Effective Dimension and Generalization of Kernel Learning

Part of Advances in Neural Information Processing Systems 15 (NIPS 2002)

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Tong Zhang


We investigate the generalization performance of some learning prob- lems in Hilbert function Spaces. We introduce a concept of scale- sensitive effective data dimension, and show that it characterizes the con- vergence rate of the underlying learning problem. Using this concept, we can naturally extend results for parametric estimation problems in finite dimensional spaces to non-parametric kernel learning methods. We de- rive upper bounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.