Asymptotic efficiency of kernel support vector machines (SVM) |
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| Authors: | V. I. Norkin M. A. Keyzer |
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| Affiliation: | (1) V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;(2) Centre for World Food Studies, Vrije Universiteit, Amsterdam, the Netherlands |
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| Abstract: | The paper analyzes the asymptotic properties of Vapnik’s SVM-estimates of a regression function as the size of the training sample tends to infinity. The estimation problem is considered as infinite-dimensional minimization of a regularized empirical risk functional in a reproducing kernel Hilbert space. The rate of convergence of the risk functional on SVM-estimates to its minimum value is established. The sufficient conditions for the uniform convergence of SVM-estimates to a true regression function with unit probability are given. Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 81–97, July–August 2009 |
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| Keywords: | machine learning estimation of dependences recognition kernel estimate support vector machine (SVM) ill-posed problems regularization consistency rate of convergence |
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