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Volumn 8, Issue , 2007, Pages 249-276

Learnability of Gaussians with flexible variances

Author keywords

Empirical covering number; Flexible variances; Gaussian kernel; Glivenko Cantelli class; Learning theory; Regularization scheme

Indexed keywords

CLASSIFICATION (OF INFORMATION); CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; LEARNING ALGORITHMS; LEAST SQUARES APPROXIMATIONS; REGRESSION ANALYSIS;

EID: 33847115868     PISSN: 15324435     EISSN: 15337928     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (58)

References (43)
  • 4
    • 0038453192 scopus 로고    scopus 로고
    • Rademacher and Gaussian complexities: Risk bounds and structural results
    • P. L. Bartlett and S. Mendelson. Rademacher and Gaussian complexities: Risk bounds and structural results. Journal of Machine Learning Research, 3:463-482, 2002.
    • (2002) Journal of Machine Learning Research , vol.3 , pp. 463-482
    • Bartlett, P.L.1    Mendelson, S.2
  • 5
    • 84898998301 scopus 로고    scopus 로고
    • Dynamically adapting kernels in support vector machines
    • M. S. Kearns, S. A. Solla, and D. A. Cohn, eds, MIT Press
    • N. Cristianini, J. Shawe-Taylor, and C. Campbell. Dynamically adapting kernels in support vector machines. In Advances in Neural Information Processing Systems 11 (M. S. Kearns, S. A. Solla, and D. A. Cohn, eds), MIT Press, 1999.
    • (1999) Advances in Neural Information Processing Systems , pp. 11
    • Cristianini, N.1    Shawe-Taylor, J.2    Campbell, C.3
  • 8
    • 34249753618 scopus 로고
    • Support-vector networks
    • C. Cortes and V. Vapnik. Support-vector networks. Machine Learning, 20:273-297, 1995.
    • (1995) Machine Learning , vol.20 , pp. 273-297
    • Cortes, C.1    Vapnik, V.2
  • 10
    • 33744770935 scopus 로고    scopus 로고
    • Learning Theory: An Approximation Theory Viewpoint. Cambridge University Press
    • to appear
    • F. Cucker and D. X. Zhou. Learning Theory: An Approximation Theory Viewpoint. Cambridge University Press, to appear, 2007.
    • (2007)
    • Cucker, F.1    Zhou, D.X.2
  • 17
    • 0035397715 scopus 로고    scopus 로고
    • Rademacher penalties and structural risk minimization
    • V. Koltchinskii. Rademacher penalties and structural risk minimization. IEEE Transactions on Information Theory, 47:1902-1914, 2001.
    • (2001) IEEE Transactions on Information Theory , vol.47 , pp. 1902-1914
    • Koltchinskii, V.1
  • 18
    • 0036104545 scopus 로고    scopus 로고
    • Empirical margin distributions and bounding the generalization error of combined classifiers
    • V. Koltchinskii and V. Panchenko. Empirical margin distributions and bounding the generalization error of combined classifiers. The Annals of Statistics, 30:1-50, 2002.
    • (2002) The Annals of Statistics , vol.30 , pp. 1-50
    • Koltchinskii, V.1    Panchenko, V.2
  • 21
    • 84898948162 scopus 로고    scopus 로고
    • Mixture density estimation
    • S. A. Solla, K. L. Todd, K.-R. Müller eds, MIT Press
    • J. Li, and A. Barron. Mixture density estimation. In Advances in Neural Information Processing Systems 12 (S. A. Solla, K. L. Todd, K.-R. Müller eds.), MIT Press, 2000.
    • (2000) Advances in Neural Information Processing Systems , pp. 12
    • Li, J.1    Barron, A.2
  • 22
    • 0000482137 scopus 로고    scopus 로고
    • On the relationships between generalization error, hypothesis complexity and sample complexity for radial basis functions
