The representer theorem for Hilbert spaces: A necessary and sufficient condition

Advances in Neural Information Processing Systems

Volumn 1, Issue , 2012, Pages 189-196

  Dinuzzo, Francesco ^a   Schölkopf, Bernhard ^a  

^a MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FINITE DIMENSIONAL; KERNEL METHODS; LOWER SEMICONTINUOUS; NON-DECREASING FUNCTIONS; REGULARIZATION TERMS; REGULARIZATION THEORY; REPRESENTER THEOREM; SUFFICIENT CONDITIONS;

EID: 84877726257     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (15)

1. A. N. Tikhonov and V. Y. Arsenin. Solutions of Ill Posed Problems. W. H. Winston, Washington, D. C., 1977.
2. G. Wahba. Spline Models for Observational Data. SIAM, Philadelphia, USA, 1990.
3. F. Cucker and S. Smale. On the mathematical foundations of learning. Bulletin of the American mathematical society, 39:1-49, 2001.
4. B. Schölkopf, A. J. Smola, and K-R Müller. Nonlinear component analysis as a kernel eigenvalue problem. Neural Computation, 10(5):1299-1319, 1998.
5. F. Riesz. Sur une espèce de géométrie analytique des systèmes de fonctions sommables. Comptes rendus de l'Académie des sciences Paris, 144:1409-1411, 1907.
6. M. Fréchet. Sur les ensembles de fonctions et les opérations linéaires. Comptes rendus de l'Académie des sciences Paris, 144:1414-1416, 1907.
7. V. Vapnik. Statistical Learning Theory. Wiley, New York, NY, USA, 1998.
8. B. Schölkopf and A. J. Smola. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. (Adaptive Computation and Machine Learning). MIT Press, 2001.
9. J. Shawe-Taylor and N. Cristianini. Kernel Methods for Pattern Analysis. Cambridge University Press, New York, NY, USA, 2004.
10. N. Aronszajn. Theory of reproducing kernels. Transactions of the American Mathematical Society, 68:337-404, 1950.
11. B. Schölkopf, R. Herbrich, and A. J. Smola. A generalized representer theorem. In In Proceedings of the Annual Conference on Computational Learning Theory, pages 416-426, 2001.
12. G. Kimeldorf and G. Wahba. Some results on Tchebycheffian spline functions. Journal of Mathematical Analysis and Applications, 33(1):82-95, 1971.
13. D. Cox and F. O' Sullivan. Asymptotic analysis of penalized likelihood and related estimators. The Annals of Statistics, 18:1676-1695, 1990.
14. T. Poggio and F. Girosi. Networks for approximation and learning. In Proceedings of the IEEE, volume 78, pages 1481-1497, 1990.
15. A. Argyriou, C. A. Micchelli, and M. Pontil. When is there a representer theorem? Vector versus matrix regularizers. Journal of Machine Learning Research, 10:2507-2529, 2009.