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Volumn 8, Issue 5, 1997, Pages 985-996

Asymptotic statistical theory of overtraining and cross-validation

Author keywords

Asymptotic analysis; Cross validation; Early stopping; Generalization; Overtraining; Stochastic neural networks

Indexed keywords

COMPUTER SIMULATION; ERROR CORRECTION; RANDOM PROCESSES; STATISTICAL METHODS;

EID: 0031236925     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.623200     Document Type: Article
Times cited : (291)

References (34)
  • 1
    • 0000920843 scopus 로고
    • Theory of adaptive pattern classifiers
    • S. Amari, "Theory of adaptive pattern classifiers," IEEE Trans. Electron. Comput., vol. EC-16, pp. 299-307, 1967.
    • (1967) IEEE Trans. Electron. Comput. , vol.EC-16 , pp. 299-307
    • Amari, S.1
  • 2
    • 0027257001 scopus 로고
    • A universal theorem on learning curves
    • _, "A universal theorem on learning curves," Neural Networks, vol. 6, pp. 161-166, 1993.
    • (1993) Neural Networks , vol.6 , pp. 161-166
  • 3
    • 0000729504 scopus 로고
    • Statistical theory of learning curves under entropie loss criterion
    • S. Amari and N. Murata, "Statistical theory of learning curves under entropie loss criterion," Neural Computa., vol. 5, pp. 140-153, 1993.
    • (1993) Neural Computa. , vol.5 , pp. 140-153
    • Amari, S.1    Murata, N.2
  • 4
    • 0001504093 scopus 로고    scopus 로고
    • Statistical theory of overtraining - Is cross-validation effective?
    • D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, Eds. Cambridge, MA: MIT Press
    • S. Amari, N. Murata, K.-R. Müller, M. Finke, and H. Yang, "Statistical theory of overtraining - Is cross-validation effective?," in NIPS'95: Advances in Neural Information Processing Systems 8, D. S. Touretzky, M. C. Mozer, and M. E. Hasselmo, Eds. Cambridge, MA: MIT Press, 1996.
    • (1996) NIPS'95: Advances in Neural Information Processing Systems 8
    • Amari, S.1    Murata, N.2    Müller, K.-R.3    Finke, M.4    Yang, H.5
  • 5
    • 0016355478 scopus 로고
    • A new look at statistical model identification
    • H. Akaike, "A new look at statistical model identification," IEEE Trans. Automat. Contr., vol. AC-19, pp. 716-723, 1974.
    • (1974) IEEE Trans. Automat. Contr. , vol.AC-19 , pp. 716-723
    • Akaike, H.1
  • 6
    • 33747622314 scopus 로고
    • Test error fluctuations in finite linear perceptrons
    • D. Barber, D. Saad, and P. Sollich, "Test error fluctuations in finite linear perceptrons," Neural Computa. vol. 7, pp. 809-821, 1995.
    • (1995) Neural Computa. , vol.7 , pp. 809-821
    • Barber, D.1    Saad, D.2    Sollich, P.3
  • 7
    • 22244458712 scopus 로고
    • Finite-size effects and optimal test size in linear perceptrons
    • _, "Finite-size effects and optimal test size in linear perceptrons," J. Phys. A, vol. 28, pp. 1325-1334, 1995.
    • (1995) J. Phys. A , vol.28 , pp. 1325-1334
  • 8
    • 7244243460 scopus 로고
    • On-line learning of dichotomies
    • NIPS 7, G. Tesauro, D. S. Touretzky, and T. K. Leen, Eds. Cambridge, MA: MIT Press
    • N. Barkai, H. S. Seung, and H. Sompolinsky, "On-line learning of dichotomies," in Advances in Neural Information Processing Systems NIPS 7, G. Tesauro, D. S. Touretzky, and T. K. Leen, Eds. Cambridge, MA: MIT Press, 1995.
    • (1995) Advances in Neural Information Processing Systems
