  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.
