LLASSO: A linear unified LASSO for multicollinear situations

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.