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Results of a simulation experiment for Markov processes identification methods comparison

Keywords:

P.A. Marmalyuk- Ph.D. (Eng.), Head of the Laboratory of Mathematical Psychology and Applied Software, Moscow State University of Psychology and Education. E-mail: pavel.marmalyuk@gmail.com G.A. Yuryev - Ph.D. (Phys.-Math.), Vice Dean of Academic Affairs of the «Information technologies» Faculty, Moscow State University of Psychology and Education. E-mail: nezdeshni@gmail.com L.S. Kuravsky - Dr. Sc. (Eng.), Professor, Dean of the «Information technologies» Faculty, Moscow State University of Psychology and Education. E-mail: l.s.kuravsky@gmail.com P.N. Dumin - Programmer at the Laboratory of Mathematical Psychology and Applied Software, Moscow State University of Psychology and Education. E-mail: dumin.pn@gmail.com


A numerical technique for the identification of discrete-state continuous-time Markov models has been developed and described in paper [6]. The given method is characterized by utilizing both initial approximations derived from the observed data and sensi-tivity estimates of the minimized criterion to small variations of identified parameters. Proposed approach is experimentally compared with a first order gradient method with adaptive steps [1], which is traditionally applied for solving multivariate nonlinear optimization problems. In order to assess computational efficiency of suggested algo-rithms a set of models was generated, which are structurally similar to models commonly used in practice. Essential structure of these models corresponds to the non-homogeneous birth-death process. Details of data generation stage are presented in Section 1 whereas specifications of a computing machine used in the experiment are listed in Section 2. Results of the computational experiments with algorithm-specific settings presented in Section 3 are described in Section 4. The results obtained demonstrate that, in the considered range of numbers of identified parameters, the developed modified identifi-cation method provides substantial speedup compared to the classical gradient method.
References:

 

  1. Kuravskijj L.S., Margolis A.A., JUrev G.A., Marmaljuk P.A. Koncepcija sistemy podderzhki prinjatija reshenijj dlja psikhologicheskogo testirovanija // Psikhologicheskaja nauka i obrazovanie. 2012. № 1. C. 56–65.
  2. Kuravskijj L.S., Margolis A.A., Marmaljuk P.A., JUrev G.A., Dumin P.N. Obuchaemye markovskie modeli v zadachakh optimizacii porjadka predjavlenija psikhologicheskikh testov // Nejjrokompjutery: razrabotka i primenenie. 2013. № 4. S. 28–38.
  3. Kuravskijj L.S., Marmaljuk P.A., Alkhimov V.I., JUrev G.A. Novyjj podkhod k postroeniju intellektualnykh i kompetentnostnykh testov // Modelirovanie i analiz dannykh. 2013. № 1. S. 4–28.
  4. Kuravskijj L.S., Marmaljuk P.A., Barabanshhikov V.A., Bezrukikh M.M., Demidov A.A., Ivanov V.V., JUrev G.A. Ocenka stepeni sformirovannosti navykov i kompetencijj na osnove verojatnostnykh raspredelenijj glazodvigatelnojj aktivnosti // Voprosy psikhologii. 2013. № 5. S. 64–81.
  5. Kuravskijj L.S., Margolis A.A., Marmaljuk P.A., JUrev G.A., Dumin P.N. Obuchaemye markovskie modeli v zadachakh optimizacii porjadka predjavlenija psikhologicheskikh testov // Nejjrokompjutery: razrabotka i primenenie. 2013. № 4. S. 28–38.
  6. Kuravskijj L.S., Marmaljuk P.A., JUrev G.A., Dumin P.N. Identifikacija markovskikh processov po statisticheskim dannym // Nejjrokompjutery: razrabotka i primenenie. 2015. № 5. S. 42–47.
  7. Markovskie modeli v zadachakh diagnostiki i prognozirovanija: Ucheb. posobie / pod red. L.S. Kuravskogo. M.: RUSAVIA. 2013. 172 s.
  8. Formalev V.F., Reviznikov D.L. CHislennye metody. M.: FIZMATLIT. 2004. 400 s.
  9. Kuravsky L.S., Marmalyuk P.A., Yuryev G.A. and Dumin P.N. A Numerical Technique for the Identification of Discrete-State Continuous-Time Markov Models // Applied Mathematical Sciences. 2015. V. 9. № 8. P. 379–391.
  10. Kuravsky L.S., Marmalyuk P.A., Baranov S.N., Alkhimov V.I., Yuryev G.A. and Artyukhina S.V. A New Technique for Testing Professional Skills and Competencies and Examples of its Practical Applications // Applied Mathematical Sciences. 2015. V. 9. № 21. P. 1003–1026.
  11. The R Project for Statistical Computing. [EHlektronnyjj resurs]. http://r-project.org/.

 

May 29, 2020

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