
Digital
Library of the European Council for Modelling and Simulation 
Title: 
Probability Model Of
Concepts Recovery In Small Sample Learning 
Authors: 
Alexander
A. Grusho, Nick A. Grusho,
Michael I. Zabezhailo, Elena E. Timonina,
Vladislav V. Kulchenkov 
Published in: 
2020). ECMS 2020 Proceedings
Edited by: Mike Steglich, Christian Muller, Gaby
Neumann, Mathias Walther, European Council for Modeling and Simulation. DOI: http://doi.org/10.7148/2020 ISSN:
25222422 (ONLINE) ISSN:
25222414 (PRINT) ISSN:
25222430 (CDROM) ISBN: 9783937436685 Communications of the ECMS , Volume 34, Issue 1, June 2020, United Kingdom 
Citation
format: 
Alexander A. Grusho,
Nick A. Grusho, Michael I. Zabezhailo,
Elena E. Timonina, Vladislav
V. Kulchenkov (2020). Probability Model Of Concepts
Recovery In Small Sample Learning, ECMS
2020 Proceedings Edited By: Mike Steglich,
Christian Mueller, Gaby Neumann, Mathias Walther European Council for
Modeling and Simulation. doi:
10.7148/20200393 
DOI: 
https://doi.org/10.7148/20200393 
Abstract: 
Many information security monitoring systems and controlling of IoT systems receive information in the form of short messages, which can be considered as small samples. Concepts are considered as classes of small samples that allow you to determine the correctness of monitoring systems. The paper is devoted to the problem of recovering concepts on observations of series of small samples. Probabilistic model of appearance of series of small samples is introduced. To deﬁne concepts, the probabilistic dependency is used within series of small samples. The case of series of length 2 of small samples is considered. This assumption allowed the construction of a random graph and provided its probabilitystatistical analysis. Asymptotic approximations of probability distributions in the series scheme are used to identify ranges of parameter values that better deﬁne the structure of concepts. The set of parameter values is deﬁned, at which the structure of concepts is uniquely determined with probability which tends to 1. 
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