메뉴 건너뛰기




Volumn 8, Issue 4, 1996, Pages 819-842

On the Relationship between Generalization Error, Hypothesis Complexity, and Sample Complexity for Radial Basis Functions

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0000482137     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/neco.1996.8.4.819     Document Type: Article
Times cited : (121)

References (48)
  • 1
    • 0000710299 scopus 로고
    • Queries and concept learning
    • Angluin, D. 1988. Queries and concept learning. Mach. Learn. 2, 319-342.
    • (1988) Mach. Learn. , vol.2 , pp. 319-342
    • Angluin, D.1
  • 2
    • 0027599793 scopus 로고
    • Universal approximation bounds for superpositions of a sigmoidal function
    • Barron, A. 1993. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39(3), 930-945.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , Issue.3 , pp. 930-945
    • Barron, A.1
  • 3
    • 0001325515 scopus 로고
    • Approximation and estimation bounds for artificial neural networks
    • Barron, A. 1994. Approximation and estimation bounds for artificial neural networks. Mach. Learn. 14, 115-133.
    • (1994) Mach. Learn. , vol.14 , pp. 115-133
    • Barron, A.1
  • 4
    • 0026190366 scopus 로고
    • Minimum complexity density estimation
    • Barron, A., and Cover, T. 1991. Minimum complexity density estimation. IEEE Trans. Theory 37(4).
    • (1991) IEEE Trans. Theory , vol.37 , Issue.4
    • Barron, A.1    Cover, T.2
  • 5
    • 0001160588 scopus 로고
    • What size net gives valid generalization?
    • Baum, E. B., and Haussler, D. 1989. What size net gives valid generalization? Neural Comp. 1, 151-160.
    • (1989) Neural Comp. , vol.1 , pp. 151-160
    • Baum, E.B.1    Haussler, D.2
  • 7
    • 0008995203 scopus 로고
    • Generalization properties of Radial Basis Functions
    • R. Lippmann, J. Moody, and D. Touretzky, eds., Morgan Kaufmann, San Mateo, CA
    • Botros, S., and Atkeson, C. G. 1991. Generalization properties of Radial Basis Functions. In Advances in Neural Information Processing Systems 3, R. Lippmann, J. Moody, and D. Touretzky, eds., pp. 707-713. Morgan Kaufmann, San Mateo, CA.
    • (1991) Advances in Neural Information Processing Systems 3 , pp. 707-713
    • Botros, S.1    Atkeson, C.G.2
  • 8
    • 0000966291 scopus 로고
    • Can neural networks do better than the VC bounds?
    • R. Lippmann, J. Moody, and D. Touretzky, eds., Morgan Kaufmann, San Mateo, CA
    • Cohn, D., and Tesauro, G. 1991. Can neural networks do better than the VC bounds? In Advances in Neural Information Processing Systems 3, R. Lippmann, J. Moody, and D. Touretzky, eds., pp. 911-917. Morgan Kaufmann, San Mateo, CA.
    • (1991) Advances in Neural Information Processing Systems 3 , pp. 911-917
    • Cohn, D.1    Tesauro, G.2
  • 9
    • 34250263445 scopus 로고
    • Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross validation
    • Craven, P., and Wahba, G. 1979. Smoothing noisy data with spline functions: Estimating the correct degree of smoothing by the method of generalized cross validation. Numer. Math. 31, 377-403.
    • (1979) Numer. Math. , vol.31 , pp. 377-403
    • Craven, P.1    Wahba, G.2
  • 10
    • 0024861871 scopus 로고
    • Approximation by superposition of a sigmoidal function
    • Cybenko, G. 1989. Approximation by superposition of a sigmoidal function. Math. Control Syst. Signals 2(4), 303-314.
    • (1989) Math. Control Syst. Signals , vol.2 , Issue.4 , pp. 303-314
    • Cybenko, G.1
  • 11
    • 0001244757 scopus 로고
    • On the almost everywhere convergence of nonparametric regression function estimate
    • Devroye, L. 1981. On the almost everywhere convergence of nonparametric regression function estimate. Ann. Statist. 9, 1310-1319.