    • Barkai, N.1    Seung, H.S.2    Sompolinsky, H.3
  • 9
    • 0000852384 scopus 로고
    • Regularization and complexity control in feedforward networks
    • C. M. Bishop, "Regularization and complexity control in feedforward networks," Aston Univ., Tech. Rep. NCRG/95/022, 1995.
    • (1995) Aston Univ., Tech. Rep. NCRG/95/022
    • Bishop, C.M.1
  • 10
    • 0001576846 scopus 로고
    • Generalization ability of perceptrons with continuous outputs
    • S. Bös, W. Kinzel, and M. Opper, "Generalization ability of perceptrons with continuous outputs," Phys. Rev., vol. E47, pp. 1384-1391, 1993.
    • (1993) Phys. Rev. , vol.E47 , pp. 1384-1391
    • Bös, S.1    Kinzel, W.2    Opper, M.3
  • 11
    • 0344710496 scopus 로고
    • Avoiding overfitting by finite temperature learning and cross-validation
    • Pans
    • _, "Avoiding overfitting by finite temperature learning and cross-validation," in Proc. Int. Conf. Artificial Neural Networks ICANN'95, Pans, 1995, pp. 111-116.
    • (1995) Proc. Int. Conf. Artificial Neural Networks ICANN'95 , pp. 111-116
  • 13
    • 0009545605 scopus 로고
    • Estimating a posteriori probabilities using stochastic network models
    • M. Mozer, P. Smolensky, D. S. Touretzky, J. L. Elman, and A. S. Weigend, Eds. Hillsdale, NJ: Lawrence Erlbaum
    • M. Finke and K.-R. Müller, "Estimating a posteriori probabilities using stochastic network models," in Proc. 1993 Connectionist Models Summer School, M. Mozer, P. Smolensky, D. S. Touretzky, J. L. Elman, and A. S. Weigend, Eds. Hillsdale, NJ: Lawrence Erlbaum, 1994, p. 324.
    • (1994) Proc. 1993 Connectionist Models Summer School , pp. 324
    • Finke, M.1    Müller, K.-R.2
  • 17
    • 0000071615 scopus 로고
    • Learning process in neural networks
    • T. Heskes and B. Kappen, Learning process in neural networks, Phys. Rev., vol. A44, pp. 2718-2762, 1991.
    • (1991) Phys. Rev. , vol.A44 , pp. 2718-2762
    • Heskes, T.1    Kappen, B.2
  • 18
    • 0003921982 scopus 로고    scopus 로고
    • A bound on the error of cross validation using the approximation and estimation rates, with consequences for the training-test split
    • D. S. Touretzky, M. C. Mozer and M. E. Hasselmo, Eds. Cambridge, MA: MIT Press
    • M. Kearns, "A bound on the error of cross validation using the approximation and estimation rates, with consequences for the training-test split," in NIPS'95: Advances in Neural Information Processing Systems 8, D. S. Touretzky, M. C. Mozer and M. E. Hasselmo, Eds. Cambridge, MA: MIT Press, 1996.
    • (1996) NIPS'95: Advances in Neural Information Processing Systems 8
    • Kearns, M.1
  • 19
    • 0000821295 scopus 로고
    • Generalization in a linear perceptron in the presence of noise
    • A. Krogh and J. Hertz, "Generalization in a linear perceptron in the presence of noise," J. Phys. A, vol. 25, pp. 1135-1147, 1992.
    • (1992) J. Phys. A , vol.25 , pp. 1135-1147
    • Krogh, A.1    Hertz, J.2
  • 20
    • 0000902690 scopus 로고
    • The effective number of parameters: An analysis of generalization and regularization in nonlinear learning systems
    • J. E. Moody, S. J. Hanson, and R. P. Lippmann, Eds. San Mateo, CA: Morgan Kaufmann
    • J. E. Moody, "The effective number of parameters: An analysis of generalization and regularization in nonlinear learning systems," in NIPS 4: Advances in Neural Information Processing Systems, J. E. Moody, S. J. Hanson, and R. P. Lippmann, Eds. San Mateo, CA: Morgan Kaufmann, 1992.
