Topological properties of measurable structures and sufficient conditions for uniform convergence of frequencies to probabilities / Pytkeev E.G., Khachai M.Yu. // Automation and Remote Control. - 2012. - V. 73, l. 2. - P. 291-299.

ISSN:

00051179

Type:

Article

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. © 2012 Pleiades Publishing, Ltd.

Author keywords:

Index keywords:

Sufficient conditions; Theory of learning; Topological properties; Uniform convergence; Learning algorithms; Pattern recognition; Topology

DOI:

10.1134/S0005117912020075

Смотреть в Scopus:

https://www.scopus.com/inward/record.uri?eid=2-s2.0-84862143406&doi=10.1134%2fS0005117912020075&partnerID=40&md5=2f10fa0c8659fa37110f8e49c16b3d1e

Соавторы в МНС:

Другие поля

Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-84862143406&doi=10.1134%2fS0005117912020075&partnerID=40&md5=2f10fa0c8659fa37110f8e49c16b3d1e
Affiliations	Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russian Federation
References	Vapnik, V.N., Chervonenkis, A.Ya., (1974) Teoriya Raspoznavaniya Obrazov (Pattern Recognition Theory), , Moscow: Nauka; Vapnik, V.N., (1998) Statistical Learning Theory, , New York: Wiley; Pytkeev, E.G., Khachai, M.Yu., Sigma-compactness of the metric boolean algebras and uniform convergence of frequencies to probabilities (2010) Tr. Inst. Mat. Mekh., 16 (1), pp. 127-139; Kadets, V.M., (2006) Kurs funktsional'Nogo Analiza (Course of Functional Analysis), , Khar'kov: Khar'k. Nat-sional. Univ; Borovkov, A.A., (1997) Matematicheskaya Statistika (Mathematical Statistics), , Novosibirsk: Nauka; Bulinskii, A.V., Shiryaev, A.N., (2005) Teoriya Sluchainykh Protsessov (Theory of Random Processes), , Moscow: Fizmatlit; Kosorok, M.R., (2008) Introduction to Empirical Processes and Semiparametric Inference, , New York: Springer
Correspondence Address	Pytkeev, E.G.; Institute of Mathematics and Mechanics, Ural Branch, Russian Academy of Sciences, Yekaterinburg, Russian Federation
Language of Original Document	English
Abbreviated Source Title	Autom. Remote Control
Source	Scopus