LLASSO: A linear unified LASSO for multicollinear situations

TL;DR

The paper introduces LLASSO, a rescaled LASSO method designed for multicollinear data, which often outperforms traditional LASSO and elastic net in sparse modeling and variable selection tasks.

Contribution

It proposes a novel rescaled LASSO (LLASSO) that effectively handles multicollinearity and can be solved with existing efficient algorithms, extending LASSO's applicability.

Findings

LLASSO performs comparably or better than LASSO and elastic net.

Numerical studies demonstrate LLASSO's effectiveness in multicollinear situations.

The method can be integrated into existing algorithms for penalized estimators.

Abstract

We propose a rescaled LASSO, by premultipying the LASSO with a matrix term, namely linear unified LASSO (LLASSO) for multicollinear situations. Our numerical study has shown that the LLASSO is comparable with other sparse modeling techniques and often outperforms the LASSO and elastic net. Our findings open new visions about using the LASSO still for sparse modeling and variable selection. We conclude our study by pointing that the LLASSO can be solved by the same efficient algorithm for solving the LASSO and suggest to follow the same construction technique for other penalized estimators.