Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

A. Dalalyan; A. B. Tsybakov

doi:10.1007/s10994-008-5051-0

Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

A. Dalalyan
, A. B. Tsybakov

Research output: Contribution to journal › Article › peer-review

Abstract

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities.

Original language	English
Pages (from-to)	39-61
Number of pages	23
Journal	Machine Learning
Volume	72
Issue number	1-2
DOIs	https://doi.org/10.1007/s10994-008-5051-0
Publication status	Published - 1 Jan 2008
Externally published	Yes

Keywords

Aggregation
Nonparametric regression
Oracle inequalities
Sparsity

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title = "Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity",

abstract = "We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities.",

keywords = "Aggregation, Nonparametric regression, Oracle inequalities, Sparsity",

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AB - We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities.

KW - Aggregation

KW - Nonparametric regression

KW - Oracle inequalities

KW - Sparsity

U2 - 10.1007/s10994-008-5051-0

DO - 10.1007/s10994-008-5051-0

M3 - Article

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VL - 72

SP - 39

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JO - Machine Learning

JF - Machine Learning

IS - 1-2

ER -

Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

Abstract

Keywords

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