Generalized LASSO with under-determined regularization matrices.
Generalized LASSO with under-determined regularization matrices.
复制标题
具有欠定正则化矩阵的广义 LASSO
DOI：
10.1016/j.sigpro.2016.03.001
复制
发表时间：
2016-10
影响因子：
4.4
通讯作者：
Wang YP
中科院分区：
文献类型：
--
作者：
Duan J;Soussen C;Brie D;Idier J;Wan M;Wang YP
本文研究了广义套索与基本套索公式之间的内在联系。前者是后者的扩展形式，通过在系数中引入正则化矩阵来实现。我们证明了当正则化矩阵是偶数或欠定且满足满秩性条件时，广义套索可以通过拉格朗日框架转化为套索形式。此外，我们还证明了一些已发表的结果可以推广到广义套索上，并且一些套索的变种，如稳健套索，可以重写为广义套索形式，从而可以转化为基本套索形式。基于这种联系，许多现有的关于套索的结果，例如有效的套索求解器，可以用于广义套索。
This paper studies the intrinsic connection between a generalized LASSO and a basic LASSO formulation. The former is the extended version of the latter by introducing a regularization matrix to the coefficients. We show that when the regularization matrix is even- or under-determined with full rank conditions, the generalized LASSO can be transformed into the LASSO form via the Lagrangian framework. In addition, we show that some published results of LASSO can be extended to the generalized LASSO, and some variants of LASSO, e.g., robust LASSO, can be rewritten into the generalized LASSO form and hence can be transformed into basic LASSO. Based on this connection, many existing results concerning LASSO, e.g., efficient LASSO solvers, can be used for generalized LASSO.