Classification with a reject option using a hinge loss

Bartlett, Peter L. & Wegkamp, Marten H. (2008) Classification with a reject option using a hinge loss. Journal of Machine Learning Research, 9, pp. 1823-1840.

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We consider the problem of binary classification where the classifier can, for a particular cost, choose not to classify an observation. Just as in the conventional classification problem, minimization of the sample average of the cost is a difficult optimization problem. As an alternative, we propose the optimization of a certain convex loss function φ, analogous to the hinge loss used in support vector machines (SVMs). Its convexity ensures that the sample average of this surrogate loss can be efficiently minimized. We study its statistical properties. We show that minimizing the expected surrogate loss—the φ-risk—also minimizes the risk. We also study the rate at which the φ-risk approaches its minimum value. We show that fast rates are possible when the conditional probability P(Y=1|X) is unlikely to be close to certain critical values.

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97 citations in Scopus
63 citations in Web of Science®
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ID Code: 43997
Item Type: Journal Article
Refereed: Yes
Additional Information: Fulltext freely available see link above
Additional URLs:
Keywords: OAVJ
ISSN: 1533-7928
Subjects: Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > ARTIFICIAL INTELLIGENCE AND IMAGE PROCESSING (080100)
Australian and New Zealand Standard Research Classification > PSYCHOLOGY AND COGNITIVE SCIENCES (170000) > COGNITIVE SCIENCE (170200)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Copyright Owner: Copyright 2008 Journal of Machine Learning Research and the authors.
Deposited On: 17 Aug 2011 23:37
Last Modified: 29 Feb 2012 14:34

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