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

A. B. Tsybakov; S. A.D.E. Van Geer

doi:10.1214/009053604000001066

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

A. B. Tsybakov
, S. A.D.E. Van Geer

University of Leiden

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	1203-1224
Number of pages	22
Journal	Annals of Statistics
Volume	33
Issue number	3
DOIs	https://doi.org/10.1214/009053604000001066
Publication status	Published - 1 Jun 2005

Keywords

Adaptation
Binary classification
Block thresholding
Edge estimation
Margin
Penalized classification rule
Sparsity
Square root penalty

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10.1214/009053604000001066

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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.",

keywords = "Adaptation, Binary classification, Block thresholding, Edge estimation, Margin, Penalized classification rule, Sparsity, Square root penalty",

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year = "2005",

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AU - Van Geer, S. A.D.E.

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N2 - 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.

AB - 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.

KW - Adaptation

KW - Binary classification

KW - Block thresholding

KW - Edge estimation

KW - Margin

KW - Penalized classification rule

KW - Sparsity

KW - Square root penalty

UR - https://www.scopus.com/pages/publications/23744505130

U2 - 10.1214/009053604000001066

DO - 10.1214/009053604000001066

M3 - Article

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SP - 1203

EP - 1224

JO - Annals of Statistics

JF - Annals of Statistics

IS - 3

ER -

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

Abstract

Keywords

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