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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 148490, 6 pages
ERM Scheme for Quantile Regression
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004, China
Received 30 November 2012; Accepted 21 February 2013
Academic Editor: Ding-Xuan Zhou
Copyright © 2013 Dao-Hong Xiang. 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.
- I. Steinwart and A. Christman, How SVMs Can Estimate Quantile and the Median, vol. 20 of Advances in Neural Information Processing Systems, MIT Press, Cambridge, Mass, USA, 2008.
- D. H. Xiang, “Conditional quantiles with varying Gaussians,” Advances in Computational Mathematics, 2011.
- D.-H. Xiang, T. Hu, and D.-X. Zhou, “Learning with varying insensitive loss,” Applied Mathematics Letters, vol. 24, no. 12, pp. 2107–2109, 2011.
- D.-H. Xiang, T. Hu, and D.-X. Zhou, “Approximation analysis of learning algorithms for support vector regression and quantile regression,” Journal of Applied Mathematics, vol. 2012, Article ID 902139, 17 pages, 2012.
- N. Aronszajn, “Theory of reproducing kernels,” Transactions of the American Mathematical Society, vol. 68, pp. 337–404, 1950.
- F. Cucker and D.-X. Zhou, Learning Theory: An Approximation Theory Viewpoint, vol. 24, Cambridge University Press, Cambridge, UK, 2007.
- D.-X. Zhou, “The covering number in learning theory,” Journal of Complexity, vol. 18, no. 3, pp. 739–767, 2002.
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- T. Hu and D.-X. Zhou, “Online learning with samples drawn from non-identical distributions,” Journal of Machine Learning Research, vol. 10, pp. 2873–2898, 2009.
- S. Smale and D.-X. Zhou, “Online learning with Markov sampling,” Analysis and Applications, vol. 7, no. 1, pp. 87–113, 2009.
- Z.-C. Guo and L. Shi, “Classification with non-i.i.d. sampling,” Mathematical and Computer Modelling, vol. 54, no. 5-6, pp. 1347–1364, 2011.