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August 2007 Simultaneous adaptation to the margin and to complexity in classification
Guillaume Lecué
Ann. Statist. 35(4): 1698-1721 (August 2007). DOI: 10.1214/009053607000000055


We consider the problem of adaptation to the margin and to complexity in binary classification. We suggest an exponential weighting aggregation scheme. We use this aggregation procedure to construct classifiers which adapt automatically to margin and complexity. Two main examples are worked out in which adaptivity is achieved in frameworks proposed by Steinwart and Scovel [Learning Theory. Lecture Notes in Comput. Sci. 3559 (2005) 279–294. Springer, Berlin; Ann. Statist. 35 (2007) 575–607] and Tsybakov [Ann. Statist. 32 (2004) 135–166]. Adaptive schemes, like ERM or penalized ERM, usually involve a minimization step. This is not the case for our procedure.


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Guillaume Lecué. "Simultaneous adaptation to the margin and to complexity in classification." Ann. Statist. 35 (4) 1698 - 1721, August 2007.


Published: August 2007
First available in Project Euclid: 29 August 2007

zbMATH: 1209.62146
MathSciNet: MR2351102
Digital Object Identifier: 10.1214/009053607000000055

Primary: 62G05
Secondary: 62H30 , 68T10

Keywords: Aggregation , ‎classification‎ , complexity of classes of sets , excess risk , fast rates of convergence , margin , Statistical learning , SVM

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 4 • August 2007
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