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Volumn 44, Issue 2, 1998, Pages 525-536

The sample complexity of pattern classification with neural networks: The size of the weights is more important than the size of the network

Author keywords

Computational learning theory; Neural networks; Pattern recognition; Scale sensitive dimensions; Weight decay

Indexed keywords

BACKPROPAGATION; COMPUTATIONAL COMPLEXITY; ERROR ANALYSIS; LEARNING ALGORITHMS; LEARNING SYSTEMS; PATTERN RECOGNITION; PROBABILITY; TRANSFER FUNCTIONS;

EID: 0032028728     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.661502     Document Type: Article
Times cited : (1075)

References (41)
  • 3
    • 0041805140 scopus 로고
    • A result of Vapnik with applications
    • M. Anthony and J. Shawe-Taylor, "A result of Vapnik with applications," Discr. Appl. Math., vol. 47, pp. 207-217, 1993.
    • (1993) Discr. Appl. Math. , vol.47 , pp. 207-217
    • Anthony, M.1    Shawe-Taylor, J.2
  • 4
    • 0027599793 scopus 로고
    • Universal approximation bounds for superposition of a sigmoidal function
    • A. R. Barron, "Universal approximation bounds for superposition of a sigmoidal function," IEEE Trans. Inform. Theory, vol. 39, pp. 930-945, 1993.
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 5
    • 84898957627 scopus 로고    scopus 로고
    • For valid generalization, the size of the weights is more important than the size of the network
    • P. L. Bartlett, "For valid generalization, the size of the weights is more important than the size of the network," Neural Inform. Process. Syst., vol. 9, pp. 134-140, 1997.
    • (1997) Neural Inform. Process. Syst. , vol.9 , pp. 134-140
    • Bartlett, P.L.1
  • 6
    • 0031235711 scopus 로고    scopus 로고
    • Covering numbers for real-valued function classes
    • Sept.
    • P. L. Bartlett, S. R. Kulkarni, and S. E. Posner, "Covering numbers for real-valued function classes," IEEE Trans. Inform. Theory, vol. 43, pp. 1721-1724, Sept. 1997.
    • (1997) IEEE Trans. Inform. Theory , vol.43 , pp. 1721-1724
    • Bartlett, P.L.1    Kulkarni, S.R.2    Posner, S.E.3
  • 7
    • 0032046897 scopus 로고    scopus 로고
    • Prediction, learning, uniform convergence, and scale-sensitive dimensions
    • to be published
    • P. L. Bartlett and P. M. Long, "Prediction, learning, uniform convergence, and scale-sensitive dimensions," J. Comput. and Syst. Sci., 1998, to be published.
    • (1998) J. Comput. and Syst. Sci.
    • Bartlett, P.L.1    Long, P.M.2
  • 8
    • 0001160588 scopus 로고
    • What size net gives valid generalization?
    • E. Baum and D. Haussler, "What size net gives valid generalization?" Neural Computation, vol. 1, no. 1, pp. 151-160, 1989.
    • (1989) Neural Computation , vol.1 , Issue.1 , pp. 151-160
    • Baum, E.1    Haussler, D.2
  • 9
    • 0029252255 scopus 로고
    • Characterizations of learnability for classes of {0, ⋯, n}-valued functions
    • S. Ben-David, N. Cesa-Bianchi, D. Haussler, and P. M. Long, "Characterizations of learnability for classes of {0, ⋯, n}-valued functions," J. Comput. Syst. Sci., vol. 50, no. 1, pp. 74-86, 1995.
    • (1995) J. Comput. Syst. Sci. , vol.50 , Issue.1 , pp. 74-86
    • Ben-David, S.1    Cesa-Bianchi, N.2    Haussler, D.3    Long, P.M.4
  • 13
    • 0024739191 scopus 로고
