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The Group-Lasso: ℓ1, ∞  Regularization versus ℓ1,2 Regularization

Julia E. Vogt, and Volker Roth, . (2010) The Group-Lasso: ℓ1, ∞  Regularization versus ℓ1,2 Regularization. In: Pattern Recognition : 32nd DAGM Symposium, Darmstadt, Germany, September 22-24, 2010. Proceedings. Berlin, Heidelberg, pp. 252-261.

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Official URL: http://edoc.unibas.ch/dok/A5840196

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Abstract

The ℓ1, ∞ norm and the ℓ1,2 norm are well known tools for joint regularization in Group-Lasso methods. While the ℓ1,2 version has been studied in detail, there are still open questions regarding the uniqueness of solutions and the efficiency of algorithms for the ℓ1, ∞ variant. For the latter, we characterize the conditions for uniqueness of solutions, we present a simple test for uniqueness, and we derive a highly efficient active set algorithm that can deal with input dimensions in the millions. We compare both variants of the Group-Lasso for the two most common application scenarios of the Group-Lasso, one is to obtain sparsity on the level of groups in “standard” prediction problems, the second one is multi-task learning where the aim is to solve many learning problems in parallel which are coupled via the Group-Lasso constraint. We show that both version perform quite similar in “standard” applications. However, a very clear distinction between the variants occurs in multi-task settings where the ℓ1,2 version consistently outperforms the ℓ1, ∞ counterpart in terms of prediction accuracy.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Informatik > Datenanalyse (Roth)
UniBasel Contributors:Roth, Volker and Vogt, Julia
Item Type:Conference or Workshop Item, refereed
Conference or workshop item Subtype:Conference Paper
Bibsysno:Link to catalogue
Publisher:Springer-Verlag Berlin Heidelberg
ISBN:978-3-642-15986-2 ; 978-3-642-15985-5
Series Name:Lecture Notes in Computer Science
Issue Number:6376
Note:Publication type according to Uni Basel Research Database: Conference paper
Identification Number:
Last Modified:06 Mar 2014 14:13
Deposited On:08 Jun 2012 06:32

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