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Topological properties of measurable structures and sufficient conditions for uniform convergence of frequencies to probabilities

  • Linear and Nonlinear Programming Problems
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Abstract

The event-uniform convergence of frequencies to probabilities is one of the main tools of the today theory of learning pattern recognition which enables one to substantiate the generalizability of the learning algorithms. Proposed was a new approach to derivation of the sufficient conditions for such convergence on the basis of only the topological properties of the event σ-algebra induced by the class under consideration.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia

    E. G. Pytkeev & M. Yu. Khachai

Authors
  1. E. G. Pytkeev
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  2. M. Yu. Khachai
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Original Russian Text © E.G. Pytkeev, M.Yu. Khachai, 2012, published in Avtomatika i Telemekhanika, 2012, No. 2, pp. 89–98.

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Pytkeev, E.G., Khachai, M.Y. Topological properties of measurable structures and sufficient conditions for uniform convergence of frequencies to probabilities. Autom Remote Control 73, 291–299 (2012). https://doi.org/10.1134/S0005117912020075

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  • DOI: https://doi.org/10.1134/S0005117912020075

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