and coefficient estimation, especially those
based on the lasso of Tibshirani (1996), have received a great
deal of attention in recent years, mostly through frequentist
models. Properties such as consistency have been studied, and
are achieved by different lasso variations. Here we look at a
fully Bayesian formulation of the problem, which is flexible
enough to encompass most versions of the lasso that have been
previously considered. The advantages of the hierarchical
Bayesian formulations are many. In addition to the usual
ease-of-interpretation of hierarchical models, the Bayesian
formulation produces valid standard errors (which can be
problematic for the frequentist lasso), and is based on a
geometrically ergodic Markov chain. We compare the performance
of the Bayesian lassos to their frequentist counterparts using
simulations and data sets that previous lasso papers have used,
and see that in terms of prediction mean squared error, the
Bayesian lasso performance is similar to and, in some cases,
better than, the frequentist lasso. 

http://polmeth.wustl.edu/retrieve.php?id=893

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