    • A general lower bound on the number of examples needed for learning
    • A. Ehrenfeucht, D. Haussler, M. Kearns, and L. Valiant, "A general lower bound on the number of examples needed for learning," Inform. Computat., vol. 82, pp. 247-261, 1989.
    • (1989) Inform. Computat. , vol.82 , pp. 247-261
    • Ehrenfeucht, A.1    Haussler, D.2    Kearns, M.3    Valiant, L.4
  • 15
    • 33747140061 scopus 로고    scopus 로고
    • Experiments with a new boosting algorithm
    • _, "Experiments with a new boosting algorithm," in Machine Learning: Proc. 13th Int. Conf., 1996.
    • (1996) Machine Learning: Proc. 13th Int. Conf.
  • 16
    • 0029256399 scopus 로고
    • Bounding the Vapnik-Chervonenkis dimension of concept classes parametrized by real numbers
    • P. W. Goldberg and M. R. Jerrum, "Bounding the Vapnik-Chervonenkis dimension of concept classes parametrized by real numbers," Mach. Learning, vol. 18, no. 2/3, pp. 131-148, 1995.
    • (1995) Mach. Learning , vol.18 , Issue.2-3 , pp. 131-148
    • Goldberg, P.W.1    Jerrum, M.R.2
  • 18
    • 0005396750 scopus 로고
    • Automatic capacity tuning of very large VC-dimension classifiers
    • Los Altos, CA: Morgan Kaufmann
    • I. Guyon, B. Boser, and V. Vapnik, "Automatic capacity tuning of very large VC-dimension classifiers," in NIPS 5. Los Altos, CA: Morgan Kaufmann, 1993, pp. 147-155.
    • (1993) NIPS 5 , pp. 147-155
    • Guyon, I.1    Boser, B.2    Vapnik, V.3
  • 19
    • 0002192516 scopus 로고
    • Decision theoretic generalizations of the PAC model for neural net and other learning applications
    • D. Haussler, "Decision theoretic generalizations of the PAC model for neural net and other learning applications," Inform. Computat., vol. 100, no. 1, pp. 78-150, 1992.
    • (1992) Inform. Computat. , vol.100 , Issue.1 , pp. 78-150
    • Haussler, D.1
  • 20
    • 0343384240 scopus 로고
    • A generalization of Sauer's lemma
    • D. Haussler and P. M. Long, "A generalization of Sauer's lemma," J. Comb. Theory, Ser. A, vol. 71, no. 2, pp. 219-240, 1995.
    • (1995) J. Comb. Theory, Ser. A , vol.71 , Issue.2 , pp. 219-240
    • Haussler, D.1    Long, P.M.2
  • 22
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • W. Hoeffding, "Probability inequalities for sums of bounded random variables," Amer. Statist. Assoc. J., vol. 58, pp. 13-30, 1963.
    • (1963) Amer. Statist. Assoc. J. , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 23
    • 33747146721 scopus 로고    scopus 로고
    • A data-dependent skeleton estimate and a scale-sensitive dimension for classification
    • Pompeu Fabra Univ., Dec.
    • M. Horvath and G. Lugosi, "A data-dependent skeleton estimate and a scale-sensitive dimension for classification," Tech. Rep., Pompeu Fabra Univ., Dec. 1996.
    • (1996) Tech. Rep.
    • Horvath, M.1    Lugosi, G.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
    • L. K. Jones, "A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training," Ann. Statist., vol. 20, no. 1, pp. 608-613, 1992.
    • (1992) Ann. Statist. , vol.20 , Issue.1 , pp. 608-613
    • Jones, L.K.1
  • 26
    • 0025794545 scopus 로고
    • Efficient distribution-free learning of probabilistic concepts
    • Los Alamitos, CA: IEEE Computer Soc. Press
