|
NeuroCOLT
Technical Report NC-TR-00-081
A
Generalized Representer Theorem
Bernhard Schoelkopf
Ralf Herbrich
Alex J. Smola
Robert C. Williamson
Abstract
Wahba's classical representer theorem states that the solutions
of certain risk minimization problems involving an empirical risk
term and a quadratic regularizer can be written as expansions in terms
of the training examples. We generalize the theorem to a larger class
of regularizers and empirical risk terms, and give a self-contained
proof utilizing the feature space associated with a support vector
kernel. The result shows that a wide range of problems have optimal
solutions that live in the finite dimensional span of the training
examples mapped into feature space, thus enabling us to carry out
kernel algorithms independent of the (potentially infinite) dimensionality
of the feature space
Download
Compressed Postscript
|