Weakly decomposable regularization penalties and structured sparsity
Article first published online: 12 AUG 2013
© 2014 Board of the Foundation of the Scandinavian Journal of Statistics.
Scandinavian Journal of Statistics
Volume 41, Issue 1, pages 72–86, March 2014
How to Cite
van de Geer, S. (2014), Weakly decomposable regularization penalties and structured sparsity. Scandinavian Journal of Statistics, 41: 72–86. doi: 10.1111/sjos.12032
- Issue published online: 21 FEB 2014
- Article first published online: 12 AUG 2013
- Manuscript Accepted: 12 JUN 2013
- Manuscript Revised: 17 JAN 2013
- Manuscript Received: 18 JAN 2012
- sharp oracle inequality;
- weakly decomposable norm
It has been shown in literature that the Lasso estimator, or ℓ1-penalized least squares estimator, enjoys good oracle properties. This paper examines which special properties of the ℓ1-penalty allow for sharp oracle results, and then extends the situation to general norm-based penalties that satisfy a weak decomposability condition.