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Generalization Performance of Regularization Networks and Support . . .
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 2001
"... We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use of a viewpoint that is apparently novel in the field of statistical learning theory. The hy ..."
Abstract

Cited by 70 (18 self)
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We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use of 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 infinitedimensional unit ball in feature space into a finitedimensional 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 function on the generalization performance of support vector machines.
Entropy Numbers, Operators and Support Vector Kernels
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... 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 ..."
Abstract

Cited by 12 (3 self)
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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.
Produced as part of the ESPRIT Working Group in Neural and Computational Learning II,
, 1998
"... We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use ..."
Abstract
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We derive new bounds for the generalization error of kernel machines, such as support vector machines and related regularization networks by obtaining new bounds on their covering numbers. The proofs make use
ENTROPY NUMBERS OF (R,W)NUCLEAR OPERATORS ACTING BETWEEN BANACH SPACES OF CERTAIN WEAK TYPE
"... Abstract. We characterize (r, w)nuclear operators acting from a Banach space whose dual has weak type q into a Banach space of weak type p by the asymptotic behaviour of their entropy numbers. 1. ..."
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Abstract. We characterize (r, w)nuclear operators acting from a Banach space whose dual has weak type q into a Banach space of weak type p by the asymptotic behaviour of their entropy numbers. 1.