Recursive Aggregation of Estimators by the Mirror Descent Algorithm with Averaging

Recursive Aggregation of Estimators by the Mirror Descent Algorithm with Averaging We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the ℓ1-constraint. It is defined by a stochastic version of the mirror descent algorithm which performs descent of the gradient type in the dual space with an additional averaging. The main result of the paper is an upper bound for the expected accuracy of the proposed estimator. This bound is of the order $$C\sqrt {(\log M)/t}$$ with an explicit and small constant factor C, where M is the dimension of the problem and t stands for the sample size. A similar bound is proved for a more general setting, which covers, in particular, the regression model with squared loss. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

Recursive Aggregation of Estimators by the Mirror Descent Algorithm with Averaging

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Publisher
Nauka/Interperiodica
Copyright
Copyright © 2005 by MAIK "Nauka/Interperiodica"
Subject
Engineering; Communications Engineering, Networks; Electrical Engineering; Information Storage and Retrieval; Systems Theory, Control
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1007/s11122-006-0005-2
Publisher site
See Article on Publisher Site

Abstract

We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the ℓ1-constraint. It is defined by a stochastic version of the mirror descent algorithm which performs descent of the gradient type in the dual space with an additional averaging. The main result of the paper is an upper bound for the expected accuracy of the proposed estimator. This bound is of the order $$C\sqrt {(\log M)/t}$$ with an explicit and small constant factor C, where M is the dimension of the problem and t stands for the sample size. A similar bound is proved for a more general setting, which covers, in particular, the regression model with squared loss.

Journal

Problems of Information TransmissionSpringer Journals

Published: Jan 23, 2006

References

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