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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 694181, 10 pages
http://dx.doi.org/10.1155/2013/694181
Research Article

The Learning Rates of Regularized Regression Based on Reproducing Kernel Banach Spaces

1Department of Mathematics, Shaoxing University, Shaoxing 312000, China
2School of Mathematics and LPMC, Nankai University, Tianjin 300071, China

Received 13 August 2013; Accepted 16 October 2013

Academic Editor: Qiang Wu

Copyright © 2013 Baohuai Sheng and Peixin Ye. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We study the convergence behavior of regularized regression based on reproducing kernel Banach spaces (RKBSs). The convex inequality of uniform convex Banach spaces is used to show the robustness of the optimal solution with respect to the distributions. The learning rates are derived in terms of the covering number and -functional.