Random lasso

TL;DR

The paper introduces a computationally intensive random lasso method for variable selection in linear models, improving upon existing methods by handling correlated variables better and allowing more variables to be selected.

Contribution

It presents a novel two-step bootstrap-based random lasso approach that enhances variable selection and coefficient estimation, especially for microarray data.

Findings

Outperforms traditional lasso and elastic-net in simulations

Selects highly correlated variables more effectively

Achieves competitive or superior prediction accuracy

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.