The structured elastic net for quantile regression and support vector classification

Statistics and Computing

Volumn 22, Issue 1, 2012, Pages 153-168

  Slawski, Martin ^a  

^a SAARLAND UNIVERSITY   (Germany)

Author keywords

Double regularization; Elastic net; Quantile regression; Solution path; Support vector classification

Indexed keywords

EID: 81955167663     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11222-010-9214-z     Document Type: Article

References (41)

1. Bartlett, P., Jordan, M., McAuliffe, J.: Convexity, classification, and risk bounds. J. Am. Stat. Assoc. 101, 138-156 (2006).
2. Bennett, K., Mangasarian, O.: Multicategory separation via linear programming. Optim. Methods Softw. 3, 27-39 (1993).
3. Bondell, H., Reich, B.: Simultaneous regression shrinkage, variable selection and clustering of predictors with OSCAR. Biometrics 64, 115-123 (2008).
4. Bradley, P., Mangasarian, O.: Feature selection via concave minimization and support vector machines. In: International Conference on Machine Learning (1998).
5. Christianini, N., Shawe-Taylor, J.: An Introduction to Support Vector Machines. Cambridge University Press, Cambridge (2000).
6. Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression (with discussion). Ann. Stat. 32, 407-499 (2004).
7. El Anbari, M., Mkhadri, A.: Penalized regression combing the L1 norm and a correlation based penalty. Technical report, Université Paris Sud 11 (2008).
8. Hans, C.: Bayesian lasso regression. Biometrika 96, 221-229 (2009).
9. Hans, C.: Model uncertainty and variable selection in Bayesian lasso regression. Stat. Comput. 20, 221-229 (2010).
10. Hastie, T., Tibshirani, R., Friedman, J.: The Elements of Statistical Learning. Springer, New York (2001).
11. Hastie, T., Rosset, S., Tibshirani, R., Zhu, J.: The entire regularization path for the support vector machine. J. Mach. Learn. Res. 5, 1391-1415 (2004).
12. James, G., Wang, J., Zhu, J.: Functional linear regression that's interpretable. Ann. Stat. 37, 2083-2108 (2008).
13. Koenker, R.: Quantile Regression. Cambridge University Press, Cambridge (2005).
14. Lancaster, T., Jun, S. J.: Bayesian quantile regression methods. J. Appl. Econom. 25, 287-307 (2009).
15. Landau, S., Ellison-Wright, I., Bullmore, E.: Tests for a difference in timing of physiological response between two brain regions measured by using functional magnetic resonance imaging. Appl. Stat. 63-82, 53 (2003).
16. Le Cun, Y., Boser, B., Denker, J., Henderson, D., Howard, R., Hubbard, W., Jackel, L.: Backpropagation applied to handwritten zip code recognition. Neural Comput. 2, 541-551 (1989).
17. Li, C., Li, H.: Variable selection and regression analysis for graph-structured covariates with an application to genomics. Ann. Appl. Stat. 4(3), 1498-1516 (2010).
18. 1-norm Quantile regression. J. Comput. Graph. Stat. 17, 163-185 (2008).
19. Li, Y., Liu, Y., Zhu, J.: Quantile regression in reproducing kernel Hilbert spaces. J. Am. Stat. Assoc. 102, 255-268 (2007).
20. Lin, Y.: Support vector machines and the Bayes rule in classification. Data Min. Knowl. Discov. 6, 259-275 (2002).
21. Park, T., Casella, G.: The Bayesian lasso. J. Am. Stat. Assoc. 103, 681-686 (2008).
22. Ramsay, J., Silverman, B.: Functional Data Analysis. Springer, New York (2006).
23. Rosset, S.: Bi-level path following for cross validated solution of kernel quantile regression. In: International Conference on Machine Learning (2008).
24. Rosset, S., Zhu, J.: Piecewise linear regularized solution paths. Ann. Stat. 35, 1012-1030 (2007).
25. Schölkopf, B., Smola, A.: Learning with Kernels. MIT Press, Cambridge (2002).
26. Slawski, M., zu Castell, W., Tutz, G.: Feature selection guided by structural information. Ann. Appl. Stat. 4(2), 1056-1080 (2010).
27. Sollich, P.: Bayesian methods for support vector machines: evidence and predictive class probabilities. Mach. Learn. 46, 21-52 (2002).
28. Stein, M.: Interpolation of Spatial Data. Springer, New York (1999).
29. Steinwart, I., Christmann, A.: Support Vector Machines. Springer, Berlin (2008).
30. Takeuchi, I., Le, Q., Sears, T., Smola, A.: Nonparametric quantile regression. J. Mach. Learn. Res. 7, 1231-1264 (2006).
31. Tibshirani, R.: Regression shrinkage and variable selection via the lasso. J. R. Stat. Soc. Ser. B 58, 671-686 (1996).
32. Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., Knight, K.: Sparsity and smoothness via the fused lasso. J. R. Stat. Soc. Ser. B 67, 91-108 (2005).
33. Tutz, G., Gertheiss, J.: Feature extraction in signal regression: a boosting technique for functional data regression. J. Comput. Graph. Stat. 19, 154-174 (2010).
34. Tutz, G., Ulbricht, J.: Penalized regression with correlation based penalty. Stat. Comput. 19, 239-253 (2009).
35. Wang, L., Shen, X.: Multi-category support vector machines, feature selection, and solution path. Stat. Sin. 16, 617-634 (2005).
36. Wang, L., Zhu, J., Zou, H.: The doubly regularized support vector machine. Stat. Sin. 16, 589-616 (2006).
37. Wood, S.: R package gamair: Data for GAMs: An Introduction with R, Version 0. 0-4. Available from www.r-project.org (2006).
38. Yuan, M., Lin, Y.: Model selection and estimation in regression with grouped variables. J. R. Stat. Soc. Ser. B 68, 49-67 (2006).
39. Zhao, P., Rocha, G., Yu, B.: The composite absolute penalties family for grouped and hierarchical variable selection. Ann. Stat. 37, 3468-3497 (2009).
40. 1 norm support vector machine. Adv. Neural Inf. Process. Syst. 16, 55-63 (2003).
41. Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. J. R. Stat. Soc. Ser. B 67, 301-320 (2005).