    • (1981) Ann. Statist. , vol.9 , pp. 1310-1319
    • Devroye, L.1
  • 12
    • 0001605679 scopus 로고
    • Universal Donsker classes and metric entropy
    • Dudley, R. M. 1987. Universal Donsker classes and metric entropy. Ann. Prob. 14(4), 1306-1326.
    • (1987) Ann. Prob. , vol.14 , Issue.4 , pp. 1306-1326
    • Dudley, R.M.1
  • 13
    • 0003875839 scopus 로고
    • Mathematics Series. Wadsworth and Brooks/Cole, Pacific Grove, CA
    • Dudley, R. M. 1989. Real Analysis and Probability, Mathematics Series. Wadsworth and Brooks/Cole, Pacific Grove, CA.
    • (1989) Real Analysis and Probability
    • Dudley, R.M.1
  • 15
    • 0001942829 scopus 로고
    • Neural networks and the bias/variance dilemma
    • Geman, S., Bienenstock, E., and Doursat, R. 1992. Neural networks and the bias/variance dilemma. Neural Comp. 4, 1-58.
    • (1992) Neural Comp. , vol.4 , pp. 1-58
    • Geman, S.1    Bienenstock, E.2    Doursat, R.3
  • 16
    • 0000065292 scopus 로고
    • Regularization theory, Radial Basis Functions and networks
    • V. Cherkassky, J. H. Friedman, and H. Wechsler, eds. Subseries F, Computer and Systems Sciences, Springer-Verlag, Berlin
    • Girosi, F. 1994. Regularization theory, Radial Basis Functions and networks. In From Statistics to Neural Networks. Theory and Pattern Recognition Applications, V. Cherkassky, J. H. Friedman, and H. Wechsler, eds. Subseries F, Computer and Systems Sciences, Springer-Verlag, Berlin.
    • (1994) From Statistics to Neural Networks. Theory and Pattern Recognition Applications
    • Girosi, F.1
  • 17
    • 0003085388 scopus 로고
    • Rates of convergence for Radial Basis Functions and neural networks
    • R. J. Mammone, ed., Chapman & Hall, London
    • Girosi, F., and Anzellotti, G. 1993. Rates of convergence for Radial Basis Functions and neural networks. In Artificial Neural Networks for Speech and Vision, R. J. Mammone, ed., pp. 97-113. Chapman & Hall, London.
    • (1993) Artificial Neural Networks for Speech and Vision , pp. 97-113
    • Girosi, F.1    Anzellotti, G.2
  • 18
    • 0001219859 scopus 로고
    • Regularization theory and neural networks architectures
    • Girosi, F., Jones, M., and Poggio, T. 1995. Regularization theory and neural networks architectures. Neural Comp. 7, 219-269.
    • (1995) Neural Comp. , vol.7 , pp. 219-269
    • Girosi, F.1    Jones, M.2    Poggio, T.3
  • 19
    • 0025671510 scopus 로고
    • A probabilistic approach to the understanding and training of neural network classifiers
    • Albuquerque, NM
    • Gish, H. 1990. A probabilistic approach to the understanding and training of neural network classifiers. In Proceedings of the ICASSP-90, pp. 1361-1365, Albuquerque, NM.
    • (1990) Proceedings of the ICASSP-90 , pp. 1361-1365
    • Gish, H.1
  • 20
    • 0001770345 scopus 로고
    • Equivalence proofs for multilayer perceptron classifiers and the bayesian discriminant function
    • J. Elman, D. Touretzky, and G. Hinton, eds. Morgan Kaufmann, San Mateo, CA
    • Hampshire, J. B. II, and Pearlmutter, B. A. 1990. Equivalence proofs for multilayer perceptron classifiers and the bayesian discriminant function. In Proceedings of the 1990 Connectionist Models Summer School, J. Elman, D. Touretzky, and G. Hinton, eds. Morgan Kaufmann, San Mateo, CA.
    • (1990) Proceedings of the 1990 Connectionist Models Summer School
    • Hampshire II, J.B.1    Pearlmutter, B.A.2
  • 21
    • 0002192516 scopus 로고
    • Decision-theoretic generalizations of the PAC model for neural net and other learning applications
    • Haussler, D. 1992. Decision-theoretic generalizations of the PAC model for neural net and other learning applications. Information and Computation 100(1), 78-150.
