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Potential-reduction methods in mathematical programming
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A decision-theoretic generalization of on-line learning and an application to boosting
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Scale-sensitive dimensions, uniform convergence, and learnability
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Generalization performance of support vector machines and other pattern classifiers
Advances in kernel methods
Entropy numbers, operators and support vector kernels
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Theoretical analysis of a class of randomized regularization methods
COLT '99 Proceedings of the twelfth annual conference on Computational learning theory
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Covering numbers for support vector machines
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Linear hinge loss and average margin
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An introduction to support Vector Machines: and other kernel-based learning methods
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General Convergence Results for Linear Discriminant Updates
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Sample complexity of linear learning machines with different restrictions over weights
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The Journal of Machine Learning Research
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Recently, sample complexity bounds have been derived for problems involving linear functions such as neural networks and support vector machines. In many of these theoretical studies, the concept of covering numbers played an important role. It is thus useful to study covering numbers for linear function classes. In this paper, we investigate two closely related methods to derive upper bounds on these covering numbers. The first method, already employed in some earlier studies, relies on the so-called Maurey's lemma; the second method uses techniques from the mistake bound framework in online learning. We compare results from these two methods, as well as their consequences in some learning formulations.