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Bayesian estimation of mixtures with dynamic transitions and known component parameters
Kybernetika, Tome 47 (2011) no. 4, pp. 572-594 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Probabilistic mixtures provide flexible “universal” approximation of probability density functions. Their wide use is enabled by the availability of a range of efficient estimation algorithms. Among them, quasi-Bayesian estimation plays a prominent role as it runs “naturally” in one-pass mode. This is important in on-line applications and/or extensive databases. It even copes with dynamic nature of components forming the mixture. However, the quasi-Bayesian estimation relies on mixing via constant component weights. Thus, mixtures with dynamic components and dynamic transitions between them are not supported. The present paper fills this gap. For the sake of simplicity and to give a better insight into the task, the paper considers mixtures with known components. A general case with unknown components will be presented soon.
Probabilistic mixtures provide flexible “universal” approximation of probability density functions. Their wide use is enabled by the availability of a range of efficient estimation algorithms. Among them, quasi-Bayesian estimation plays a prominent role as it runs “naturally” in one-pass mode. This is important in on-line applications and/or extensive databases. It even copes with dynamic nature of components forming the mixture. However, the quasi-Bayesian estimation relies on mixing via constant component weights. Thus, mixtures with dynamic components and dynamic transitions between them are not supported. The present paper fills this gap. For the sake of simplicity and to give a better insight into the task, the paper considers mixtures with known components. A general case with unknown components will be presented soon.
Classification : 68T05, 93E12
Keywords: mixture model; Bayesian estimation; approximation; clustering; classification 
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     title = {Bayesian estimation of mixtures with dynamic transitions and known component parameters},
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}
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Nagy, Ivan; Suzdaleva, Evgenia; Kárný, Miroslav. Bayesian estimation of mixtures with dynamic transitions and known component parameters. Kybernetika, Tome 47 (2011) no. 4, pp. 572-594. http://geodesic.mathdoc.fr/item/KYB_2011_47_4_a5/

[1] Bernardo, J. M.: Expected information as expected utility. Ann. Statist. 7 (1979), 3, 686–690. | DOI | MR

[2] Böhm, J., Kárný, M.: Transformation of user’s knowledge into initial values for identification. In: Preprints DYCOMANS Workshop Industrial Control and Management Methods: Theory and Practice (M. Součková and J. Böhm, eds.), ÚTIA AV ČR, Prague 1995, pp. 17–24.

[3] Chen, W., Jovanis, P.: Method for identifying factors contributing to driver-injury severity in traffic crashes. Highway And Traffic Safety: Crash Data, Analysis Tools, And Statistical Methods 1717 (2000), 1–9.

[4] Chinnaswamy, G., Chirwa, E., Nammi, S., Nowpada, S., Chen, T., Mao, M.: Benchmarking and accident characteristics of flat-fronted commercial vehicles with respect to pedestrian safety. Internat. J. Crashworthiness 12 (2007), 279–291. | DOI

[5] Dempster, A. P., Laird, N., Rubin, D.: Maximum likelihood from incomplete data via the EM algorithm. J. Roy. Statist. Soc. Ser. B (Methodological) 39 (1977), 1, 1–38. | MR | Zbl

[6] Hamilton, J. D., Susmel, R.: Autoregressive conditional heteroskedasticity and changes in regime. J. Econometrics 64 (1994), 307–333. | DOI | Zbl

[7] Haykin, S.: Neural Networks: A Comprehensive Foundation. MacMillan, New York 1994. | Zbl

[8] Wang, Jianyong, Zhang, Yuzhou, Zhou, Lizhu, Karypis, G. , Aggarwal, Charu C.: Contour: An efficient algorithm for discovering discriminating subsequences. In: Data Mining and Knowledge Discovery, Springer 18 (2009), 1, pp. 1–29. | MR

[9] Kárný, M.: Tools for computer-aided design of adaptive controllers. IEE Control Theory Appl. 150 (2003), 6, 643.

[10] Kárný, M., Böhm, J., Guy, T. V., Jirsa, L., Nagy, I., Nedoma, P., Tesař, L.: Optimized Bayesian Dynamic Advising: Theory and Algorithms. Springer, London 2005.

[11] Kárný, M., Kadlec, J., Sutanto, E. L.: Quasi-Bayes estimation applied to normal mixture. in In: Preprints 3rd European IEEE Workshop on Computer-Intensive Methods in Control and Data Processing (J. Rojíček, M. Valečková, M. Kárný, and K. Warwick, eds.), ÚTIA AV ČR, Prague 1998, pp. 77–82.

[12] Kárný, M., Nagy, I., Novovičová, J.: Mixed-data multi-modelling for fault detection and isolation. Internat. J. Adaptive Control Signal Process. 16 (2002), 1, 61–83. | DOI | Zbl

[13] Kerridge, D. F.: Inaccuracy and Inference. J. Royal Statist. Soc. Ser. B (Methodological) 23 (1961), 1, 184–194. | MR | Zbl

[14] Kulhavý, R.: A Bayes-closed approximation of recursive non-linear estimation. Internat. J. Adaptive Control Signal Process. 4 (1990), 271–285. | DOI

[15] Ljung, L.: System Identification: Theory for the User. Prentice-Hall, London 1987. | Zbl

[16] Murray-Smith, R., Johansen, T.: Multiple Model Approaches to Modelling and Control. Taylor &Francis, London 1997. | MR

[17] Oppenheim, A., Wilsky, A.: Signals and Systems. Englewood Clifts, Jersey 1983.

[18] Opper, M., Saad, D.: Advanced Mean Field Methods: Theory and Practice. The MIT Press, Cambridge 2001. | MR | Zbl

[19] Qu, H. B., Hu, B. G.: Variational learning for Generalized Associative Functional Networks in modeling dynamic process of plant growth. Ecological Informatics 4 (2009), 3, 163–176. | DOI

[20] Roberts, W. A.: Convex Functions. Academic Press, New York 1973. | MR | Zbl

[21] Sander, J., Ester, M., Kriegel, H.-P., Xu, X.: Density-based clustering in spatial databases: The algorithm gdbscan and its applications. In: Data Mining and Knowledge Discovery, Springer, 2 (1998), 2, pp. 169–194.

[22] Titterington, D., Smith, A., Makov, U.: Statistical Analysis of Finite Mixtures. John Wiley, New York 1985. | MR

[23] Xu, Xiaowei, Jäger, J., Kriegel, H.-P.: A fast parallel clustering algorithm for large spatial databases. In: Data Mining and Knowledge Discovery, Springer, 3 (1999), 3, pp. 263–290.

[24] Zhang, T., Ramakrishnan, R., Livny, M.: Birch: A new data clustering algorithm and its applications. In: Data Mining and Knowledge Discovery, Springer, 1 (1997), 2, pp. 141–182.