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RESEARCH PRODUCT
La Géométrie pour l'Unicité, la Parcimonie et l'Appariement des Estimateurs Pénalisés
Patrick TardivelUlrike Schneidersubject
vecteur signe accessiblepoursuite de baseUniquenessLASSOaccessible sign vector[MATH] Mathematics [math]basis pursuitUnicitédescription
During the talk we will give a necessary and sufficient condition for the uniqueness of a penalized least squares estimator whose penalty term is a polyhedral norm. Our results cover many methods including the OSCAR, SLOPE and LASSO estimators as well as the related method of basis pursuit. The geometrical condition for uniqueness involves how the row span of the design matrix intersects the faces of the dual normunit ball. Theoretical results on sparsity by LASSO and basis pursuit estimators are deduced from this condition via the characterization of accessible sign vectors for these two methods.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2022-01-01 |