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.
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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|Item Type:||Journal Article|
|Additional Information:||Fulltext freely available see link above|
|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:||18 Aug 2011 09:37|
|Last Modified:||01 Mar 2012 00:34|
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