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NeuroCOLT
Technical Report NC-TR-98-023
Entropy
Numbers, Operators and Support Vector Kernels
Alex J. Smola GMD
Robert C. Williamson ANU
Bernhard Schoelkopf GMD
Keywords:
Received:
07-JUL-98
Abstract
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.
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