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Applicable Analysis
An International Journal
Volume 98, 2019 - Issue 9
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Articles

Support vector machines regression with unbounded sampling

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Pages 1626-1635 | Received 18 Jun 2017, Accepted 02 Feb 2018, Published online: 08 Feb 2018

References

  • Vapnik V . The nature of statistical learning theory. New York (NY): Springer-Verlag; 1995.
  • Vapnik V . Statistical learning theory. New York (NY): Wiley; 1998.
  • Tong HZ , Ng M . Calibration of ∈-insensitive loss in support vector machines regression. Peprint, 2016.
  • Aronszajn N . Theory of reproducing kernels. Trans Amer Math Soc. 1950;68:337–404.
  • Cristianini N , Shawe-Taylor J . An introduction to support vector machines. Cambridge: Cambridge University Press; 2000.
  • Evgeniou T , Pontil M , Poggio T . Regularization networks and support vector machines. Adv Comput Math. 2000;13:1–50.
  • Steinwart I , Christmann A . Support vector machines. New York (NY): Springer; 2008.
  • Tong HZ , Chen DR , Peng LZ . Analysis of support vector machines regression. Found Comput Math. 2009;9:243–257.
  • Xiang DH , Hu T , Zhou DX . Approximation analysis of learning algorithms for support vector regression and quantile regression. J Appl Math. 2012;2012: Article ID 902139, 17 p.
  • Caponnetto A , De Vito E . Optimal rates for regularized least squares algorithm. Found Comput Math. 2007;7:331–368.
  • De Mol C , De Vito E , Rosasco L . Elastic-net regularization in learning theory. J Complexity. 2009;25:201–230.
  • Wang C , Zhou DX . Optimal learning rates for least square regularized regression with unbounded sampling. J Complexity. 2011;27:55–67.
  • Cai J . Coefficient-based regression with non-identical unbounded sampling. Abstract Appl Anal. 2013;2013: Article ID 134727, 8 p.
  • Cai J , Wang C . Coefficient-based regularized regression with indefinite kernels by unbouded sampling. Sci Sin Math. 2013;43:613–624. Chinese.
  • Chu XR , Sun HW . Regularized least square regression with unbounded and dependent sampling. Abstract Appl Anal. 2013;2013: Article ID 139318, 7 p.
  • Guo ZC , Wang C . Online regression with unbouded sampling. Int J Comput Math. 2011;88:2936–2941.
  • Guo ZC , Zhou DX . Concentration estimates for learning with unbouded sampling. Adv Comput Math. 2013;38:207–223.
  • He FC . Optimal convergence rates of high parzen windows with unbouded sampling. Stat Probab Lett. 2014;92:26–32.
  • He FC , Chen H , Li LQ . Statistical analysis of moving least squares method with unbouded sampling. Inform Sci. 2014;286:370–380.
  • Lv SG , Feng YL . Integral operator approach to learning theory with unbounded sampling. Complex Anal Oper Theory. 2012;6:533–548.
  • Nie WL , Wang C . Error analysis of EMR algorithm with unbounded and non-identical sampling. J Appl Math Phys. 2016;4:156–168.
  • Wang C , Cai J . Convergence analysis of coefficient-based regularization under moment incremental condition. Int J Wavelets Multiresolution Inf Process. 2014;12(1): 19 p.
  • Wang C , Guo ZC . EMR learning with unbounded sampling. Acta Math Sin (Engl Ser). 2012;28:97–104.
  • Smale S , Zhou DX . Estimating the approximation error in learning theory. Anal Appl. 2003;1:17–41.
  • Cucker F , Zhou DX . Learning theory: an approximation theory viewpoint. Cambridge: Cambridge University Press; 2007.
  • Cucker F , Smale S . On the mathematical foundations of learing theory. Bull Amer Math Soc. 2001;39:1–49.
  • Zhou DX . The covering number in learning theory. J Complexity. 2002;18:739–767.
  • Zhou DX . Capacity of reproducing kernel spaces in learning theory. IEEE Trans Inform Theory. 2003;49:1743–1752.
  • Cucker F , Smale S . Best choices for regularization parameters in learning theory: on the bias-variance problem. Found Comput Math. 2002;2:413–428.
  • Steinwart I , Scovel C . Fast rates for support vector machines using Gaussian kernels. Ann Stat. 2007;35:575–607.
  • Wu Q , Ying Y , Zhou DX . Learning rates of least-square regularized regression. Found Comput Math. 2006;6:171–192.
  • Xiang DH , Hu T , Zhou DX . Learning with varying insensitive loss. Appl Math Lett. 2011;24:2107–2109.

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