Support vector machines with a reject option

Details Support vector machines with a reject option Support vector machines with a reject option

2012-01-05

arxiv.org/abs/1201.1140v1

Bernoulli 2011, Vol. 17, No. 4, 1368-1385

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/10-BEJ320 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/10-BEJ320

This paper studies $\ell_1$ regularization with high-dimensional features for support vector machines with a built-in reject option (meaning that the decision of classifying an observation can be withheld at a cost lower than that of misclassification). The procedure can be conveniently implemented as a linear program and computed using standard software. We prove that the minimizer of the penalized population risk favors sparse solutions and show that the behavior of the empirical risk minimizer mimics that of the population risk minimizer. We also introduce a notion of classification complexity and prove that our minimizers adapt to the unknown complexity. Using a novel oracle inequality for the excess risk, we identify situations where fast rates of convergence occur.

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