Soft and hard classification by reproducing kernel Hilbert space methods

Proceedings of the National Academy of Sciences of the United States of America

Volumn 99, Issue 26, 2002, Pages 16524-16530

  Wahba, Grace ^a  

^a University of Wisconsin Madison   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; ARTICLE; KERNEL HILBER SPACE METHOD; MATHEMATICAL ANALYSIS; PRIORITY JOURNAL; PROBABILITY; STATISTICAL MODEL;

CLASSIFICATION; LIKELIHOOD FUNCTIONS; MATHEMATICS; MODELS, STATISTICAL; PROBABILITY;

EID: 0037168506     PISSN: 00278424     EISSN: None     Source Type: Journal    
DOI: 10.1073/pnas.242574899     Document Type: Article

References (47)

1. Vapnik, V. (1998) Statistical Learning Theory (Wiley, New York).
2. Scholkopf, B. & Smola, A. (2002) Learning with Kernels Support Vector Machines, Regularization, Optimization, and Beyond (MIT Press, Cambridge, MA).
3. Cristianini, N. & Shawe-Taylor, J. (2000) An Introduction to Support Vector Machines (Cambridge Univ. Press, Cambridge, U.K.).
4. Wahba, G. (1999) in Advances in Kernel Methods: Support Vector Learning, eds. Scholkopf, B., Burges, C. & Smola, A. (MIT Press, Cambridge, MA), pp. 69-88.
5. Evgeniou, T., Pontil, M. & Poggio, T. (2000) Adv. Comput. Math. 13, 1-50.
6. Kimeldorf, G. & Wahba, G. (1971) J. Math. Anal. Appl. 33, 82-95.
7. Aronszajn, N. (1950) Trans. Am. Math. Soc. 68, 337-404.
8. Wahba, G. (1990) Spline Models for Observational Data (Soc. Indust. Appl. Math., Philadelphia), Vol. 59.
9. Xiang, D. & Wahba, G. (1998) Proceedings of the 1997 ASA Joint Statistical Meetings, Tech. Rep. 982 (Dept. of Stat., Univ. of Wisconsin, Madison), pp. 94-98.
10. Luo, Z. & Wahba, G. (1997) J. Am. Stat. Assoc. 92, 107-114.
11. O'Sullivan, F., Yandell, B. & Raynor, W. (1986) J. Am. Stat. Assoc. 81, 96-103.
12. Wahba, G., Wang, Y., Gu, C., Klein, R. & Klein, B. (1995) Ann. Statist. 23, 1865-1895.
13. Gu, C. (2002) Smoothing Spline ANOVA Models (Springer, New York).
14. Klein, R., Klein, B. E. K., Moss, S. E., Davis, M. D. & DeMets, D. L. (1984) Arch. Ophthalmol. 102, 520-526.
15. Wang, Y. (1997) Commun. Stat. Simul. Comput. 26, 765-782.
16. Gu, C. (1992) J. Comput. Graph. Stat. 1, 169-179.
17. Xiang, D. & Wahba, G. (1996) Stat. Sin. 6, 675-692.
18. Wahba, G., Lin, X., Gao, F., Xiang, D., Klein, R. & Klein, B. (1999) in Advances in Information Processing Systems 11, eds. Kearns, M., Solla, S. & Cohn, D. (MIT Press, Cambridge, MA), pp. 620-626.
19. Zhang, H., Wahba, G., Lin, Y., Voelker, M., Ferris, M., Klein, R. & Klein, B. (2001) Proceedings of the ASA Joint Statistical Meetings, Tech. Rep. 1042 (Dept. of Stat., Univ. of Wisconsin, Madison).
20. Zhang, H., Wahba, G., Lin, Y., Voelker, M., Ferris, M., Klein, R. & Klein, B. (2000) Tech. Rep. 1059 (Dept. of Stat., Univ. of Wisconsin, Madison).
21. Cox, D. & O'Sullivan, F. (1990) Ann. Statist. 18, 1676-1695.
22. Lin, Y. (2000) Ann. Statist. 28, 734-755.
23. Lin, Y. (2002) Data Mining Knowl. Discov. 6, 259-275.
24. Wahba, G., Lin, Y. & Zhang, H. (2000) in Advances in Large Margin Classifiers, eds. Smola, A., Bartlett, P., Scholkopf, B. & Schuurmans, D. (MIT Press, Cambridge, MA), pp. 297-311.
25. Lin, X. (1998) Ph.D. thesis (Univ. of Wisconsin, Madison); Tech. Rep. 1003 (Dept. of Stat., Univ. of Wisconsin, Madison).
26. Ramaswamy, S., Tamayo, P., Rifkin, R., Mukherjee, S., Yeang, C., Angelo, M., Ladd, C., Reich, M., Latulippe, E., Mesirov, J., et al. (2001) Proc. Natl. Acad. Sci. USA 98, 15149-15154.
27. Lee, Y., Lin, Y. & Wahba, G. (2002) Comput. Sci. 33, in press; Tech. Rep. 1043 (Dept. of Stat., Univ. of Wisconsin, Madison).
28. Lee, Y. & Lee, C.-K. (2002) Tech. Rep. 1051 (Dept. of Star., Univ. of Wisconsin, Madison).
29. Lee, Y. (2002) Ph.D. thesis (Univ. of Wisconsin, Madison); Tech. Rep. 1062 (Dept. of Stat., Univ. of Wisconsin, Madison).
30. Lin, Y., Lee, Y. & Wahba, G. (2002) Mach. Learn. 46, 191-202.
31. Lin, Y., Lee, Y. & Wahba, G. (2002) Tech. Rep. 1063 (Dept. of Stat., Univ. of Wisconsin, Madison).
32. Wahba, G., Lin, Y., Lee, Y. & Zhang, H. (2002) in Nonlinear Estimation and Classification, eds. Denison, D., Hansen, M., Holmes, C., Mallick, B. & Yu, B. (Springer, New York), pp. 129-148.
33. Craven, P. & Wahba, G. (1979) Numer. Math. 31, 377-403.
34. Golub, G. H., Heath, M. & Wahba, G. (1979) Technometrics 21, 215-224.
35. Li, K. C. (1986)Ann. Statist. 14, 1101-1112.
36. Speckman, P. (1985) Ann. Statist. 13, 970-983.
37. Hutchinson, M. (1989) Commun. Stat. Simul. 18, 1059-1076.
38. Girard, D. (1989) Numer. Math. 56, 1-23.
39. Joachims, T. (2000) in Proceedings of the International Conference on Machine Learning (Morgan Kaufmann, San Mateo, CA).
40. Chapelle, O., Vapnik, V., Bousquet, O. & Mukherjee, S. (2002) Mach. Learn. 46, 131-159.
41. Lin, Y. (2002) Tech. Rep. 1044 (Dept. of Stat., Univ. of Wisconsin, Madison).
42. Micchelli, C. (1986) Constr. Approximation 2, 11-22.
43. Wahba, G. (1987) in Proceedings of the Alpine-U.S. Seminar on Inverse and Ill Posed Problems, eds. Engl, H. & Groetsch, C. (Academic, New York), pp. 37-51.
44. Wahba, G., Johnson, D., Gao, F. & Gong, J. (1995) Mon. Weather Rev. 123, 3358-3369.
45. Nychka, D., Wahba, G., Goldfarb, S. & Pugh, T. (1984) J. Am. Stat. Assoc. 79, 832-846.
46. O'Sullivan, F. & Wahba, G. (1985) J. Comput. Phys. 59, 441-455.
47. Wahba, G. (1977) SIAM J. Numer. Anal. 14, 651-667.