    • P. Niyogi and F. Girosi. On the relationships between generalization error, hypothesis complexity and sample complexity for radial basis functions. Neural Computation, 8:819-842, 1996.
    • (1996) Neural Computation , vol.8 , pp. 819-842
    • Niyogi, P.1    Girosi, F.2
  • 25
    • 84865131152 scopus 로고    scopus 로고
    • B. Schölkopf, B. R. Herbrich, and A. J. Smola. A generalized representer theorem. In Proceedings of the 14th Annual Conference on Computational Learning Theory, Lecture Notes in Artificial Intelligence, 2111: 416-426, 2001.
    • B. Schölkopf, B. R. Herbrich, and A. J. Smola. A generalized representer theorem. In Proceedings of the 14th Annual Conference on Computational Learning Theory, Lecture Notes in Artificial Intelligence, 2111: 416-426, 2001.
  • 27
    • 0037749769 scopus 로고    scopus 로고
    • Estimating the approximation error in learning theory
    • S. Smale and D. X. Zhou. Estimating the approximation error in learning theory. Analysis and Applications, 1:17-41, 2003.
    • (2003) Analysis and Applications , vol.1 , pp. 17-41
    • Smale, S.1    Zhou, D.X.2
  • 28
  • 31
    • 0010786475 scopus 로고    scopus 로고
    • On the influence of the kernel on the consistency of support vector machines
    • I. Steinwart. On the influence of the kernel on the consistency of support vector machines. Journal of Machine Learning Research, 2:67-93, 2001.
    • (2001) Journal of Machine Learning Research , vol.2 , pp. 67-93
    • Steinwart, I.1
  • 33
    • 3142725508 scopus 로고    scopus 로고
    • Optimal aggregation of classifiers in statistical learning
    • A. B. Tsybakov. Optimal aggregation of classifiers in statistical learning. The Annals of Statistics, 32:135-166, 2004.
    • (2004) The Annals of Statistics , vol.32 , pp. 135-166
    • Tsybakov, A.B.1
  • 38
    • 55049127622 scopus 로고    scopus 로고
    • Learning and approximation by Gaussians on Riemannian manifolds
    • forthcoming
    • G. B. Ye and D. X. Zhou. Learning and approximation by Gaussians on Riemannian manifolds. Advances in Computational Mathematics, forthcoming.
    • Advances in Computational Mathematics
    • Ye, G.B.1    Zhou, D.X.2
  • 40
    • 4644257995 scopus 로고    scopus 로고
    • Statistical behavior and consistency of classification methods based on convex risk minimization
    • T. Zhang. Statistical behavior and consistency of classification methods based on convex risk minimization. The Annals of Statistics, 32:56-85, 2004.
    • (2004) The Annals of Statistics , vol.32 , pp. 56-85
    • Zhang, T.1
  • 41
    • 0036748375 scopus 로고    scopus 로고
    • The covering number in learning theory
    • D. X. Zhou. The covering number in learning theory. Journal of Complexity, 18:739-767, 2002.
    • (2002) Journal of Complexity , vol.18 , pp. 739-767
    • Zhou, D.X.1
  • 42
    • 0038105204 scopus 로고    scopus 로고
    • Capacity of reproducing kernel spaces in learning theory
    • D. X. Zhou. Capacity of reproducing kernel spaces in learning theory. IEEE Transactions on Information Theory, 49:1743-1752, 2003.
    • (2003) IEEE Transactions on Information Theory , vol.49 , pp. 1743-1752
    • Zhou, D.X.1
  • 43
    • 33745650526 scopus 로고    scopus 로고
    • Approximation with polynomial kernels and SVM classifiers
    • D. X. Zhou and K. Jetter. Approximation with polynomial kernels and SVM classifiers. Advances in Computational Mathematics, 25:323-344, 2006.
    • (2006) Advances in Computational Mathematics , vol.25 , pp. 323-344
    • Zhou, D.X.1    Jetter, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.