Square root penalty: Adaptation to the margin in classification and in edge estimation

The Annals of Statistics · 2005 · Volume 33 · Issue 3

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.

Keywords

62G07, 62G08, 62H30, 68T10, Adaptation, Binary classification, block thresholding, edge estimation, margin, penalized classification rule, Sparsity, square root penalty

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