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A primer on coupled state-switching models for multiple interacting time series. (English) Zbl 07346649
Summary: State-switching models such as hidden Markov models or Markov-switching regression models are routinely applied to analyse sequences of observations that are driven by underlying non-observable states. Coupled state-switching models extend these approaches to address the case of multiple observation sequences whose underlying state variables interact. In this article, we provide an overview of the modelling techniques related to coupling in state-switching models, thereby forming a rich and flexible statistical framework particularly useful for modelling correlated time series. Simulation experiments demonstrate the relevance of being able to account for an asynchronous evolution as well as interactions between the underlying latent processes. The models are further illustrated using two case studies related to (a) interactions between a dolphin mother and her calf as inferred from movement data and (b) electronic health record data collected on 696 patients within an intensive care unit.
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[1] Alaa, AM, Yoon, J, Hu, S, van der Schaar, M (2018) Personalized risk scoring for critical care prognosis using mixtures of Gaussian processes. IEEE Transactions on Biomedical Engineering, 65, 207-218.
[2] Alaa, AM, van der Schaar, M (2018) A hidden absorbing semi-Markov model for informatively censored temporal data: Learning and inference. Journal of Machine Learning Research, 19, 1-62. · Zbl 1445.62211
[3] Baker, J (1975) The DRAGON system — An overview. IEEE Transactions on Acoustics, Speech, and Signal Processing, 23, 24-29.
[4] Beumer, LT, Pohle, J, Schmidt, NM, Chimienti, M, Desforges, J-P, Hansen, LH, Langrock, R, Pedersen, SH, Stelvig, M, van Beest, FM (2020) An application of upscaled optimal foraging theory using hidden Markov modelling: Year-round behavioural variation in a large arctic herbivore. Movement Ecology, 8, 25.
[5] Bolton, T, Tarun, A, Sterpenich, V, Schwartz, S, De Ville, D (2017) Interactions between large-scale functional brain networks are captured by sparse coupled HMMs. IEEE Transactions on Medical Imaging, 37, 230-240.
[6] Brand, M (1997) Coupled hidden Markov models for modelling interacting processes (Technical Report 405). MIT Media Laboratory, Cambridge.
[7] Brand, M, Olivier, N, Pentland, A (1997) Coupled hidden Markov models for complex action recognition. In Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 994-99. Washington, DC: IEEE Computer Society.
[8] Brewer, N, Liu, N, De Vel, O, Caelli, T (2006). Using coupled hidden Markov models to model suspect interactions in digital forensic analysis. In Proceedings of International Workshop on Integrating AI and Data Mining, pages 58-64. Hong Kong: IEEE.
[9] Bulla, J, Bulla, I (2006) Stylized facts of financial time series and hidden semi-Markov models. Computational Statistics & Data Analysis, 51, 2192-2209. · Zbl 1157.62518
[10] Cao, W, Zhu, W, Demazeau, Y (2019) Multi-layer coupled hidden Markov model for cross-market behavior analysis and trend forecasting. IEEE Access, 7, 158563-158574.
[11] Ghajaverestan, NM, Masoudi, S, Shamsollahi, MB, Beuchee, A, Plady, P, Ge, D, Hernandez, AI (2016) Coupled hidden Markov model-based method for apnea bradycardia detection. IEEE Journal of Biomedical and Health Informatics, 20, 527-538.
[12] Ghosh, S, Li, J, Cao, L, Ramamohanarao, K (2017) Septic shock prediction for ICU patients via coupled HMM walking on sequential contrast patterns. Journal of Biomedical Informatics, 66, 19-31.
[13] Hamilton, JD (2008) Regime-switching models. The New Palgrave Dictionary of Economics, edited by SN, Durlauf, LE, Blume, pages 5471-75. London: Palgrave Macmillan.
[14] Johnson, DS, Laake, JL, Melin, SR, DeLong, RL (2016) Multivariate state hidden Markov models for mark-recapture data. Statistical Science, 31, 233-44. · Zbl 1442.62189
[15] Langrock, R, Hopcraft, JGC, Blackwell, PG, Goodall, V, King, R, Niu, M, Patterson, TA, Perdersen, MW, Skarin, A, Schick, RS (2014) Modelling group dynamic animal movement. Methods in Ecology and Evolution, 5, 190-199.