    • (1992) Information and Computation , vol.100 , Issue.1 , pp. 78-150
    • Haussler, D.1
  • 22
    • 0024880831 scopus 로고
    • Multilayer feedforward networks are universal approximators
    • Hornik, K., Stinchcombe, M., and White, H. 1989. Multilayer feedforward networks are universal approximators. Neural Networks 2, 359-366.
    • (1989) Neural Networks , vol.2 , pp. 359-366
    • Hornik, K.1    Stinchcombe, M.2    White, H.3
  • 23
    • 2342515823 scopus 로고
    • The VC dimension versus the statistical capacity of multilayer networks
    • S. J. Hanson, J. Moody, and R. P. Lippman, eds., Morgan Kaufmann, San Mateo, CA
    • Ji, C., and Psaltis, D. 1992. The VC dimension versus the statistical capacity of multilayer networks. In Advances in Neural Information Processing Systems 4, S. J. Hanson, J. Moody, and R. P. Lippman, eds., Morgan Kaufmann, San Mateo, CA.
    • (1992) Advances in Neural Information Processing Systems 4
    • Ji, C.1    Psaltis, D.2
  • 24
    • 0000796112 scopus 로고
    • A simple lemma on greedy approximation in Hilbert space and convergence rates for Projection Pursuit Regression and neural network training
    • Jones, L. K. 1992. A simple lemma on greedy approximation in Hilbert space and convergence rates for Projection Pursuit Regression and neural network training. Ann. Statist. 20(1), 608-613.
    • (1992) Ann. Statist. , vol.20 , Issue.1 , pp. 608-613
    • Jones, L.K.1
  • 26
    • 0022775261 scopus 로고
    • The rates of convergence of kernel regression estimates and classification rules
    • Krzyzak, A. 1986. The rates of convergence of kernel regression estimates and classification rules. IEEE Trans. Inform. Theory IT-32(5), 668-679.
    • (1986) IEEE Trans. Inform. Theory , vol.IT-32 , Issue.5 , pp. 668-679
    • Krzyzak, A.1
  • 27
    • 0025508916 scopus 로고
    • A statistical approach to learning and generalization in layered neural networks
    • Levin, E., Tishby, N., and Solla, S. A. 1990. A statistical approach to learning and generalization in layered neural networks. Proc. IEEE 78(10), 1568-1574.
    • (1990) Proc. IEEE , vol.78 , Issue.10 , pp. 1568-1574
    • Levin, E.1    Tishby, N.2    Solla, S.A.3
  • 28
    • 0023331258 scopus 로고
    • An introduction to computing with neural nets
    • April
    • Lippmann, R. P. 1987. An introduction to computing with neural nets. IEEE ASSP Mag. April, 4-22.
    • (1987) IEEE ASSP Mag. , pp. 4-22
    • Lippmann, R.P.1
  • 30
    • 0006863682 scopus 로고
    • Approximation properties of a multilayered feedforward artificial neural network
    • Mhaskar, H. N. 1993. Approximation properties of a multilayered feedforward artificial neural network. Adv. Comput. Math. 1, 61-80.
    • (1993) Adv. Comput. Math. , vol.1 , pp. 61-80
    • Mhaskar, H.N.1
  • 31
    • 0000358945 scopus 로고
    • Approximation by superposition of a sigmoidal function
    • Mhaskar, H. N., and Micchelli, C. A. 1992. Approximation by superposition of a sigmoidal function. Adv. Appl. Math. 13, 350-373.
    • (1992) Adv. Appl. Math. , vol.13 , pp. 350-373
    • Mhaskar, H.N.1    Micchelli, C.A.2
  • 32
    • 0000902690 scopus 로고
    • The effective number of parameters: An analysis of generalization and regularization in non-linear learning systems
    • S. J. Hanson, J. Moody, and R. P. Lippman, eds., Morgan Kaufmann, San Mateo, CA
    • Moody, J. 1991. The effective number of parameters: An analysis of generalization and regularization in non-linear learning systems. In Advances in Neural Information Processing Systems 4, S. J. Hanson, J. Moody, and R. P. Lippman, eds., pp. 847-854. Morgan Kaufmann, San Mateo, CA.
