Open Access
March 2008 Coordinate descent algorithms for lasso penalized regression
Tong Tong Wu, Kenneth Lange
Ann. Appl. Stat. 2(1): 224-244 (March 2008). DOI: 10.1214/07-AOAS147


Imposition of a lasso penalty shrinks parameter estimates toward zero and performs continuous model selection. Lasso penalized regression is capable of handling linear regression problems where the number of predictors far exceeds the number of cases. This paper tests two exceptionally fast algorithms for estimating regression coefficients with a lasso penalty. The previously known 2 algorithm is based on cyclic coordinate descent. Our new 1 algorithm is based on greedy coordinate descent and Edgeworth’s algorithm for ordinary 1 regression. Each algorithm relies on a tuning constant that can be chosen by cross-validation. In some regression problems it is natural to group parameters and penalize parameters group by group rather than separately. If the group penalty is proportional to the Euclidean norm of the parameters of the group, then it is possible to majorize the norm and reduce parameter estimation to 2 regression with a lasso penalty. Thus, the existing algorithm can be extended to novel settings. Each of the algorithms discussed is tested via either simulated or real data or both. The Appendix proves that a greedy form of the 2 algorithm converges to the minimum value of the objective function.


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Tong Tong Wu. Kenneth Lange. "Coordinate descent algorithms for lasso penalized regression." Ann. Appl. Stat. 2 (1) 224 - 244, March 2008.


Published: March 2008
First available in Project Euclid: 24 March 2008

zbMATH: 1137.62045
MathSciNet: MR2415601
Digital Object Identifier: 10.1214/07-AOAS147

Keywords: consistency , convergence , cyclic , Edgeworth’s algorithm , greedy , Model selection

Rights: Copyright © 2008 Institute of Mathematical Statistics

Vol.2 • No. 1 • March 2008
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