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October 2008 Learning by mirror averaging
A. Juditsky, P. Rigollet, A. B. Tsybakov
Ann. Statist. 36(5): 2183-2206 (October 2008). DOI: 10.1214/07-AOS546


Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, that is, we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with respect to a given risk criterion. We define our aggregate by a simple recursive procedure which solves an auxiliary stochastic linear programming problem related to the original nonlinear one and constitutes a special case of the mirror averaging algorithm. We show that the aggregate satisfies sharp oracle inequalities under some general assumptions. The results are applied to several problems including regression, classification and density estimation.


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A. Juditsky. P. Rigollet. A. B. Tsybakov. "Learning by mirror averaging." Ann. Statist. 36 (5) 2183 - 2206, October 2008.


Published: October 2008
First available in Project Euclid: 13 October 2008

zbMATH: 1274.62288
MathSciNet: MR2458184
Digital Object Identifier: 10.1214/07-AOS546

Primary: 62G08
Secondary: 62C20 , 62G05 , 62G20

Keywords: Aggregation , learning , mirror averaging , Model selection , Oracle inequalities , stochastic optimization

Rights: Copyright © 2008 Institute of Mathematical Statistics


Vol.36 • No. 5 • October 2008
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