nips nips2002 nips2002-77 nips2002-77-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Tong Zhang
Abstract: We investigate the generalization performance of some learning problems in Hilbert function Spaces. We introduce a concept of scalesensitive effective data dimension, and show that it characterizes the convergence 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 derive upper bounds on the generalization performance and show that the resulting convergent rates are optimal under various circumstances.
[1] W.S. Lee, P.L. Bartlett, and R.C. Williamson. The importance of convexity in learning with squared loss. IEEE Trans. Inform. Theory, 44(5):1974–1980, 1998.
[2] Shahar Mendelson. Learning relatively small classes. In COLT 01, pages 273–288, 2001.
[3] Charles J. Stone. Optimal global rates of convergence for nonparametric regression. Annals of Statistics, 10:1040–1053, 1982.
[4] S.A. van de Geer. Empirical Processes in -estimation. Cambridge University Press, 2000. §
[5] Vadim Yurinsky. Sums and Gaussian vectors. Springer-Verlag, Berlin, 1995.