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Abstract and Applied Analysis
Volume 2013, Article ID 139318, 7 pages
Research Article

Regularized Least Square Regression with Unbounded and Dependent Sampling

School of Mathematical Science, University of Jinan, Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Jinan 250022, China

Received 29 October 2012; Revised 22 March 2013; Accepted 22 March 2013

Academic Editor: Changbum Chun

Copyright © 2013 Xiaorong Chu and Hongwei Sun. 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.


This paper mainly focuses on the least square regression problem for the -mixing and -mixing processes. The standard bound assumption for output data is abandoned and the learning algorithm is implemented with samples drawn from dependent sampling process with a more general output data condition. Capacity independent error bounds and learning rates are deduced by means of the integral operator technique.