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

A. B. Tsybakov·S. A. van de Geer
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Abstract

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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A. B. Tsybakov, S. A. van de Geer. 2005-07-21. Square Root Penalty: Adaptation to the Margin in Classification and in Edge Estimation. https://doi.org/10.1214/009053604000001066

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