Estimation of dependences based on Bayesian correction of a committee of classification algorithms
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 wordsregression logical class regularities Bayes’ formula precedent-based recognition prediction group decisions estimate evaluation algorithms
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- 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.R. O. Duda and P. E. Hart, Pattern Classification and Scene Analysis (Mir, Moscow, 1976; Wiley, New York, 1973).Google Scholar
- 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.Yu. I. Zhuravlev, V. V. Ryazanov, and O. V. Sen’ko, Recognition: Mathematical Methods, Software, Applications (FAZIS, Moscow, 2005) [in Russian].Google Scholar
- 9.P. D. Wasserman, Neural Computing: Theory and Practice, (Van Nostrand Reinhold, New York, 1989; Mir, Moscow, 1992).Google Scholar
- 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