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March 2011 Random lasso
Sijian Wang, Bin Nan, Saharon Rosset, Ji Zhu
Ann. Appl. Stat. 5(1): 468-485 (March 2011). DOI: 10.1214/10-AOAS377

Abstract

We propose a computationally intensive method, the random lasso method, for variable selection in linear models. The method consists of two major steps. In step 1, the lasso method is applied to many bootstrap samples, each using a set of randomly selected covariates. A measure of importance is yielded from this step for each covariate. In step 2, a similar procedure to the first step is implemented with the exception that for each bootstrap sample, a subset of covariates is randomly selected with unequal selection probabilities determined by the covariates’ importance. Adaptive lasso may be used in the second step with weights determined by the importance measures. The final set of covariates and their coefficients are determined by averaging bootstrap results obtained from step 2. The proposed method alleviates some of the limitations of lasso, elastic-net and related methods noted especially in the context of microarray data analysis: it tends to remove highly correlated variables altogether or select them all, and maintains maximal flexibility in estimating their coefficients, particularly with different signs; the number of selected variables is no longer limited by the sample size; and the resulting prediction accuracy is competitive or superior compared to the alternatives. We illustrate the proposed method by extensive simulation studies. The proposed method is also applied to a Glioblastoma microarray data analysis.

Citation

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Sijian Wang. Bin Nan. Saharon Rosset. Ji Zhu. "Random lasso." Ann. Appl. Stat. 5 (1) 468 - 485, March 2011. https://doi.org/10.1214/10-AOAS377

Information

Published: March 2011
First available in Project Euclid: 21 March 2011

zbMATH: 1220.62091
MathSciNet: MR2810406
Digital Object Identifier: 10.1214/10-AOAS377

Rights: Copyright © 2011 Institute of Mathematical Statistics

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Vol.5 • No. 1 • March 2011
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