Oracle properties of SCAD-penalized support vector machine

Journal of Statistical Planning and Inference

Volumn 142, Issue 8, 2012, Pages 2257-2270

  Park, Changyi ^a   Kim, Kwang Rae ^b   Myung, Rangmi ^c   Koo, Ja Yong ^b  

^a University of Seoul   (South Korea)

^b Korea University   (South Korea)

^c Korea Development Institute   (South Korea)

Author keywords

Classification; Fisher consistency; Oracle property; Smoothly clipped absolute deviation

Indexed keywords

EID: 84862784576     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2012.03.002     Document Type: Article

References (29)

1. Bartlett P.L., Jordan M.I., McAuliffe J.D. Convexity, classification, and risk bounds. Journal of the American Statistical Association 2006, 101:138-156.
2. Blanchard G., Bousquet O., Massart P. Statistical performance of support vector machines. Annals of Statistics 2008, 36:489-531.
3. Cortes C., Vapnik V. Support-vector networks. Machine Learning 1995, 20:273-297.
4. Cristianini N., Shawe-Taylor J. An Introduction to Support Vector Machines 2000, Cambridge University Press.
5. Fan J., Li R. Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of the American Statistical Association 2001, 96:1348-1360.
6. Fan J., Li R. New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. Journal of the American Statistical Association 2004, 99:710-723.
7. Fan J., Peng H. Nonconcave penalized likelihood with a diverging number of parameters. Annals of Statistics 2004, 32:928-961.
8. Friedman, J.H., 1993. An overview of predictive learning and function approximation. In: From Statistics and Neural Networks. Springer-Verlag.
9. Hastie T., Tibshirani R., Friedman J. The Element of Statistical Learning: Data Mining, Inference, and Prediction 2001, Springer.
10. Huang, J., Xie, H., 2007. Asymptotic oracle properties of scad-penalized least squares estimators. In: Asymptotics: Particles, Processes, and Inverse Problems. IMS Lecture Notes-Monograph Series.
11. Kim Y., Choi H., Oh H.-S. Smoothly clipped absolute deviation on high dimensions. Journal of the American Statistical Association 2008, 103:1665-1673.
12. Knight K., Fu W. Asymptotics for lasso-type estimators. Annals of Statistics 2000, 28:1356-1378.
13. Koo J.-Y., Lee Y., Kim Y., Park C. A Bahadur representation of the linear support vector machine. Journal of Machine Learning Research 2008, 9:1343-1368.
14. Lee Y., Kim Y., Lee S., Koo J.-Y. Structured multicategory support vector machines with analysis of variance decomposition. Biometrika 2006, 93:555-571.
15. Lin Y. A note on margin-based loss functions in classification. Statistics and Probability Letters 2004, 68:73-82.
16. Park C. Convergence rates of generalization errors for margin-based classification. Journal of Statistical Planning and Inference 2009, 139:2543-2551.
17. Pollard D. Asymptotics for least absolute deviation regression estimators. Econometric Theory 1991, 7:186-199.
18. Rocha, G., Wang, X., Yu, B., 2009. Asymptotic distribution and sparsistency for l1 penalized parametric M-estimators, with applications to linear SVM and logistic regression, arXiv:0908.1940v1.
19. Schölkopf B., Smola A. Learning with Kernels-Support Vector Machines, Regularization, Optimization and Beyond 2002, MIT Press.
20. Steinwart I. Consistency of support vector machines and other regularized kernel classifiers. IEEE Transactions on Information Theory 2005, 51:128-142.
21. Steinwart I., Scovel J.C. Fast rates for support vector machines using gaussian kernels. Annals of Statistics 2007, 35:575-607.
22. Vapnik V. Statistical Learning Theory 1998, Wiley, New York.
23. Wu Y., Liu Y. Variable selection in quantile regression. Statistica Sinica 2009, 19:801-817.
24. Zhang H.H., Ahn J., Lin X., Park C. Gene selection using support vector machines with non-convex penalty. Bioinformatics 2005, 22:88-95.
25. Zhang T. Statistical behavior and consistency of classification methods based on convex risk minimization. Annals of Statistics 2004, 32:56-85.
26. Zhao P., Yu B. On model selection consistency of lasso. Journal of Machine Learning Research 2006, 7:2541-2563.
27. Zhu, J., Rosset, S., Hastie, T., Tibshirani, R., 2003. 1-Norm support vector machines. In: Neural Information Processing Systems. MIT Press, p. 16.
28. Zou H. The adaptive lasso and its oracle properties. Journal of the American Statistical Association 2006, 101:1418-1429.
29. Zou H., Li R. One-step sparse estimates in nonconcave penalized likelihood models. Annals of Statistics 2008, 36:1509-1533.