Aggregation by exponential weighting and sharp oracle inequalities

Arnak S. Dalalyan; Alexandre B. Tsybakov

doi:10.1007/978-3-540-72927-3_9

Aggregation by exponential weighting and sharp oracle inequalities

Arnak S. Dalalyan
, Alexandre B. Tsybakov

Sorbonne Université

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

Abstract

In the present paper, we study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp oracle inequalities for convex aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We show how these results can be applied to derive a sparsity oracle inequality.

Original language	English
Title of host publication	Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings
Publisher	Springer Verlag
Pages	97-111
Number of pages	15
ISBN (Print)	9783540729259
DOIs	https://doi.org/10.1007/978-3-540-72927-3_9
Publication status	Published - 1 Jan 2007
Externally published	Yes
Event	20th Annual Conference on Learning Theory, COLT 2007 - San Diego, CA, United States Duration: 13 Jun 2007 → 15 Jun 2007

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4539 LNAI
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	20th Annual Conference on Learning Theory, COLT 2007
Country/Territory	United States
City	San Diego, CA
Period	13/06/07 → 15/06/07

Access to Document

10.1007/978-3-540-72927-3_9

Cite this

Dalalyan, A. S., & Tsybakov, A. B. (2007). Aggregation by exponential weighting and sharp oracle inequalities. In Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings (pp. 97-111). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4539 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-540-72927-3_9

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title = "Aggregation by exponential weighting and sharp oracle inequalities",

abstract = "In the present paper, we study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp oracle inequalities for convex aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We show how these results can be applied to derive a sparsity oracle inequality.",

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Dalalyan, AS & Tsybakov, AB 2007, Aggregation by exponential weighting and sharp oracle inequalities. in Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4539 LNAI, Springer Verlag, pp. 97-111, 20th Annual Conference on Learning Theory, COLT 2007, San Diego, CA, United States, 13/06/07. https://doi.org/10.1007/978-3-540-72927-3_9

Aggregation by exponential weighting and sharp oracle inequalities. / Dalalyan, Arnak S.; Tsybakov, Alexandre B.
Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings. Springer Verlag, 2007. p. 97-111 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4539 LNAI).

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

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AB - In the present paper, we study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp oracle inequalities for convex aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We show how these results can be applied to derive a sparsity oracle inequality.

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Dalalyan AS, Tsybakov AB. Aggregation by exponential weighting and sharp oracle inequalities. In Learning Theory - 20th Annual Conference on Learning Theory, COLT 2007, Proceedings. Springer Verlag. 2007. p. 97-111. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-72927-3_9

Aggregation by exponential weighting and sharp oracle inequalities

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