The Bayesian elastic net

By Qing Li, Nan Lin. 2010

354 citations recorded by the source corpus.

. 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.

Subfields: Artificial Intelligence, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/769b70e74fd8890042841f00f39e7b982aa3193e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Davide Ferrari
2. Chris Hans
3. P. Pérez
4. Jose Crossa
5. Yuhong Yang
6. Milica Miočević
7. R. van de Schoot
8. Susanne Dreisigacker

In Control and Systems Engineering

1. Chris Hans
2. P. Pérez
3. Jose Crossa
4. Yuhong Yang
5. Davide Ferrari
6. Milica Miočević
7. R. van de Schoot
8. G. de los Campos

In Statistics and Probability

1. Davide Ferrari
2. Milica Miočević
3. Chris Hans
4. P. Pérez
5. Jose Crossa
6. Yuhong Yang
7. R. van de Schoot
8. Susanne Dreisigacker

Citations in the corpus

• Elastic Net Regression Modeling With the Orthant Normal Prior (2011, methodology): “This result was reported independently by Li and Lin (2010).”
• Small Sample Size Solutions (2020, methodology): “These Bayesian analogues of classical penalization methods have been shown to perform similarly to and in some cases better than the classical penalization methods (Kyung, Gill, Ghosh, & Casella, 2010; Li & Lin, 2010).”
• Genomic Selection and Prediction in Plant Breeding (2011, methodology): “The list of Bayesian models is extensive and includes Bayesian counterparts of RR, LASSO (eg, the Bayesian LASSO of Park & Casella 2008 ) and EN (Bayesian elastic net, eg, Li & Lin 2010 ), as well as models such as Bayes A or Bayes B ( Meuwissen, Hayes, & Goddard 2001 ) and extensions thereof.”
• Confidence sets for model selection by F -testing (2015, background): “Tibshirani (1996), Zou and Hastie (2005), Li and Lin (2010) studied these data among other authors in the model selection literature.”