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Avtomatika i Telemekhanika, 2012, Issue 2, Pages 89–98 (Mi at3613)  
Linear and Nonlinear Programming

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

E. G. Pytkeev, M. Yu. Khachai

Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russia
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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 $\sigma$-algebra induced by the class under consideration.
Presented by the member of Editorial Board: A. I. Kibzun

Received: 06.06.2011
English version:
Automation and Remote Control, 2012, Volume 73, Issue 2, Pages 291–299
DOI: https://doi.org/10.1134/S0005117912020075
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. G. Pytkeev, M. Yu. Khachai, “Topological properties of measurable structures and sufficient conditions for uniform convergence of frequencies to probabilities”, Avtomat. i Telemekh., 2012, no. 2, 89–98; Autom. Remote Control, 73:2 (2012), 291–299
Citation in format AMSBIB
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\by E.~G.~Pytkeev, M.~Yu.~Khachai
\paper Topological properties of measurable structures and sufficient conditions for uniform convergence of frequencies to probabilities
\jour Avtomat. i Telemekh.
\yr 2012
\issue 2
\pages 89--98
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\transl
\jour Autom. Remote Control
\yr 2012
\vol 73
\issue 2
\pages 291--299
\crossref{https://doi.org/10.1134/S0005117912020075}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84862143406}
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