Computational Mathematics and Mathematical Physics

, Volume 50, Issue 9, pp 1605–1614 | Cite as

Estimation of dependences based on Bayesian correction of a committee of classification algorithms

  • V. V. Ryazanov
  • Yu. I. Tkachev


Estimation of dependence of a scalar variable on the vector of independent variables based on a training sample is considered. No a priori conditions are imposed on the form of the function. An approach to the estimation of the functional dependence is proposed based on the solution of a finite number of special classification problems constructed on the basis of the training sample and on the subsequent prediction of the value of the function as a group decision. A statistical model and Bayes’ formula are used to combine the recognition results. A generic algorithm for constructing the regression is proposed for different approaches to the selection of the committee of classification algorithms and to the estimation of their probabilistic characteristics. Comparison results of the proposed approach with the results obtained using other models for the estimation of dependences are presented.

Key words

regression logical class regularities Bayes’ formula precedent-based recognition prediction group decisions estimate evaluation algorithms 


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  1. 1.
    N. R. Draper and H. Smith, Applied Regression Analysis (Wiley, New York, 1998; Vil’yams, Moscow, 2007).zbMATHGoogle Scholar
  2. 2.
    W. Härdle, Applied Nonparametric Regression (Cambridge University Press, Cambridge, 1990; Mir, Mscow, 1993).zbMATHGoogle Scholar
  3. 3.
    L. V. Baskakova and Yu. I. Zhuravlev, “A Model of Recognition Algorithms with Representative Sets and systems of Support Sets,” Zh. Vychisl. Mat. Mat. Fiz. 21, 1264–1275 (1981).zbMATHMathSciNetGoogle Scholar
  4. 4.
    A. N. Dmitriev, Yu. I. Zhuravlev, and F. P. Krendelev, “On Mathematical Principles of Classifying Objects and Phenomena,” in Discrete Analysis (Institute of Mathematics, Siberian Division, USSR Academy of Sciences, Novosibirsk, 1966), No. 7, pp. 3–11 [in Russian].Google Scholar
  5. 5.
    R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Mir, Moscow, 1976; Wiley, New York, 1973).Google Scholar
  6. 6.
    Yu. I. Zhuravlev “An Algebraic Approach to Recognition and Classification Problems,” in Problems of Cybernetics issue 33 (Nauka, Moscow, 1978; Hafner, 1986), pp. 5–68.Google Scholar
  7. 7.
    Yu. I. Zhuravlev, V. V. Ryazanov, and O. V. Sen’ko, Recognition: Mathematical Methods, Software, Applications (FAZIS, Moscow, 2005) [in Russian].Google Scholar
  8. 8.
    V. V. Ryazanov, “Logical Regularities in Pattern Recognition (Parametric Approach),” Zh. Vychisl. Mat. Mat. Fiz. 47, 1793–1808 (2007) [Comput. Math. Math. Phys. 47, 1720–1735 (2007)].MathSciNetGoogle Scholar
  9. 9.
    P. D. Wasserman, Neural Computing: Theory and Practice, (Van Nostrand Reinhold, New York, 1989; Mir, Moscow, 1992).Google Scholar
  10. 10.
    Ch. J. C. Burges “A Tutorial on Support Vector Machines for Pattern Recognition,” Data Mining Knowledge Discovery 2, 121–167 (1998).CrossRefGoogle Scholar
  11. 11.
    Yu. I. Zhuravlev, “Correct Algebras over Sets of Incorrect (Heuristic) Algorithms: Part I,” Kibernetika, No. 4, 5–17 (1977); Part II, Kibernetika, No. 6, 21–27 (1977); Part III, Kibernetika, No. 2, 35–43 (1978).Google Scholar
  12. 12.
    P. Domingos and M. Pazzani, “On the Optimality of the Simple Bayesian Classifier under Zero-One Loss,” Machine Learning 29, 103–130 (1997).zbMATHCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Dorodnicyn Computing CenterRussian Academy of SciencesMoscowRussia

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