Abstract
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.
Original language | English (US) |
---|---|
Pages (from-to) | 1978-2004 |
Number of pages | 27 |
Journal | Annals of Statistics |
Volume | 38 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2010 |
Externally published | Yes |
Keywords
- Group Lasso
- Group sparsity
- L regularization
- Lasso
- Parameter estimation
- Regression
- Sparsity
- Variable selection
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty