Optimal rates of aggregation

Alexandre B. Tsybakov

doi:10.1007/978-3-540-45167-9_23

Optimal rates of aggregation

Alexandre B. Tsybakov

Research output: Contribution to journal › Conference article › peer-review

Abstract

We study the problem of aggregation of M arbitrary estimators of a regression function with respect to the mean squared risk. Three main types of aggregation are considered: model selection, convex and linear aggregation. We define the notion of optimal rate of aggregation in an abstract context and prove lower bounds valid for any method of aggregation. We then construct procedures that attain these bounds, thus establishing optimal rates of linear, convex and model selection type aggregation.

Original language	English
Pages (from-to)	303-313
Number of pages	11
Journal	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2777
DOIs	https://doi.org/10.1007/978-3-540-45167-9_23
Publication status	Published - 1 Jan 2003
Event	16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003 - Washington, DC, United States Duration: 24 Aug 2003 → 27 Aug 2003

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10.1007/978-3-540-45167-9_23

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abstract = "We study the problem of aggregation of M arbitrary estimators of a regression function with respect to the mean squared risk. Three main types of aggregation are considered: model selection, convex and linear aggregation. We define the notion of optimal rate of aggregation in an abstract context and prove lower bounds valid for any method of aggregation. We then construct procedures that attain these bounds, thus establishing optimal rates of linear, convex and model selection type aggregation.",

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AB - We study the problem of aggregation of M arbitrary estimators of a regression function with respect to the mean squared risk. Three main types of aggregation are considered: model selection, convex and linear aggregation. We define the notion of optimal rate of aggregation in an abstract context and prove lower bounds valid for any method of aggregation. We then construct procedures that attain these bounds, thus establishing optimal rates of linear, convex and model selection type aggregation.

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DO - 10.1007/978-3-540-45167-9_23

M3 - Conference article

AN - SCOPUS:9444226947

SN - 0302-9743

VL - 2777

SP - 303

EP - 313

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

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

T2 - 16th Annual Conference on Learning Theory and 7th Kernel Workshop, COLT/Kernel 2003

Y2 - 24 August 2003 through 27 August 2003

ER -

Optimal rates of aggregation

Abstract

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