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Volumn 44, Issue 1, 1999, Pages 55-62

An inequality for uniform deviations of sample averages from their means

Author keywords

Empirical risk minimization; Uniform laws of large numbers; Vapnik Chervonenkis inequality

Indexed keywords


EID: 0012500744     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(98)00291-0     Document Type: Article
Times cited : (16)

References (16)
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    • Alexander, K.1
  • 4
    • 0001917727 scopus 로고
    • Probability inequalities for the sum of independent random variables
    • Bennett G. Probability inequalities for the sum of independent random variables. J. Amer. Statist. Assoc. 57:1962;33-45.
    • (1962) J. Amer. Statist. Assoc. , vol.57 , pp. 33-45
    • Bennett, G.1
  • 6
    • 0002457759 scopus 로고
    • Bounds for the uniform deviation of empirical measures
    • Devroye L. Bounds for the uniform deviation of empirical measures. J. Multivariate Anal. 12:1982;72-79.
    • (1982) J. Multivariate Anal. , vol.12 , pp. 72-79
    • Devroye, L.1
  • 7
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    • Lower bounds in pattern recognition and learning
    • Devroye L., Lugosi G. Lower bounds in pattern recognition and learning. Pattern Recognition. 28:1995;1011-1018.
    • (1995) Pattern Recognition , vol.28 , pp. 1011-1018
    • Devroye, L.1    Lugosi, G.2
  • 8
    • 0024739191 scopus 로고
    • A general lower bound on the number of examples needed for learning
    • Ehrenfeucht A., Haussler D., Kearns M., Valiant L. A general lower bound on the number of examples needed for learning. Inform. Comput. 82:1989;247-261.
    • (1989) Inform. Comput. , vol.82 , pp. 247-261
    • Ehrenfeucht, A.1    Haussler, D.2    Kearns, M.3    Valiant, L.4
  • 9
    • 0002192516 scopus 로고
    • Decision theoretic generalizations of the PAC model for neural net and other learning applications
    • Haussler D. Decision theoretic generalizations of the PAC model for neural net and other learning applications. Inform. Comput. 100:1992;78-150.
    • (1992) Inform. Comput. , vol.100 , pp. 78-150
    • Haussler, D.1
  • 10
    • 84947403595 scopus 로고
    • Probability inequalities for sums of bounded random variables
    • Hoeffding W. Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58:1963;13-30.
    • (1963) J. Amer. Statist. Assoc. , vol.58 , pp. 13-30
    • Hoeffding, W.1
  • 12
    • 0001191685 scopus 로고
    • Uniform ratio limit theorems for empirical processes
    • Pollard, D., 1995. Uniform ratio limit theorems for empirical processes. Scand. J. Statist. 22, 271-278.
    • (1995) Scand. J. Statist. , vol.22 , pp. 271-278
    • Pollard, D.1
  • 13
    • 0001957366 scopus 로고
    • Sharper bounds for Gaussian and empirical processes
    • Talagrand M. Sharper bounds for Gaussian and empirical processes. Ann. Probab. 22:1994;28-76.
    • (1994) Ann. Probab. , vol.22 , pp. 28-76
    • Talagrand, M.1
  • 15
    • 0001024505 scopus 로고
    • On the uniform convergence of relative frequencies of events to their probabilities
    • Vapnik V., Chervonenkis A. On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16:1971;264-280.
    • (1971) Theory Probab. Appl. , vol.16 , pp. 264-280
    • Vapnik, V.1    Chervonenkis, A.2
  • 16
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    • Nauka, Moscow. (in Russian); German translation: Theorie der Zeichenerkennung, Akademie, Berlin
    • Vapnik, V., Chervonenkis, A., 1974. Theory of Pattern Recognition. Nauka, Moscow. (in Russian); German translation: Theorie der Zeichenerkennung, Akademie, Berlin, 1979.
    • (1974) Theory of Pattern Recognition
    • Vapnik, V.1    Chervonenkis, A.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.