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A complete analysis of the l_1,p Group-Lasso

Vogt, Julia and Roth, Volker. (2012) A complete analysis of the l_1,p Group-Lasso. In: 29th International Conference on Machine Learning (ICML 2012), 8 S.. Edinburgh.

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Official URL: http://edoc.unibas.ch/dok/A6018450

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Abstract

The Group-Lasso is a well-known tool for joint regularization in machine learning methods. While the l_{1,2} and the l_{1,∞} version have been studied in detail and efficient algorithms exist, there are still open questions regarding other l_{1,p} variants. We characterize conditions for solutions of the l_{1,p} Group-Lasso for all p-norms with 1 >= p >= ∞, and we present a unified active set algorithm. For all p-norms, a highly efficient projected gradient algorithm is presented. This new algorithm enables us to compare the prediction performance of many variants of the Group-Lasso in a multi-task learning setting, where the aim is to solve many learning problems in parallel which are coupled via the Group-Lasso constraint. We conduct large-scale experiments on synthetic data and on two real-world data sets. In accordance with theoretical characterizations of the different norms we observe that the weak-coupling norms with p between 1.5 and 2 consistently outperform the strong-coupling norms with p << 2.
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:International Machine Learning Society
Note:Publication type according to Uni Basel Research Database: Conference paper
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Last Modified:13 Sep 2013 08:00
Deposited On:13 Sep 2013 07:58

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