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)

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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.

Original language	English
Title of host publication	Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings
Publisher	Springer Verlag
Pages	379-391
Number of pages	13
ISBN (Print)	3540352945, 9783540352945
DOIs	https://doi.org/10.1007/11776420_29
Publication status	Published - 1 Jan 2006
Event	19th Annual Conference on Learning Theory, COLT 2006 - Pittsburgh, PA, United States Duration: 22 Jun 2006 → 25 Jun 2006

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4005 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	19th Annual Conference on Learning Theory, COLT 2006
Country/Territory	United States
City	Pittsburgh, PA
Period	22/06/06 → 25/06/06

Access to Document

10.1007/11776420_29

Cite this

Bunea, F., Tsybakov, A. B., & Wegkamp, M. H. (2006). Aggregation and sparsity via ℓ₁ penalized least squares. In Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings (pp. 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. pp. 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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booktitle = "Learning Theory - 19th Annual Conference on Learning Theory, COLT 2006, Proceedings",

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Bunea, F, Tsybakov, AB & Wegkamp, MH 2006, Aggregation and sparsity via ℓ₁ penalized least squares. in 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, pp. 379-391, 19th Annual Conference on Learning Theory, COLT 2006, Pittsburgh, PA, United States, 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).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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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.

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Bunea F, Tsybakov AB, Wegkamp MH. Aggregation and sparsity via ℓ₁ penalized least squares. In 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