nips nips2007 nips2007-101 nips2007-101-reference knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Andreas Christmann, Ingo Steinwart
Abstract: We investigate quantile regression based on the pinball loss and the ǫ-insensitive loss. For the pinball loss a condition on the data-generating distribution P is given that ensures that the conditional quantiles are approximated with respect to · 1 . This result is then used to derive an oracle inequality for an SVM based on the pinball loss. Moreover, we show that SVMs based on the ǫ-insensitive loss estimate the conditional median only under certain conditions on P . 1
[1] H. Bauer. Measure and Integration Theory. De Gruyter, Berlin, 2001.
[2] A. Christmann and I. Steinwart. Consistency and robustness of kernel based regression. Bernoulli, 15:799–819, 2007.
[3] D.E. Edmunds and H. Triebel. Function Spaces, Entropy Numbers, Differential Operators. Cambridge University Press, 1996.
[4] C. Hwang and J. Shim. A simple quantile regression via support vector machine. In Advances in Natural Computation: First International Conference (ICNC), pages 512 –520. Springer, 2005.
[5] R. Koenker. Quantile Regression. Cambridge University Press, 2005.
[6] B. Sch¨ lkopf, A. J. Smola, R. C. Williamson, and P. L. Bartlett. New support vector algorithms. o Neural Computation, 12:1207–1245, 2000.
[7] I. Steinwart. How to compare different loss functions. Constr. Approx., 26:225–287, 2007.
[8] I. Steinwart, D. Hush, and C. Scovel. Function classes that approximate the Bayes risk. In Proceedings of the 19th Annual Conference on Learning Theory, COLT 2006, pages 79–93. Springer, 2006.
[9] I. Steinwart, D. Hush, and C. Scovel. An oracle inequality for clipped regularized risk minimizers. In Advances in Neural Information Processing Systems 19, pages 1321–1328, 2007.
[10] I. Takeuchi, Q.V. Le, T.D. Sears, and A.J. Smola. Nonparametric quantile estimation. J. Mach. Learn. Res., 7:1231–1264, 2006.