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Misclassification Probability Estimations for Linear Decision Functions

  • Victor Mikhailovich Nedel’ko
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3138)

Abstract

The work is devoted to a problem of statistical robustness of deciding functions, or risk estimation. By risk we mean some measure of decision function prediction quality, for example, an error probability. For the case of discrete “independent” variable the dependence of average risk on empirical risk for the “worst” distribution (“strategies of nature”) is obtained. The result gives exact value of empirical risk bias that allows evaluating an accuracy of Vapnik–Chervonenkis risk estimations. To find a distribution providing maximum of empirical risk bias one need to solve an optimization problem on function space. The problem being very complicate in general case appears to be solvable when the “independent” feature is a space of isolated points. The space has low practical use but it allows scaling well-known estimations by Vapnik and Chervonenkis. Such scaling appears to be available for linear decision functions.

Keywords

Risk Estimation Compatible Event Decision Function Average Risk Discrete Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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    Vapnik, V.N., Chervonenkis, A.J.: Theory of pattern recognition. Moscow “Nauka”, p. 415 (1974) (in Russian)Google Scholar
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    Raudys, S.: Statistical and neural classifiers. Springer, Heidelberg (2001)zbMATHGoogle Scholar
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    Lbov, G.S., Startseva, N.G.: Logical deciding functions and questions of statistical stability of decisions. Novosibirsk: Institute of mathematics, p. 211 (1999) (in Russian)Google Scholar
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    Nedelko, V.M.: An Asymptotic Estimate of the Quality of a Decision Function Based on Empirical Risk for the Case of a Discrete Variable. Pattern Recognition and Image Analysis 11(1), 69–72 (2001)MathSciNetGoogle Scholar
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    Berikov, V.B.: On stability of recognition algorithms in discrete statement. In: Artificial Intelligence, Ukraine, vol. (2), pp. 5–8 (2000) (in Russian)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Victor Mikhailovich Nedel’ko
    • 1
  1. 1.Institute of Mathematics SB RASLaboratory of Data AnalysisNovosibirskRussia

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