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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 619138, 9 pages
On the Convergence Rate of Kernel-Based Sequential Greedy Regression
1College of Sciences, Huazhong Agricultural University, Wuhan 430070, China
2Department of Statistics and Applied Mathematics, Hubei University of Economics, Wuhan 430205, China
Received 13 October 2012; Accepted 27 November 2012
Academic Editor: Jean M. Combes
Copyright © 2012 Xiaoyin Wang et al. 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.
- F. Cucker and S. Smale, “On the mathematical foundations of learning,” Bulletin of the American Mathematical Society, vol. 39, no. 1, pp. 1–49, 2002.
- F. Cucker and D. X. Zhou, Learning Theory: An Approximation Theory Viewpoint, Cambridge University Press, Cambridge, Mass, USA, 2007.
- Q. Wu and D. X. Zhou, “Learning with sample dependent hypothesis spaces,” Computers & Mathematics with Applications, vol. 56, no. 11, pp. 2896–2907, 2008.
- Q. W. Xiao and D. X. Zhou, “Learning by nonsymmetric kernels with data dependent spaces and -regularizer,” Taiwanese Journal of Mathematics, vol. 14, no. 5, pp. 1821–1836, 2010.
- L. Shi, Y. L. Feng, and D. X. Zhou, “Concentration estimates for learning with -regularizer and data dependent hypothesis spaces,” Applied and Computational Harmonic Analysis, vol. 31, no. 2, pp. 286–302, 2011.
- Y. L. Feng and S. G. Lv, “Unified approach to coefficient-based regularized regression,” Computers & Mathematics with Applications, vol. 62, no. 1, pp. 506–515, 2011.
- S. G. Lv and J. D. Zhu, “Error bounds for -norm multiple kernel learning with least square loss,” Abstract and Applied Analysis, vol. 2012, Article ID 915920, 18 pages, 2012.
- Y. K. Zhu and H. W. Sun, “Consistency analysis of spectral regularization algorithms,” Abstract and Applied Analysis, vol. 2012, Article ID 436510, 16 pages, 2012.
- A. R. Barron, A. Cohen, W. Dahmen, and R. A. DeVore, “Approximation and learning by greedy algorithms,” The Annals of Statistics, vol. 36, no. 1, pp. 64–94, 2008.
- S. Mannor, R. Meir, and T. Zhang, “Greedy algorithms for classification—consistency, convergence rates, and adaptivity,” Journal of Machine Learning Research, vol. 4, no. 4, pp. 713–741, 2003.
- T. Zhang, “Sequential greedy approximation for certain convex optimization problems,” IEEE Transactions on Information Theory, vol. 49, no. 3, pp. 682–691, 2003.
- H. Chen, L. Q. Li, and Z. B. Pan, “Learning rates of multi-kernel regression by orthogonal greedy algorithm,” Journal of Statistical Planning and Inference, vol. 143, no. 2, pp. 276–282, 2013.
- T. Zhang, “Approximation bounds for some sparse kernel regression algorithms,” Neural Computation, vol. 14, no. 12, pp. 3013–3042, 2002.
- D. R. Chen, Q. Wu, Y. Ying, and D. X. Zhou, “Support vector machine soft margin classifiers: error analysis,” Journal of Machine Learning Research, vol. 5, pp. 1143–1175, 2004.
- H. Chen, L. Q. Li, and J. T. Peng, “Error bounds of multi-graph regularized semi-supervised classification,” Information Sciences, vol. 179, no. 12, pp. 1960–1969, 2009.
- H. Chen, “On the convergence rate of a regularized ranking algorithm,” Journal of Approximation, vol. 164, no. 12, pp. 1513–1519, 2012.
- Z. C. Guo and D. X. Zhou, “Concentration estimates for learning with unbounded sampling,” Advances in Computational Mathematics. In press.
- Q. Wu, Y. Ying, and D. X. Zhou, “Multi-kernel regularized classifiers,” Journal of Complexity, vol. 23, no. 1, pp. 108–134, 2007.