    • (1992) NIPS 4: Advances in Neural Information Processing Systems
    • Moody, J.E.1
  • 21
    • 0040269272 scopus 로고
    • A criterion for determining the number of parameters in an artificial neural-network model
    • T. Kohonen, et al., Eds.. Amsterdam, The Netherlands: Elsevier
    • N. Murata, S. Yoshizawa, and S. Amari, "A criterion for determining the number of parameters in an artificial neural-network model," in Artificial Neural Networks, T. Kohonen, et al., Eds.. Amsterdam, The Netherlands: Elsevier, 1991, pp. 9-14.
    • (1991) Artificial Neural Networks , pp. 9-14
    • Murata, N.1    Yoshizawa, S.2    Amari, S.3
  • 22
    • 0037569066 scopus 로고
    • Learning curves, model selection and complexity of neural networks
    • S. J. Hanson et al., Eds. San Mateo, CA: Morgan Kaufmann
    • _, "Learning curves, model selection and complexity of neural networks," in NIPS 5: Advances in Neural Information Processing Systems, S. J. Hanson et al., Eds. San Mateo, CA: Morgan Kaufmann, 1993.
    • (1993) NIPS 5: Advances in Neural Information Processing Systems
  • 23
    • 0028544395 scopus 로고
    • Network information criterion - Determining the number of hidden units for an artificial neural-network model
    • _, "Network information criterion - Determining the number of hidden units for an artificial neural-network model," IEEE Trans. Neural Networks, vol. 5, pp. 865-872, 1994.
    • (1994) IEEE Trans. Neural Networks , vol.5 , pp. 865-872
  • 25
    • 0030188747 scopus 로고    scopus 로고
    • also Neural Computa., vol. 8, pp. 1085-1106, 1996.
    • (1996) Neural Computa. , vol.8 , pp. 1085-1106
  • 26
    • 0025056697 scopus 로고
    • Regularizalion algorithms for learning that are equivalent to multilayer networks
    • T. Poggio and F. Girosi, "Regularizalion algorithms for learning that are equivalent to multilayer networks," Science, vol. 247, pp. 978-982, 1990.
    • (1990) Science , vol.247 , pp. 978-982
    • Poggio, T.1    Girosi, F.2
  • 27
    • 0000318553 scopus 로고
    • Stochastic complexity and modeling
    • J. Rissanen, "Stochastic complexity and modeling," Ann. Statist., vol. 14, pp. 1080-1100, 1986.
    • (1986) Ann. Statist. , vol.14 , pp. 1080-1100
    • Rissanen, J.1
  • 29
    • 4243234689 scopus 로고    scopus 로고
    • On-line learning in soft committee machines
    • D. Saad, S. A. Solla, "On-line learning in soft committee machines," Phys. Rev. E, vol. 52, pp. 4225-4243,
    • Phys. Rev. E , vol.52 , pp. 4225-4243
    • Saad, D.1    Solla, S.A.2
  • 30
    • 4243050152 scopus 로고
    • Exact solution for on-line learning in multilayer neural nelworks
    • and "Exact solution for on-line learning in multilayer neural nelworks," Phys. Rev. Lett., vol. 74, pp. 4337-4340, 1995.
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 4337-4340
  • 32
    • 0000487861 scopus 로고
    • Optimal stopping and effective machine complexity in learning
    • to appear, revised and extended version
    • C. Wang, S. S. Venkatesh, J. S. Judd, "Optimal stopping and effective machine complexity in learning," to appear, 1994 (revised and extended version of NIPS vol. 6, pp. 303-310, 1995).
    • (1994) NIPS , vol.6 , pp. 303-310
    • Wang, C.1    Venkatesh, S.S.2    Judd, J.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.