Open Access
March 2010 The Bayesian elastic net
Qing Li, Nan Lin
Bayesian Anal. 5(1): 151-170 (March 2010). DOI: 10.1214/10-BA506


Elastic net Zou and Hastie (2005) is a flexible regularization and variable selection method that uses a mixture of $L_1$ and $L_2$ penalties. It is particularly useful when there are much more predictors than the sample size. This paper proposes a Bayesian method to solve the elastic net model using a Gibbs sampler. While the marginal posterior mode of the regression coefficients is equivalent to estimates given by the non-Bayesian elastic net, the Bayesian elastic net has two major advantages. Firstly, as a Bayesian method, the distributional results on the estimates are straightforward, making the statistical inference easier. Secondly, it chooses the two penalty parameters simultaneously, avoiding the "double shrinkage problem" in the elastic net method. Real data examples and simulation studies show that the Bayesian elastic net behaves comparably in prediction accuracy but performs better in variable selection.


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Qing Li. Nan Lin. "The Bayesian elastic net." Bayesian Anal. 5 (1) 151 - 170, March 2010.


Published: March 2010
First available in Project Euclid: 22 June 2012

zbMATH: 1330.65026
MathSciNet: MR2596439
Digital Object Identifier: 10.1214/10-BA506

Keywords: Bayesian analysis , Elastic net , Gibbs sampler , regularization , Variable selection

Rights: Copyright © 2010 International Society for Bayesian Analysis

Vol.5 • No. 1 • March 2010
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