Geometric and probabilistic estimates for entropy and approximation numbers of operators
Journal of Approximation Theory
A training algorithm for optimal margin classifiers
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
The nature of statistical learning theory
The nature of statistical learning theory
Machine Learning
Scale-sensitive dimensions, uniform convergence, and learnability
Journal of the ACM (JACM)
A Note on a Scale-Sensitive Dimension of Linear Bounded Functionals in Banach Spaces
ALT '97 Proceedings of the 8th International Conference on Algorithmic Learning Theory
Generalization Performance of Classifiers in Terms of Observed Covering Numbers
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
Structural risk minimization over data-dependent hierarchies
IEEE Transactions on Information Theory
Generalization Performance of Classifiers in Terms of Observed Covering Numbers
EuroCOLT '99 Proceedings of the 4th European Conference on Computational Learning Theory
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We derive new bounds for the generalization error of feature space machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs are based on a viewpoint that is apparently novel in the field of statistical learning theory. The hypothesis class is described in terms of a linear operator mapping from a possibly infinite dimensional unit ball in feature space into a finite dimensional space. The covering numbers of the class are then determined via the entropy numbers of the operator. These numbers, which characterize the degree of compactness of the operator, can be bounded in terms of the eigenvalues of an integral operator induced by the kernel function used by the machine. As a consequence we are able to theoretically explain the effect of the choice of kernel functions on the generalization performance of support vector machines.