Entropy Numbers of Operators and Support Vector Machines
Professor Bob Williamson, Department of Engineering, Australian National University, Canberra

Abstract: It has been known for some time that certain covering numbers of function classes are the key quantity one needs to determine in order to understand the generalization performance of a wide range of learning machines within the standard statistical learning theory framework. The direct calculation of these covering numbers has been considered to be quite difficult, and instead general results bounding them in terms of combinatorial dimensions such as the VC dimension or Pollard's pseudo-dimension have been used.

In this talk I will show how one can in fact determine covering numbers directly for a range of function classes, including in particular those induced by Support Vector machines. A consequence is that the effect of the kernel on the generalization error bounds for such machines can be explicitly determined. The proofs rely on an apparently novel viewpoint and make use of operator-theoretic techniques.

This is joint work with Bernhard Scholkopf and Alex Smola.

This seminar was held at the Department of Computer Science, Royal Holloway, University of London on 24 June 1998.

back