A Bahadur representation of the linear support vector machine

Journal of Machine Learning Research

Volumn 9, Issue , 2008, Pages 1343-1368

  Koo, Ja Yong ^a   Lee, Yoonkyung ^b   Kim, Yuwon ^c   Park, Changyi ^d  

^a Korea University   (South Korea)

^b OHIO STATE UNIVERSITY   (United States)

^c Data Mining Team   (South Korea)

^d University of Seoul   (South Korea)

Author keywords

Asymptotic normality; Bahadur representation; Classification; Convexity lemma; Radon transform

Indexed keywords

ASYMPTOTIC ANALYSIS; IMAGE RETRIEVAL; LEARNING SYSTEMS; STATISTICAL METHODS; STATISTICS; VECTORS;

APPLICATIONS.; ASYMPTOTIC BEHAVIORS; ASYMPTOTIC NORMALITY; BAHADUR REPRESENTATION; BAYES RISKS; CLASSIFICATION; CONVEXITY LEMMA; RADON TRANSFORM; STATISTICAL INFERENCES; STATISTICAL PROPERTIES; STATISTICAL VARIABILITY;

SUPPORT VECTOR MACHINES;

EID: 48849101115     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. R. R. Bahadur. A note on quantiles in large samples. Annals of Mathematical Statistics, 37:577-580, 1966.
2. P. L. Bartlett, M. I. Jordan, and J. D. McAuliffe. Convexity, classification, and risk bounds. Journal of the American Statististical Association, 101:138-156, 2006.
3. G. Blanchard, O. Bousquet, and P. Massart. Statistical performance of support vector machines. The Annals of Statistics, 36:489-531, 2008.
4. P. Chaudhuri. Nonparametric estimates of regression quantiles and their local Bahadur representation. The Annals of Statistics, 19:760-777, 1991.
5. C. Cortes and V. Vapnik. Support-vector networks. Machine Learning, 20:273-297, 1995.
6. N. Cristianini and J. Shawe-Taylor. An Introduction to Support Vector Machines and Other Kernel-based Learning Methods. Cambridge University Press, Cambridge, 2000.
7. S. R. Deans. The Radon Transform and Some of Its Applications. Krieger Publishing Company, Florida, 1993.
8. I. Guyon and A. Elisseeff. Introduction to variable and feature selection. Journal of Machine Learning Research, 3:1157-1182, 2003.
9. I. Guyon, J. Weston, S. Barnhill, and V. Vapnik. Gene selection for cancer classification using support vector machines. Machine Learning, 46:389-422, 2002.
10. A. B. Ishak and B. Ghattas. An efficient method for variable selection using svm-based criteria. Preprint, Institut de Mathématiques de Luminy, 2005.
11. R. Koenker. Quantile Regression. Econometric Society Monographs. Cambridge University Press, 2005.
12. Y. Lin. Some asymptotic properties of the support vector machine. Technical report 1029, Department of Statistics, University of Wisconsin-Madison, 2000.
13. Y. Lin. A note on margin-based loss functions in classification. Statististics and Probability Letters, 68:73-82, 2002.
14. F. Natterer. The Mathematics of Computerized Tomography. Wiley & Sons, New York, 1986.
15. D. Pollard. Asymptotics for least absolute deviation regression estimators. Econometric Theory, 7: 186-199, 1991.
16. A. G. Ramm and A. I. Katsevich. The Radon Transform and Local Tomography. CRC Press, Boca Raton, 1996.
17. B. Schölkopf and A. Smola. Learning with Kernels - Support Vector Machines, Regularization, Optimization and Beyond. MIT Press, 2002.
18. J. C. Scovel and I. Steinwart. Fast rates for support vector machines using gaussian kernels. The Annals of Statistics, 35:575-607, 2007.
19. X. Shen. On methods of sieves and penalization. The Annals of Statistics, 25:2555-2591, 1997.
20. I. Steinwart. Consistency of support vector machines and other regularized kernel machines. IEEE Transactions on Information Theory, 51:128-142, 2005.
21. V. Vapnik. The Nature of Statistical Learning Theory. Springer, New York, 1996.
22. T. Zhang. Statistical behavior and consistency of classification methods based on convex risk minimization. The Annals of Statistics, 32:56-84, 2004.