    • M. J. Kearns and R. E. Schapire, "Efficient distribution-free learning of probabilistic concepts," in Proc. 31st Symp. on Foundations of Computer Science. Los Alamitos, CA: IEEE Computer Soc. Press, 1990, pp. 382-391.
    • (1990) Proc. 31st Symp. on Foundations of Computer Science , pp. 382-391
    • Kearns, M.J.1    Schapire, R.E.2
  • 29
    • 0003979410 scopus 로고    scopus 로고
    • What size neural network gives optimal generalization? Convergence properties of backpropagation
    • Institute for Advanced Computer Studies, Univ. of Maryland, Apr.
    • S. Lawrence, C. L. Giles, and A. C. Tsoi, "What size neural network gives optimal generalization? Convergence properties of backpropagation," Tech. Rep. UMIACS-TR-96-22 and CS-TR-3617, Institute for Advanced Computer Studies, Univ. of Maryland, Apr. 1996.
    • (1996) Tech. Rep. UMIACS-TR-96-22 and CS-TR-3617
    • Lawrence, S.1    Giles, C.L.2    Tsoi, A.C.3
  • 30
    • 0001556720 scopus 로고    scopus 로고
    • Efficient agnostic learning of neural networks with bounded fan-in
    • Nov.
    • W. S. Lee, P. L. Bartlett, and R. C. Williamson, "Efficient agnostic learning of neural networks with bounded fan-in," IEEE Trans. Inform. Theory, vol. 42, pp. 2118-2132, Nov. 1996.
    • (1996) IEEE Trans. Inform. Theory , vol.42 , pp. 2118-2132
    • Lee, W.S.1    Bartlett, P.L.2    Williamson, R.C.3
  • 32
    • 33747121274 scopus 로고    scopus 로고
    • Generalization and the size of the weights: An experimental study
    • M. Dale, A. Kowalczyk, R. Slaviero, and J Szymanski, Eds., Telstra Res. Labs.
    • G. Loy and P. L. Bartlett, "Generalization and the size of the weights: An experimental study," in Proc. 8th Australian Conf. on Neural Networks, M. Dale, A. Kowalczyk, R. Slaviero, and J Szymanski, Eds., Telstra Res. Labs., 1997, pp. 60-64.
    • (1997) Proc. 8th Australian Conf. on Neural Networks , pp. 60-64
    • Loy, G.1    Bartlett, P.L.2
  • 34
    • 0010687655 scopus 로고
    • Vapnik-Chervonenkis dimension of neural nets
    • M. A. Arbib, Ed. Cambridge, MA: MIT Press
    • W. Maass, "Vapnik-Chervonenkis dimension of neural nets," in The Handbook of Brain Theory and Neural Networks, M. A. Arbib, Ed. Cambridge, MA: MIT Press, 1995, pp. 1000-1003.
    • (1995) The Handbook of Brain Theory and Neural Networks , pp. 1000-1003
    • Maass, W.1
  • 38
    • 33747142704 scopus 로고    scopus 로고
    • Structural risk minimization over data-dependent hierarchies, September 1996
    • _, "Structural risk minimization over data-dependent hierarchies, September 1996," Tech. Rep.
    • Tech. Rep.
  • 39
    • 0026904597 scopus 로고
    • Feedforward nets for interpolation and classification
    • E. D. Sontag, "Feedforward nets for interpolation and classification," J. Comput. Syst. Sci., vol. 45, pp. 20-48, 1992.
    • (1992) J. Comput. Syst. Sci. , vol.45 , pp. 20-48
    • Sontag, E.D.1
  • 41
    • 0001024505 scopus 로고
    • On the uniform convergence of relative frequencies of events to their probabilities
    • V. N. Vapnik and A. Y. Chervonenkis, "On the uniform convergence of relative frequencies of events to their probabilities," Theory Probab. Its Applicat., vol. 16, no. 2, pp. 264-280, 1971.
    • (1971) Theory Probab. Its Applicat. , vol.16 , Issue.2 , pp. 264-280
    • Vapnik, V.N.1    Chervonenkis, A.Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.