Weakly decomposable regularization penalties and structured sparsity

Weakly decomposable regularization penalties and structured sparsity

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...

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Veröffentlicht in:Scandinavian journal of statistics 2014-03, Vol.41 (1), p.72-86
1. Verfasser: van de Geer, Sara
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Convexity
Eigenvalues
Estimating techniques
Estimators
Fines & penalties
Index sets
lasso
Least squares
Machine learning
Oracles
regularization
sharp oracle inequality
sparsity
Statistical analysis
Statistical methods
Statistical theories
Studies
Triangle inequalities
weakly decomposable norm
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Beschreibung
Zusammenfassung: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.
ISSN:0303-6898
1467-9469
DOI:10.1111/sjos.12032