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Matematicheskoe modelirovanie, 2015, Volume 27, Number 6, Pages 14–32 (Mi mm3606)  
This article is cited in 5 scientific papers (total in 5 papers)

Parallel Monte Carlo for entropy-robust estimation

Y. S. Popkovabcd, A. Y. Popkovb, B. S. Darkhovskiybd

a Lomonosov Moscow State University
b Institute for Systems Analysis of RAS
c National Research University Higher School of Economics
d Moscow Institute of Physics and Technology
Full-text PDF (878 kB) Citations (5)
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Abstract: A new method of entropy-robust nonparametric estimation of probability density functions (PDF) is proposed in the paper. Characteristics of dynamic randomized models with structured nonlinearities are estimated under small amount of data. We have shown that optimal PDF are of exponential class, where parameters are Lagrange multipliers. To determine the parameters a system of equations with integral components has been built. We developed an algorithm for solving this problem, based on parallel Monte Carlo techniques. Estimates of solutions’s accuracy for the class of given integral components and probability of its achivement have been obtained. The method was applied to the problem with nonlinear dynamic system with given structured nonlinearity.
Keywords: entropy, robustness, randomized model, structure of exponential nonlinearity, functional entropy-linear programming, Monte Carlo trials, numerical integration, entropy estimation, small amounts of data, graphic processor.
Received: 08.09.2014
English version:
Mathematical Models and Computer Simulations, 2016, Volume 8, Issue 1, Pages 27–39
DOI: https://doi.org/10.1134/S2070048216010087
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: Y. S. Popkov, A. Y. Popkov, B. S. Darkhovskiy, “Parallel Monte Carlo for entropy-robust estimation”, Mat. Model., 27:6 (2015), 14–32; Math. Models Comput. Simul., 8:1 (2016), 27–39
Citation in format AMSBIB
\Bibitem{PopPopDar15}
\by Y.~S.~Popkov, A.~Y.~Popkov, B.~S.~Darkhovskiy
\paper Parallel Monte Carlo for entropy-robust estimation
\jour Mat. Model.
\yr 2015
\vol 27
\issue 6
\pages 14--32
\mathnet{http://mi.mathnet.ru/mm3606}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3541798}
\elib{https://elibrary.ru/item.asp?id=24850031}
\transl
\jour Math. Models Comput. Simul.
\yr 2016
\vol 8
\issue 1
\pages 27--39
\crossref{https://doi.org/10.1134/S2070048216010087}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84955575452}
Linking options:
  • https://www.mathnet.ru/eng/mm3606
  • https://www.mathnet.ru/eng/mm/v27/i6/p14
    • This publication is cited in the following 5 articles:
    1. Yu. S. Popkov, “Randomized machine learning procedures”, Autom. Remote Control, 80:9 (2019), 1653–1670  mathnet  crossref  crossref  isi  elib
    2. Yu. S. Popkov, “Mathematical methods of randomized machine teaching”, J. Math. Sci. (N. Y.), 254:5 (2021), 652–676  mathnet  crossref  mathscinet
    3. Yuri S. Popkov, Yuri A. Dubnov, Alexey Y. Popkov, Studies in Computational Intelligence, 756, Learning Systems: From Theory to Practice, 2018, 199  crossref
    4. Yu. S. Popkov, Yu. A. Dubnov, “Entropy-robust randomized forecasting under small sets of retrospective data”, Autom. Remote Control, 77:5 (2016), 839–854  mathnet  crossref  isi  elib  elib
    5. Popkov Yu.S., Dubnov Yu.A., Popkov A.Yu., “Randomized Machine Learning: Statement, Solution, Applications”, 2016 IEEE 8Th International Conference on Intelligent Systems (Is), eds. Yager R., Sgurev V., Hadjiski M., Jotsov V., IEEE, 2016, 27–39  crossref  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математическое моделирование
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    Full-text PDF :137
    References:75
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