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Generalized LASSO with under-determined regularization matrices

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-01295086
Contributor : Charles Soussen Connect in order to contact the contributor
Submitted on : Wednesday, March 30, 2016 - 1:38:22 PM
Last modification on : Wednesday, April 27, 2022 - 4:40:10 AM

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Junbo Duan, Charles Soussen, David Brie, Jérôme Idier, Mingxi Wan, et al.. Generalized LASSO with under-determined regularization matrices. Signal Processing, Elsevier, 2016, 127, pp.239-246. ⟨10.1016/j.sigpro.2016.03.001⟩. ⟨hal-01295086⟩

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