Abstract
This paper adapts the Gibbs sampling method to the problem of hybrid system identification. We define a Generalized Linear Hiddenl Markov Model (GLHMM) that combines switching dynamics from Hidden Markov Models, with a Generalized Linear Model (GLM) to govern the continuous dynamics. This class of models, which includes conventional ARX models as a special case, is particularly well suited to this identification approach. Our use of GLMs is also driven by potential applications of this approach to the field of neural prosthetics, where neural Poisson-GLMs can model neural firing behavior. The paper gives a concrete algorithm for identification, and an example motivated by neuroprosthetic considerations.
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References
Juloski, A., et al.: Comparison of four procedures for the identification of hybrid systems. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 354–369. Springer, Heidelberg (2005)
Bemporad, A., et al.: A greedy approach to identification of piecewise affine models. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, p. 97. Springer, Heidelberg (2003)
Juloski, A., Weiland, S., Heemels, W.: A Bayesian approach to identification of hybrid systems. In: IEEE Conf. on Decision and Control, vol. 1, Nassau, Bahamas, pp. 13–19. IEEE Computer Society Press, Los Alamitos (2004)
Vidal, R., et al.: An algebraic geometric approach to the identification of a class of linear hybrid systems. In: IEEE Conference on Decision and Control, IEEE Computer Society Press, Los Alamitos (2003)
Ferrari-Trecate, G., et al.: A clustering technique for the identification of piecewise affine systems. Automatica 39, 205–217 (2003)
Nicolelis, M.A.L.: Brain-machine interfaces to restore motor function and probe neural circuit. Nature Reviews Neuroscience 4, 417–422 (2003)
Pesaran, B., Musallam, S., Andersen, R.: Cognitive neural prosthetics. Current Biology 16, 77–80 (2006)
Shenoy, K., et al.: Neural prosthetic control signals from plan activity. Neuroreport 14(4), 591–596 (2003)
Truccolo, W., et al.: A point process framework for relating neural spiking activity to spiking history, neural ensemble, and extrinsic covariate effects. J. Neurophysiol. 93(2), 1074–1089 (2005)
Oh, S.M., Rehg, J.M., Dellaert, F.: Parameterized duration modeling for switching linear dynamic systems. In: IEEE Conf. on Computer Vision and Pattern Recog., IEEE Computer Society Press, Los Alamitos (2006)
Rosti, A.V.: Linear Gaussian Models for Speech Recognition. PhD thesis, Wolfson College, University of Cambridge (2004)
Ljung, L.: System Identification, Theory for the User, 2nd edn. Prentice-Hall, Englewood Cliffs (1999)
Rabiner, L.: A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77, 257–286 (1989)
Robert, C., Celeux, G., Diebolt, J.: Bayesian estimation of hidden Markov chains: A stochastic implementation. Statistics & Probability Letters 16, 77–83 (1993)
Hoffmann, J.P.: Generalized Linear Models: an Applied Approach. Pearson Education, London (2004)
Djuric, P.M., Chun, J.H.: An MCMC sampling approach to estimation of nonstationary hidden Markov models. IEEE Trans. on Signal Processing 50(5), 1113–1123 (2002)
McCulloch, C.E.: Maximum likelihood algorithms for generalized linear mixed models. Journal of the American Statistical Association 92(437), 162–170 (1997)
Dellaportas, P., Smith, A.F.M.: Bayesian inference for generalized linear and proportional hazards models via Gibbs sampling. App. Stat. 42(3), 443–459 (1993)
Gilks, W.R., Wild, P.: Adaptive rejection sampling for Gibbs sampling. Applied Statistics 41(2), 337–348 (1992)
Gilks, W.R., Richardson, S., Spiegelhalter, D.J. (eds.): Markov Chain Monte Carlo in Practice. Chapman and Hall, Boca Raton (1996)
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Hudson, N., Burdick, J. (2007). A Stochastic Framework for Hybrid System Identification with Application to Neurophysiological Systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds) Hybrid Systems: Computation and Control. HSCC 2007. Lecture Notes in Computer Science, vol 4416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71493-4_23
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DOI: https://doi.org/10.1007/978-3-540-71493-4_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71492-7
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