The Annals of Statistics

Assessing robustness of classification using an angular breakdown point

Junlong Zhao, Guan Yu, and Yufeng Liu

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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.

Article information

Ann. Statist., Volume 46, Number 6B (2018), 3362-3389.

Received: April 2016
Revised: November 2017
First available in Project Euclid: 11 September 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 62G35: Robustness

Breakdown point classification loss function reproducing kernel Hilbert spaces robustness


Zhao, Junlong; Yu, Guan; Liu, Yufeng. Assessing robustness of classification using an angular breakdown point. Ann. Statist. 46 (2018), no. 6B, 3362--3389. doi:10.1214/17-AOS1661.

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Supplemental materials

  • Supplement to “Assessing robustness of classification using an angular breakdown point”. The supplementary material contains the remaining proof of the theoretical results.