Development of Psychological Diagnostics Systems Basing on New Mathematical Representations

Suggested is a new approach to development of the adaptive systems for psychological diagnostics, which can be considered as artificial intelligence tools for assessing the subject activities. It is based on the convolution of the applied Markovian process representing a diagnostic procedure under study into the quantum representation, which makes it possible to reveal the structure of this procedure with the aid of the quantum spectral analysis. When small samples of empirical data are in use to set up diagnostic tools, the considered quantum estimates have significant advantages over the relevant likelihood and Bayesian estimates as well as over the simpler estimates based on the neural networks.

1. Ermakov S.S., Shepeleva E.A., Savenkov E.A. Analiz vozmozhnostei metoda komp'yuterizirovannogo adaptivnogo podkhoda k zadacham psikhologicheskoi diagnostiki i obucheniya [Analysis of the possibilities of the method of a computerized adaptive approach to the tasks of psychological diagnosis and training]. Eksperimental’naya psikhologiya = Experimental Psychology (Russia), 2023. (In print). (In Russ.).
2. Kuravsky L.S., Yuryev G.A. Adaptivnoe testirovanie kak markovskii protsess: modeli i ikh identifikatsiya [Adaptive testing as a Markov process: models and their identification]. Neirokomp'yutery: razrabotka i primenenie = Neurocomputers: development and application, No. 2, pp. 21—29. (In Russ.).
3. Kuravsky L.S., Yuryev G.A. Veroyatnostnyi metod fil'tratsii artefaktov pri adaptivnom testirovanii[Probabilistic method of filtering artifacts in adaptive testing]. Eksperimental'naya psikhologiya = Experimental psychology (Russia), No. 1(5), pp. 119—131. (In Russ.).
4. Kuravsky L.S., Yuryev G.A. Ob odnom podkhode k adaptivnomu testirovaniyu i ustraneniyu ego artefaktov [On one approach to adaptive testing and elimination of its artifacts]. Neirokomp'yutery: razrabotka i primenenie = Neurocomputers: development and application, 2012. No. 1, pp. 54—66. (In Russ.).
5. Kuravsky L.S., Artemenkov S.L., Yuryev G.A., Grigorenko E.L. Novyi podkhod k komp'yuterizirovannomu adaptivnomu testirovaniyu [A new approach to computerized adaptive testing]. Eksperimental'naya psikhologiya = Experimental psychology (Russia), Vol. 10, no. 3, pp. 33—45. DOI:10.17759/exppsy.2017100303 (In Russ.).
6. Markovskie modeli v zadachakh diagnostiki i prognozirovaniya [Markov models in problems of diagnostics and forecasting]: Textbook / Ed. by L.S. Kuravsky. 2nd ed., add. M.: MGPPU Publishing House Publ., 2017. 197 p. (In Russ.).
7. Ovcharov L.A. Prikladnye zadachi teorii massovogo obsluzhivaniya [Applied problems of the theory of queuing]. M.: Mechanical Engineering, 1969. 324 p. (In Russ.).
8. Raven J., Raven J.K., Kort J.H. A Rukovodstvo k Progressivnym Matritsam Ravena i Slovarnym Shkalam. Razdel 3. Standartnye Progreccivnye Matritsy (vklyuchaya Parallel'nye i Plyus versii) [Guide to Progressive Raven Matrices and Vocabulary Scales. Section 3. Standard Progressive Matrices (including Parallel and Plus versions)]. M.: Kogito Center, 2012. (In Russ.).
9. Amosov G.G. On Markovian Cocycle Perturbations in Classical and Quantum Probability. J. Math. & Math. Sci., 2003. No. 54, pp. 3443—3467.
10. Amosov G.G. On Markovian Perturbations of the Group of Unitary Operators Associated with a Stochastic Process with Stationary Increments. Theory Prob. & its Applications, No. 49(1), pp. 123—132.
11. Borg I., Groenen P.J.F. Modern Multidimensional Scaling Theory and Applications. Springer, New York, 2005.
12. Cox T.F., Cox M.A.A. Multidimensional Scaling, 2nd ed. New York: Chapman and Hall/CRC, 2001.
13. Holevo S. Probabilistic and Statistical Aspects of Quantum Theory, 2nd ed.Edizioni della Normale, Pisa, 2011.
14. Kuravsky L.S., Margolis A.A., Marmalyuk P.A., Panfilova A.S., Yuryev G.A., Dumin P.N. A Probabilistic Model of Adaptive Training. Applied Math. Sciences, 2016. Vol. 10, no. 48, pp. 2369—2380.
15. Kuravsky L.S., Marmalyuk P.A., Yuryev G.A., Dumin P.N. A Numerical Technique for the Identification of Discrete-State Continuous-Time Markov Models. Applied Mathematical Sciences, Vol. 9, no. 8, pp. 379—391. DOI:10.12988/ams.2015.410882
16. Kuravsky L.S. Discriminant analysis based on the approaches of quantum computing. Lobachevskii J. Math., 2020. 41, no. 12, pp. 2338—2344.
17. Kuravsky L.S. Modeling Dynamical Behavior of Stochastic Systems: Spectral Analysis of Qubit Representations vs the Mutual Markovian Model Likelihood Estimations. Lobachevskii J. Math., 2021. 42, no. 10, pp. 2364—2376.
18. Kuravsky L.S. Simplification of Solving Diagnostics Problems by Convolution of Applied Markovian Models into the Quantum Representations. Lobachevskii J. Math., 2022. Vol. 43, no. 7, pp. 1669—1682.
19. Kuravsky L.S., Greshnikov I.I., Zlatomrezhev V.I., Yuryev G.A. Synthesis of Civil Aircraft Control using Empirical Data and Quantum Filtering. Lobachevskii J. Math., 2023. Vol. 44. (In print).
20. Kuravsky L.S., Baranov S.N., Yuryev G.A. Synthesis and Identification of Hidden Markov Models Based on a Novel Statistical Technique in Condition Monitoring. In: Proc. 7th Int. Conf. on Condition Monitoring & Machinery Failure Prevention Technologies. Stratford-upon-Avon, England, 2010.
21. Lloyd E. Handbook of Applicable Mathematics, Vol. 6: Statistics / Ed. by W. Ledermann. Hoboken: Wiley, 1984.
22. Morrison D.F. Multivariate Statistical Methods, 2nd ed. McGraw-Hill, New York, 1976.
23. Nielsen M.A., Chuang I.L. Quantum Computation and Quantum Information. Cambridge University Press, 2010.
24. von Neumann J. Mathematical Foundations of Quantum Mechanics. Princeton Univ. Press, Princeton, 1955.