Simultaneous adaptation to the margin and to complexity in classification

Details Simultaneous adaptation to the margin and to complexity in classification Simultaneous adaptation to the margin and to complexity in classification

2005-09-29

arxiv.org/abs/math/0509696v2

Annals of Statistics 2007, Vol. 35, No. 4, 1698-1721

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.1214/009053607000000055 the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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