The Bounds on the Rate of Uniform Convergence of Learning Process on Uncertainty Space

Authors:
Xiankun Zhang;Minghu Ha;Jing Wu;Chao Wang
Affiliations:
College of Mathematical and Computer Sciences, Hebei University, Baoding, China 071002;College of Mathematical and Computer Sciences, Hebei University, Baoding, China 071002;College of Mathematical and Computer Sciences, Hebei University, Baoding, China 071002;College of Mathematical and Computer Sciences, Hebei University, Baoding, China 071002
Venue:
ISNN '09 Proceedings of the 6th International Symposium on Neural Networks on Advances in Neural Networks
Year:
2009

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Abstract

Statistical Learning Theory on uncertainty space is investigated. The definitions of empirical risk functional, expected risk functional and empirical risk minimization principle on uncertainty space are introduced. Based on these concepts, the bounds on the rate of uniform convergence of learning process are given, which estimate the value of achieved risk for the function minimizing the empirical risk and the difference between the value of achieved risk and the value of minimal possible risk for a given set of functions.