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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 134727, 8 pages
http://dx.doi.org/10.1155/2013/134727
Research Article

Coefficient-Based Regression with Non-Identical Unbounded Sampling

School of Mathematics and Computational Science, Guangdong University of Business Studies, Guangzhou, Guangdong 510320, China

Received 18 January 2013; Accepted 15 April 2013

Academic Editor: Qiang Wu

Copyright © 2013 Jia Cai. 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.

Linked References

  1. S. Smale and D.-X. Zhou, “Online learning with Markov sampling,” Analysis and Applications, vol. 7, no. 1, pp. 87–113, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  2. N. Aronszajn, “Theory of reproducing kernels,” Transactions of the American Mathematical Society, vol. 68, pp. 337–404, 1950. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. F. Cucker and D.-X. Zhou, Learning Theory: An Approximation Theory Viewpoint, Cambridge University Press, Cambridge, UK, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  4. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. H. Sun and Q. Wu, “Indefinite kernel network with dependent sampling,” Analysis and Applications. Accepted.
  7. Q. Wu and D.-X. Zhou, “Learning with sample dependent hypothesis spaces,” Computers and Mathematics with Applications, vol. 56, no. 11, pp. 2896–2907, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. Q. Wu, “Regularization networks with indefinite kernels,” Journal of Approximation Theory, vol. 166, pp. 1–18, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  9. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. L. Shi, “Learning theory estimate for coefficient-based regularized regression,” Applied and Computational Harmonic Analysis, vol. 34, no. 2, pp. 252–265, 2013. View at Publisher · View at Google Scholar
  11. H. Sun and Q. Guo, “Coefficient regularized regression with non-iid sampling,” International Journal of Computer Mathematics, vol. 88, no. 15, pp. 3113–3124, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. B. Conway, A Course in Operator Theory, American Mathematical Society, 2000. View at MathSciNet
  13. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. E. De Vito, A. Caponnetto, and L. Rosasco, “Model selection for regularized least-squares algorithm in learning theory,” Foundations of Computational Mathematics, vol. 5, no. 1, pp. 59–85, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  16. S. Mendelson and J. Neeman, “Regularization in kernel learning,” The Annals of Statistics, vol. 38, no. 1, pp. 526–565, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. I. Steinwart, D. Hush, and C. Scovel, “Optimal rates for regularized least-squares regression,” in Proceedings of the 22nd Annual Conference on Learning Theory, pp. 79–93, 2009.
  18. 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. D.-X. Zhou, “Capacity of reproducing kernel spaces in learning theory,” IEEE Transactions on Information Theory, vol. 49, no. 7, pp. 1743–1752, 2003. View at Publisher · View at Google Scholar · View at MathSciNet