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Technical Report NC-TR-98-022
Generalization
Bounds for Convex Combinations of Kernel Functions
Alex J. Smola, GMD
Robert C. Williamson, ANU
Bernhard Schoelkopf, GMD
Keywords:
AdaBoost, Arcing, Large Margin, Hard Margin, Soft Margin, Classification,
Support Vectors
Received:
07-AUG-98
Abstract
We derive new bounds on covering numbers
for hypothesis classes generated by convex combinations of basis functions.
These are useful in bounding the generalization performance of algorithms
such as RBF-networks, boosting and a new class of linear programming
machines similar to SV machines. We show that p-convex combinations
with p>1 lead to diverging bounds, whereas for p=1 good bounds
in terms of entropy numbers can be obtained. In the case of kernel
expansions, significantly better bounds can be obtained depending
on the eigenvalues of the corresponding integral operators.
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