- About this Journal
- Abstracting and Indexing
- Aims and Scope
- Annual Issues
- Article Processing Charges
- Articles in Press
- Author Guidelines
- Bibliographic Information
- Citations to this Journal
- Contact Information
- Editorial Board
- Editorial Workflow
- Free eTOC Alerts
- Publication Ethics
- Reviewers Acknowledgment
- Submit a Manuscript
- Subscription Information
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 139318, 7 pages
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.
- T. Evgeniou, M. Pontil, and T. Poggio, “Regularization networks and support vector machines,” Advances in Computational Mathematics, vol. 13, no. 1, pp. 1–50, 2000.
- S. Smale and D.-X. Zhou, “Shannon sampling. II. Connections to learning theory,” Applied and Computational Harmonic Analysis, vol. 19, no. 3, pp. 285–302, 2005.
- S. Smale and D.-X. Zhou, “Learning theory estimates via integral operators and their approximations,” Constructive Approximation, vol. 26, no. 2, pp. 153–172, 2007.
- Q. Wu, Y. Ying, and D.-X. Zhou, “Learning rates of least-square regularized regression,” Foundations of Computational Mathematics, vol. 6, no. 2, pp. 171–192, 2006.
- D. S. Modha and E. Masry, “Minimum complexity regression estimation with weakly dependent observations,” IEEE Transactions on Information Theory, vol. 42, no. 6, pp. 2133–2145, 1996.
- S. Smale and D.-X. Zhou, “Online learning with Markov sampling,” Analysis and Applications, vol. 7, no. 1, pp. 87–113, 2009.
- H. Sun and Q. Wu, “A note on application of integral operator in learning theory,” Applied and Computational Harmonic Analysis, vol. 26, no. 3, pp. 416–421, 2009.
- H. Sun and Q. Wu, “Regularized least square regression with dependent samples,” Advances in Computational Mathematics, vol. 32, no. 2, pp. 175–189, 2010.
- K. B. Athreya and S. G. Pantula, “Mixing properties of Harris chains and autoregressive processes,” Journal of Applied Probability, vol. 23, no. 4, pp. 880–892, 1986.
- A. Caponnetto and E. De Vito, “Optimal rates for the regularized least-squares algorithm,” Foundations of Computational Mathematics, vol. 7, no. 3, pp. 331–368, 2007.
- Z.-C. Guo and D.-X. Zhou, “Concentration estimates for learning with unbounded sampling,” Advances in Computational Mathematics, vol. 38, no. 1, pp. 207–223, 2013.
- S.-G. Lv and Y.-L. Feng, “Integral operator approach to learning theory with unbounded sampling,” Complex Analysis and Operator Theory, vol. 6, no. 3, pp. 533–548, 2012.
- C. Wang and D.-X. Zhou, “Optimal learning rates for least squares regularized regression with unbounded sampling,” Journal of Complexity, vol. 27, no. 1, pp. 55–67, 2011.
- C. Wang and Z. C. Guo, “ERM learning with unbounded sampling,” Acta Mathematica Sinica, vol. 28, no. 1, pp. 97–104, 2012.
- X. R. Chu and H. W. Sun, “Half supervised coefficient regularization for regression learning with unbounded sampling,” International Journal of Computer Mathematics, 2013.
- S. Smale and D.-X. Zhou, “Shannon sampling and function reconstruction from point values,” The American Mathematical Society, vol. 41, no. 3, pp. 279–305, 2004.
- H. Sun and Q. Wu, “Application of integral operator for regularized least-square regression,” Mathematical and Computer Modelling, vol. 49, no. 1-2, pp. 276–285, 2009.
- F. Bauer, S. Pereverzev, and L. Rosasco, “On regularization algorithms in learning theory,” Journal of Complexity, vol. 23, no. 1, pp. 52–72, 2007.
- L. Lo Gerfo, L. Rosasco, F. Odone, E. De Vito, and A. Verri, “Spectral algorithms for supervised learning,” Neural Computation, vol. 20, no. 7, pp. 1873–1897, 2008.
- H. Sun and Q. Wu, “Least square regression with indefinite kernels and coefficient regularization,” Applied and Computational Harmonic Analysis, vol. 30, no. 1, pp. 96–109, 2011.
- P. Billingsley, Convergence of Probability Measures, John Wiley & Sons, New York, NY, USA, 1968.