Journal
ANNALS OF STATISTICS
Volume 38, Issue 4, Pages 1978-2004Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/09-AOS778
Keywords
L-1 regularization; Lasso; group Lasso; regression; sparsity; group sparsity; variable selection; parameter estimation
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Funding
- NSF [DMS-07-06805, NSA-081024, AFOSR-10097389]
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This paper develops a theory for group Lasso using a concept called strong group sparsity. Our result shows that group Lasso is superior to standard Lasso for strongly group-sparse signals. This provides a convincing theoretical justification for using group sparse regularization when the underlying group structure is consistent with the data. Moreover, the theory predicts some limitations of the group Lasso formulation that are confirmed by simulation studies.
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