Square Root Penalty: Adaptation to the Margin in Classification and in Edge Estimation

Details Square Root Penalty: Adaptation to the Margin in Classification and in Edge Estimation Square Root Penalty: Adaptation to the Margin in Classification and in Edge Estimation

2005-07-21

arxiv.org/abs/math/0507422v1

Annals of Statistics 2005, Vol. 33, No. 3, 1203-1224

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000001066 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

10.1214/009053604000001066

We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the excess risk, that is, rates that can be faster than n^{-1/2}, where n is the sample size. We show that our method also gives adaptive estimators for the problem of edge estimation.

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