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

Preprint

21 July 2005

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0507422

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

RATES OF CONVERGENCE
ADAPTIVE ESTIMATORS
EDGE ESTIMATION
CLASSIFICATION
FAST OPTIMAL
ROOT PENALTY
SQUARE ROOT
ATTAINS

All Related Versions

Version 1, 2005-07-21, ArXiv
Published version: The Annals of Statistics, 33 (3), 1203.

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