    • (1991) Advances in Neural Information Processing Systems 4 , pp. 847-854
    • Moody, J.1
  • 33
    • 0000672424 scopus 로고
    • Fast learning in networks of locally-tuned processing units
    • Moody, J., and Darken, C. 1989. Fast learning in networks of locally-tuned processing units. Neural Comp. 1(2), 281-294.
    • (1989) Neural Comp. , vol.1 , Issue.2 , pp. 281-294
    • Moody, J.1    Darken, C.2
  • 36
    • 0025490985 scopus 로고
    • Networks for approximation and learning
    • Poggio, T., and Girosi, F. 1990. Networks for approximation and learning. Proc. IEEE 78(9).
    • (1990) Proc. IEEE , vol.78 , Issue.9
    • Poggio, T.1    Girosi, F.2
  • 39
    • 0001595997 scopus 로고
    • Neural network classifier estimates bayesian a-posteriori probabilities
    • Richard, M. D., and Lippman, R. P. 1991. Neural network classifier estimates bayesian a-posteriori probabilities. Neural Comp. 3, 461-483.
    • (1991) Neural Comp. , vol.3 , pp. 461-483
    • Richard, M.D.1    Lippman, R.P.2
  • 42
    • 0001300994 scopus 로고
    • Solution of incorrectly formulated problems and the regularization method
    • Tikhonov, A. N. 1963. Solution of incorrectly formulated problems and the regularization method. Soviet Math. Dokl. 4, 1035-1038.
    • (1963) Soviet Math. Dokl. , vol.4 , pp. 1035-1038
    • Tikhonov, A.N.1
  • 44
    • 0001024505 scopus 로고
    • On the uniform convergence of relative frequencies of events to their probabilities
    • Vapnik, V. N., and Chervonenkis, A. Y. 1971. On the uniform convergence of relative frequencies of events to their probabilities. Th. Prob. Appl. 17(2), 264-280.
    • (1971) Th. Prob. Appl. , vol.17 , Issue.2 , pp. 264-280
    • Vapnik, V.N.1    Chervonenkis, A.Y.2
  • 45
    • 0000864140 scopus 로고
    • The necessary and sufficient conditions for consistency in the empirical risk minimization method
    • Vapnik, V. N., and Chervonenkis, A. Y. 1991. The necessary and sufficient conditions for consistency in the empirical risk minimization method. Patt. Recogn. Image Analysis 1(3), 283-305.
    • (1991) Patt. Recogn. Image Analysis , vol.1 , Issue.3 , pp. 283-305
    • Vapnik, V.N.1    Chervonenkis, A.Y.2
  • 46
    • 0003466536 scopus 로고
    • Series in Applied Mathematics, SIAM, Philadelphia
    • Wahba, G. 1990. Spline Models for Observational Data, Series in Applied Mathematics, Vol. 59. SIAM, Philadelphia.
    • (1990) Spline Models for Observational Data , vol.59
    • Wahba, G.1
  • 47
    • 0000539096 scopus 로고
    • Generalization by weight elimination with applications to forecasting
    • R. Lippmann, J. Moody, and D. Touretzky, eds., Morgan Kaufmann, San Mateo, CA
    • Weigand, A. S., Rumelhart, D. E., and Huberman, B. A. 1991. Generalization by weight elimination with applications to forecasting. In Advances in Neural Information Processing Systems 3, R. Lippmann, J. Moody, and D. Touretzky, eds., Morgan Kaufmann, San Mateo, CA.
    • (1991) Advances in Neural Information Processing Systems 3
    • Weigand, A.S.1    Rumelhart, D.E.2    Huberman, B.A.3
  • 48
    • 0025635525 scopus 로고
    • Connectionist nonparametric regression: Multilayer perceptrons can learn arbitrary mappings
    • White, H. 1990. Connectionist nonparametric regression: Multilayer perceptrons can learn arbitrary mappings. Neural Networks 3, 535-549.
    • (1990) Neural Networks , vol.3 , pp. 535-549
    • White, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.