[16] Langrock, R, King, R, Matthiopoulos, J, Thomas, L, Fortin, D, Morales, JM (2012) Flexible and practical modeling of animal telemetry data: Hidden Markov models and extensions. Ecology, 93, 2336-2342.
[17] Langrock, R, Kneib, T, Glennie, R, Michelot, T (2017) Markov-switching generalized additive models. Statistics and Computing, 27, 259-270. · Zbl 06696863
[18] Langrock, R, Swihart, BJ, Caffo, BS, Crainiceanu, CM, Punjabi, NM (2013) Combining hidden Markov models for comparing the dynamics of multiple sleep electroencephalograms. Statistics in Medicine, 32, 3342-3356.
[19] Lin, J, Wu, C, Wei, W (2012) Error weighted semi-coupled hidden Markov model for audio-visual emotion recognition. IEEE Transactions on Multimedia, 14, 142-156.
[20] Maruotti, A, Punzo, A, Bagnato, L (2019) Hidden Markov and semi-Markov models with multivariate leptokurtic-normal components for robust modeling of daily returns series. Journal of Financial Econometrics, 17, 91-117.
[21] Michalopoulos, K, Bourbakis, N (2014) Using dynamic Bayesian networks for modeling EEG topographic sequences. 36th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 7, 4928-31.
[22] Michelot, T, Langrock, R, Patterson, TA (2016) moveHMM: An R package for analysing animal movement data using hidden Markov models. Methods in Ecology and Evolution, 7, 1308-1315.
[23] Nean, AV, Liang, L, Pi, X, Liu, X, Murphy, K (2002) Dynamic Bayesian networks for audio-visual speech recognition. EURASIP Journal on Advances in Signal Processing, 11, 1274-1288. · Zbl 1057.68107
[24] Oliveira, J, Sousa, C, Coimbra, MT (2002) Coupled hidden Markov model for automatic ECG and PCG segmentation. IEEE International Conference on Acoustics, Speech and Signal Processing, >1023-1027 IEEE.
[25] R Core Team (2018) R: A Language and Environment for Statistical Computing. Vienna: R Foundation for Statistical Computing. URL: https://www.R-project.org/ (last accessed 25 August 2020).
[26] Raftery, A (1985) A model for high-order Markov chains. Journal of the Royal Statistical Society B, 47, 528-539. · Zbl 0593.62091
[27] Rezek, I, Sykacek, P, Roberts, SJ (2000) Learning interaction dynamics with coupled hidden Markov models. IEE Proceedings: Science, Measurement and Technology, 147, 345-350. Erratum in IEE Proceedings: Science, Measurement and Technology, 148, 221.
[28] Rydén, T (2008) EM versus Markov chain Monte Carlo for estimation of hidden Markov models: A computational perspective. Bayesian Analysis, 3, 659-688. · Zbl 1330.65023
[29] Saul, LK, Jordan, MI (1999) Mixed memory Markov models: Decomposing complex stochastic processes as mixtures of simpler ones. Machine Learning, 37, 75-87. · Zbl 0948.68096
[30] Sherlock, C, Xifara, T, Telfer, S, Begon, M (2013) A coupled hidden Markov model for disease interactions. Journal of the Royal Statistical Society, Series C, 62, 609-627.
[31] Stoner, O, Economou, T (2019) A comprehensive hidden Markov model for hourly rainfall time series. arXiv preprint arXiv:1906.03846.
[32] Touloupou, P, Finkenstädt, B, Spencer, SEF (2020) Scalable Bayesian inference for coupled hidden Markov and semi-Markov models. Journal of Computational and Graphical Statistics, 29, 238-249.
[33] Visser, I, Raijmakers, MEJ, Molenaar, P (2002) Fitting hidden Markov models to psychological data. Scientific Programming, 10, 185-199.
[34] Zhang, D, Gatica-Perez, D, Bengio, S, Roy, D (2006) Learning influence among interacting Markov chains. Advances in Neural Information Processing Systems, 61, 1577-1584.
[35] Zhou, H, Chen, J, Dong, G, Wang, H, Yuan, H (2016) Bearing fault recognition method based on neighbourhood component analysis and coupled hidden Markov model. Mechanical Systems and Signal Processing, 66-67, 568-581.
[36] Zucchini, W, MacDonald, IL, Langrock, R (2016) Hidden Markov Models for Time Series: An Introduction Using R, 2nd edition. Boca Raton, FL: Chapman and Hall/CRC. · Zbl 1362.62005
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