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The l_1,p Group-Lasso for Multi-Task Learning

The Group-Lasso is a well known tool for joint regularization in machine learning methods. While the l_1,2 version has been studied in detail, there are still open questions regarding the uniqueness of solutions and the efficiency of algorithms for other l_1,p variants. We characterize conditions for uniqueness of solutions for the Group-Lasso for all p with 1<= p <= infinity. We present a simple test for uniqueness of solutions in high dimensions and derive a highly efficient active set algorithm that can deal with input dimensions in the millions. Hence we are able to compare the prediction performance of all 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 experiments on synthetic data and on real world data sets.

Type of Seminar:
IfA BISON Seminar
Julia Vogt
Uni Basel
Jan 25, 2011   13:30

Contact Person:

Elias August
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