Aggregation and sparsity via ℓ1 penalized least squares

Florentina Bunea; Alexandre B. Tsybakov; Marten H. Wegkamp

doi:10.1007/11776420_29

Aggregation and sparsity via ℓ₁ penalized least squares

Florentina Bunea
, Alexandre B. Tsybakov
, Marten H. Wegkamp

Florida State University
Institute for Information Transmission Problems (RAS)

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

Résumé

This paper shows that near optimal rates of aggregation and adaptation to unknown sparsity can be simultaneously achieved via ℓ₁ penalized least squares in a nonparametric regression setting. The main tool is a novel oracle inequality on the sum between the empirical squared loss of the penalized least squares estimate and a term reflecting the sparsity of the unknown regression function.

langue originale	Anglais
titre	Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings
Editeur	Springer Verlag
Pages	379-391
Nombre de pages	13
ISBN (imprimé)	3540352945, 9783540352945
Les DOIs	https://doi.org/10.1007/11776420_29
état	Publié - 1 janv. 2006
Evénement	19th Annual Conference on Learning Theory, COLT 2006 - Pittsburgh, PA, États-Unis Durée: 22 juin 2006 → 25 juin 2006

Série de publications

Nom	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4005 LNAI
ISSN (imprimé)	0302-9743
ISSN (Electronique)	1611-3349

Une conférence

Une conférence	19th Annual Conference on Learning Theory, COLT 2006
Pays/Territoire	États-Unis
La ville	Pittsburgh, PA
période	22/06/06 → 25/06/06

Accès au document

10.1007/11776420_29

Contient cette citation

Bunea, F., Tsybakov, A. B., & Wegkamp, M. H. (2006). Aggregation and sparsity via ℓ₁ penalized least squares. Dans Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings (p. 379-391). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol 4005 LNAI). Springer Verlag. https://doi.org/10.1007/11776420_29

Bunea, Florentina ; Tsybakov, Alexandre B. ; Wegkamp, Marten H. / Aggregation and sparsity via ℓ₁ penalized least squares. Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings. Springer Verlag, 2006. p. 379-391 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Aggregation and sparsity via ℓ1 penalized least squares",

abstract = "This paper shows that near optimal rates of aggregation and adaptation to unknown sparsity can be simultaneously achieved via ℓ1 penalized least squares in a nonparametric regression setting. The main tool is a novel oracle inequality on the sum between the empirical squared loss of the penalized least squares estimate and a term reflecting the sparsity of the unknown regression function.",

author = "Florentina Bunea and Tsybakov, \{Alexandre B.\} and Wegkamp, \{Marten H.\}",

year = "2006",

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doi = "10.1007/11776420\_29",

language = "English",

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Bunea, F, Tsybakov, AB & Wegkamp, MH 2006, Aggregation and sparsity via ℓ₁ penalized least squares. Dans Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), VOL. 4005 LNAI, Springer Verlag, p. 379-391, 19th Annual Conference on Learning Theory, COLT 2006, Pittsburgh, PA, États-Unis, 22/06/06. https://doi.org/10.1007/11776420_29

Aggregation and sparsity via ℓ₁ penalized least squares. / Bunea, Florentina; Tsybakov, Alexandre B.; Wegkamp, Marten H.
Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings. Springer Verlag, 2006. p. 379-391 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol 4005 LNAI).

Résultats de recherche: Le chapitre dans un livre, un rapport, une anthologie ou une collection › Contribution à une conférence › Revue par des pairs

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N2 - This paper shows that near optimal rates of aggregation and adaptation to unknown sparsity can be simultaneously achieved via ℓ1 penalized least squares in a nonparametric regression setting. The main tool is a novel oracle inequality on the sum between the empirical squared loss of the penalized least squares estimate and a term reflecting the sparsity of the unknown regression function.

AB - This paper shows that near optimal rates of aggregation and adaptation to unknown sparsity can be simultaneously achieved via ℓ1 penalized least squares in a nonparametric regression setting. The main tool is a novel oracle inequality on the sum between the empirical squared loss of the penalized least squares estimate and a term reflecting the sparsity of the unknown regression function.

U2 - 10.1007/11776420_29

DO - 10.1007/11776420_29

M3 - Conference contribution

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SN - 9783540352945

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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BT - Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings

PB - Springer Verlag

T2 - 19th Annual Conference on Learning Theory, COLT 2006

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Bunea F, Tsybakov AB, Wegkamp MH. Aggregation and sparsity via ℓ₁ penalized least squares. Dans Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings. Springer Verlag. 2006. p. 379-391. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/11776420_29