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December 2018 Assessing robustness of classification using an angular breakdown point
Junlong Zhao, Guan Yu, Yufeng Liu
Ann. Statist. 46(6B): 3362-3389 (December 2018). DOI: 10.1214/17-AOS1661

Abstract

Robustness is a desirable property for many statistical techniques. As an important measure of robustness, the breakdown point has been widely used for regression problems and many other settings. Despite the existing development, we observe that the standard breakdown point criterion is not directly applicable for many classification problems. In this paper, we propose a new breakdown point criterion, namely angular breakdown point, to better quantify the robustness of different classification methods. Using this new breakdown point criterion, we study the robustness of binary large margin classification techniques, although the idea is applicable to general classification methods. Both bounded and unbounded loss functions with linear and kernel learning are considered. These studies provide useful insights on the robustness of different classification methods. Numerical results further confirm our theoretical findings.

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Junlong Zhao. Guan Yu. Yufeng Liu. "Assessing robustness of classification using an angular breakdown point." Ann. Statist. 46 (6B) 3362 - 3389, December 2018. https://doi.org/10.1214/17-AOS1661

Information

Received: 1 April 2016; Revised: 1 November 2017; Published: December 2018
First available in Project Euclid: 11 September 2018

zbMATH: 1408.62121
MathSciNet: MR3852655
Digital Object Identifier: 10.1214/17-AOS1661

Subjects:
Primary: 62H30
Secondary: 62G35

Keywords: Breakdown point , ‎classification‎ , loss function , reproducing kernel Hilbert spaces , robustness

Rights: Copyright © 2018 Institute of Mathematical Statistics

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Vol.46 • No. 6B • December 2018
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