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Section B

Optimal rate of the regularized regression learning algorithm

, &
Pages 1471-1483 | Received 14 Apr 2010, Accepted 09 Aug 2010, Published online: 11 Mar 2011

References

  • Aronszajn , N. 1950 . Theory of reproducing kernels . Trans. Am. Math. Soc. , 68 : 337 – 404 .
  • Bertlett , P. L. 1998 . The sample complexity of pattern classification with neural networks: The size of the weights is more important than the size of network . IEEE Trans. Inform. Theory , 44 : 525 – 536 .
  • Caponnetto , A. and DeVito , E. 2007 . Optimal rates for the regularized least-squares algorithm . Found. Comput. Math. , 7 : 331 – 368 .
  • Chen , D. R. , Wu , Q. , Ying , Y. M. and Zhou , D. X. 2004 . Support vector machine soft margin classifiers: Error analysis . J. Mach. Learn. Res. , 5 : 1143 – 1175 .
  • Cucker , F. and Smale , S. 2001 . On the mathematical foundations of learning . Bull. Am. Math. Soc. , 39 : 1 – 49 .
  • Dong , X. M. and Zhou , D. X. 2008 . Learning gradients by a gradient descent algorithm . J. Math. Anal. Appl. , 341 : 1018 – 1027 .
  • Guo , Y. , Bartlett , P. L. , Shawe-Taylor , J. and Williamson , R. C. 2002 . Covering numbers for support vector machines . IEEE Trans. Inform. Theory , 48 : 239 – 250 .
  • Li , B. Z. and Wang , G. M. 2009 . Learning rates of least-square regularized regression with polynomial kernels . Sci. China, Ser. A-Math. , 52 ( 4 ) : 687 – 700 .
  • Pontil , M. 2003 . A note different covering numbers in learning theory . J. Complexity , 19 : 665 – 671 .
  • Scholkopf , B. , Herbrich , R. and Smola , A. J. 2001 . “ A generalized representer theorem ” . In Proceedings of the 14th Annual Conference on Computational Learning Theory , Edited by: Helmbold , D. and Williamson , B. 416 – 426 . New York : Springer .
  • Smale , S. and Zhou , D. X. 2003 . Estimating the approximation error in learning theory . Anal. Appl. , 1 : 17 – 41 .
  • Smale , S. and Zhou , D. X. 2004 . Shannon sampling and function reconstruction from point values . Bull. Am. Math. Soc. , 41 : 279 – 305 .
  • Steinwart , I. , Hush , D. and Scovel , C. 2009 . Optimal rates for regularized least squares regression . Proceedings of the 22nd Conference on Learning Theory, 2009 , Los Alamos National Laboratory Technical Report LA-UR-09-00901
  • Temlyakov , V. 2006 . Optimal estimators in learning theory, Banach Center Publications . Inst. Math. Polish Acad. Sci. , 72 : 341 – 366 .
  • Tong , H. Z. , Chen , D. R. and Li , Z. P. 2008 . Learning rates for regularized classifiers using multivariate polynomial kernels . J. Complexity , 24 : 619 – 631 .
  • Vapnik , V. 1998 . Statistical Learning Theory , New York : Wiley .
  • Williamson , R. C. , Smola , A. J. and Schoˇkopf , B. 2001 . Generalization performance of regularization networks and support vector machines via entropy numbers of compact operators . IEEE Trans. Inform. Theory , 47 : 2516 – 2532 .
  • Wu , Q. , Ying , Y. M. and Zhou , D. X. 2006 . “ Learning theory: From regression to classification ” . In Topics in Multivariate Approximation and Interpolation , Edited by: Jetter , K. , Buhmann , M. D. , Haussmann , W. , Schaback , R. and Stockler , J. Vol. 12 , 257 – 290 . Elsevier . Amsterdam
  • Wu , Q. , Ying , Y. M. and Zhou , D. X. 2006 . Learning rates of least-square regularized regression . Found. Comput. Math. , 6 : 171 – 192 .
  • Yan , S. J. , Wang , J. X. and Liu , X. F. 1982 . Foundation of Probability Theory , Beijing : Science Press . in Chinese
  • Zhou , D. X. 2002 . The covering number in learning theory . J. Complexity , 18 : 739 – 767 .
  • Zhou , D. X. 2003 . Capacity of reproducing kernel spaces in learning theory . IEEE Trans. Inform. Theory , 49 : 1734 – 1752 .
  • Zhou , D. X. and Jetter , K. 2006 . Approximation with polynomial kernels and SVM classifiers . Adv. Comput. Math. , 25 : 323 – 344 .

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