Effective Dimension and Generalization of Kernel Learning

We investigate the generalization performance of some learning problems inHilbert function Spaces. We introduce a concept of scalesensitive effectivedata dimension, and show that it characterizes the convergence rateof the underlying learning problem. Using this concept, we can naturally extend results for parametric estimation problems in finite dimensional spaces to nonparametric kernel learning methods. We derive upperbounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.