Optimal learning rates for Kernel Conjugate Gradient regression

Advances in Neural Information Processing Systems 23: 24th Annual Conference on Neural Information Processing Systems 2010, NIPS 2010

Volumn , Issue , 2010, Pages

  Blanchard, Gilles ^a   Krämer, Nicole ^b  

^a UNIVERSITY OF POTSDAM   (Germany)

^b WEIERSTRASS INSTITUTE FOR APPLIED ANALYSIS AND STOCHASTICS   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

LEAST SQUARES APPROXIMATIONS; REGRESSION ANALYSIS;

CONJUGATE GRADIENT ALGORITHMS; EARLY STOPPING; LEARNING RATES; LEAST SQUARES REGRESSION; LOW BOUND; OVERFITTING; PARTIAL LEAST-SQUARES; RATE OF CONVERGENCE; REGRESSION FUNCTION; REGULARISATION;

CONJUGATE GRADIENT METHOD;

EID: 85162008544     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (22)

1. F. Bauer, S. Pereverzev, and L. Rosasco. On Regularization Algorithms in Learning Theory. Journal of Complexity, 23:52-72, 2007.
2. N. Bissantz, T. Hohage, A. Munk, and F. Ruymgaart. Convergence Rates of General Regularization Methods for Statistical Inverse Problems and Applications. SIAM Journal on Numerical Analysis, 45(6):2610-2636, 2007.
3. G. Blanchard and N. Krämer. Kernel Partial Least Squares is Universally Consistent. Proceedings of the 13th International Conference on Artificial Intelligence and Statistics, JMLR Workshop & Conference Proceedings, 9:57-64, 2010.
4. G. Blanchard and P. Massart. Discussion of V. Koltchinskii's "Local Rademacher complexities and oracle inequalities in risk minimization". Annals of Statistics, 34(6):2664-2671, 2006.
5. A. Caponnetto. Optimal Rates for Regularization Operators in Learning Theory. Technical Report CBCL Paper 264/ CSAIL-TR 2006-062, Massachusetts Institute of Technology, 2006.
6. A. Caponnetto and E. De Vito. Optimal Rates for Regularized Least-squares Algorithm. Foundations of Computational Mathematics, 7(3):331-368, 2007.
7. A. Caponnetto and Y. Yao. Cross-validation based Adaptation for Regularization Operators in Learning Theory. Analysis and Applications, 8(2):161-183, 2010.
8. H. Chun and S. Keles. Sparse Partial Least Squares for Simultaneous Dimension Reduction and Variable Selection. Journal of the Royal Statistical Society B, 72(1):3-25, 2010.
9. E. De Vito, L. Rosasco, A. Caponnetto, U. De Giovannini, and F. Odone. Learning from Examples as an Inverse Problem. Journal of Machine Learning Research, 6(1):883, 2006.
10. L. Györfi, M. Kohler, A. Krzyzak, and H.Walk. A Distribution-Free Theory of Nonparametric Regression. Springer, 2002.
11. M. Hanke. Conjugate Gradient Type Methods for Linear Ill-posed Problems. Pitman Research Notes in Mathematics Series, 327, 1995.
12. L. Lo Gerfo, L. Rosasco, E. Odone, F.and De Vito, and A. Verri. Spectral Algorithms for Supervised Learning. Neural Computation, 20:1873-1897, 2008.
13. S. Mendelson and J. Neeman. Regularization in Kernel Learning. The Annals of Statistics, 38(1):526-565, 2010.
14. P. Naik and C.L. Tsai. Partial Least Squares Estimator for Single-index Models. Journal of the Royal Statistical Society B, 62(4):763-771, 2000.
15. A. S. Nemirovskii. The Regularizing Properties of the Adjoint Gradient Method in Ill-posed Problems. USSR Computational Mathematics and Mathematical Physics, 26(2):7-16, 1986.
16. C. S. Ong. Kernels: Regularization and Optimization. Doctoral dissertation, Australian National University, 2005.
17. C. S. Ong, X. Mary, S. Canu, and A. J. Smola. Learning with Non-positive Kernels. In Proceedings of the 21st International Conference on Machine Learning, pages 639 - 646, 2004.
18. R. Rosipal and L.J. Trejo. Kernel Partial Least Squares Regression in Reproducing Kernel Hilbert Spaces. Journal of Machine Learning Research, 2:97-123, 2001.
19. R. Rosipal, L.J. Trejo, and B. Matthews. Kernel PLS-SVC for Linear and Nonlinear Classification. In Proceedings of the Twentieth International Conference on Machine Learning, pages 640-647, Washington, DC, 2003.
20. I. Steinwart, D. Hush, and C. Scovel. Optimal Rates for Regularized Least Squares Regression. In Proceedings of the 22nd Annual Conference on Learning Theory, pages 79-93, 2009.
21. S.Wold, H. Ruhe, H.Wold, andW.J. Dunn III. The Collinearity Problem in Linear Regression. The Partial Least Squares (PLS) Approach to Generalized Inverses. SIAM Journal of Scientific and Statistical Computations, 5:735-743, 1984.
22. T. Zhang. Learning bounds for kernel regression using effective data dimensionality. Neural Computation, 17(9):2077-2098, 2005.