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The Use of Gaussian Processes in System Identification

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Encyclopedia of Systems and Control

Abstract

Gaussian processes are used in machine learning to learn input-output mappings from observed data. Gaussian process regression is based on imposing a Gaussian process prior on the unknown regressor function and statistically conditioning it on the observed data. In system identification, Gaussian processes are used to form time series prediction models such as nonlinear finite-impulse response (NFIR) models as well as nonlinear autoregressive (NARX) models. Gaussian process state-space (GPSS) models can be used to learn the dynamic and measurement models for a state-space representation of the input-output data. Temporal and spatiotemporal Gaussian processes can be directly used to form regressor on the data in the time domain. The aim of this article is to briefly outline the main directions in system identification methods using Gaussian processes.

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Bibliography

  • Ackermann ER, De Villiers JP, Cilliers P (2011) Nonlinear dynamic systems modeling using Gaussian processes: predicting ionospheric total electron content over South Africa. J Geophys Res Space Phys 116(10):13

    Google Scholar 

  • Álvarez MA, Luengo D, Lawrence ND (2013) Linear latent force models using Gaussian processes. IEEE Trans Pattern Anal Mach Intell 35(11):2693–2705

    Article  Google Scholar 

  • Brooks S, Gelman A, Jones GL, Meng XL (2011) Handbook of Markov chain Monte Carlo. Chapman & Hall/CRC, Boca Raton

    Book  Google Scholar 

  • Cressie NAC (1993) Statistics for spatial data. Wiley, New York

    Book  Google Scholar 

  • Damianou AC, Lawrence ND (2013) Deep Gaussian processes. In: International conference on artificial intelligence and statistics (AISTATS), pp 207–215

    Google Scholar 

  • Deisenroth MP, Turner RD, Huber MF, Hanebeck UD, Rasmussen CE (2011) Robust filtering and smoothing with Gaussian processes. IEEE Trans Autom Control 57(7):1865–1871

    Article  MathSciNet  Google Scholar 

  • Deisenroth MP, Fox D, Rasmussen CE (2015) Gaussian processes for data-efficient learning in robotics and control. IEEE Trans Pattern Anal Mach Intell 37(2):408–423

    Article  Google Scholar 

  • Frigola R (2016) Bayesian time series learning with Gaussian processes. Ph.D thesis, University of Cambridge

    Google Scholar 

  • Frigola R, Lindsten F, Schön TB, Rasmussen CE (2013) Bayesian inference and learning in Gaussian process state-space models with particle MCMC. In: Advances in neural information processing systems. Curran Associates, Inc., Red Hook, pp 3156–3164

    Google Scholar 

  • Frigola R, Chen Y, Rasmussen CE (2014a) Variational Gaussian process state-space models. In: Advances in neural information processing systems. Curran, Red Hook, pp 3680–3688

    Google Scholar 

  • Frigola R, Lindsten F, Schön TB, Rasmussen CE (2014b) Identification of Gaussian process state-space models with particle stochastic approximation EM. IFAC Proc Vol 47(3):4097–4102. Proceedings of the 19th IFAC world congress

    Google Scholar 

  • Hartikainen J, Sarkka S (2010) Kalman filtering and smoothing solutions to temporal Gaussian process regression models. In: IEEE international workshop on machine learning for signal processing (MLSP), pp 379–384

    Google Scholar 

  • Ko J, Fox D (2009) GP-BayesFilters: Bayesian filtering using Gaussian process prediction and observation models. Auton Robot 27(1):75–90

    Article  Google Scholar 

  • Kocijan J (2016) Modelling and control of dynamic systems using Gaussian process models. Springer, Cham

    Book  Google Scholar 

  • Kocijan J, Petelin D (2011) Output-error model training for Gaussian process models. In: International conference on adaptive and natural computing algorithms. Springer, Berlin, pp 312–321

    Chapter  Google Scholar 

  • Kocijan J, Girard A, Banko B, Murray-Smith R (2005) Dynamic systems identification with Gaussian processes. Math Comput Model Dyn Syst 11(4):411–424

    Article  MathSciNet  Google Scholar 

  • Lindgren F, Rue H, Lindström J (2011) An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach. JRSS B 73(4):423–498

    Article  MathSciNet  Google Scholar 

  • Matérn B (1960) Spatial variation. Technical report, Meddelanden från Statens Skogforskningsinstitut, band 49 – Nr 5

    Google Scholar 

  • McHutchon AJ (2015) Nonlinear modelling and control using Gaussian processes. Ph.D thesis, University of Cambridge

    Google Scholar 

  • Quiñonero-Candela J, Rasmussen CE (2005) A unifying view of sparse approximate Gaussian process regression. JMLR 6:1939–1959

    MathSciNet  MATH  Google Scholar 

  • Quiñonero-Candela J, Rasmussen CE, Figueiras-Vidal AR et al (2010) Sparse spectrum Gaussian process regression. J Mach Learn Res 11:1865–1881

    MathSciNet  MATH  Google Scholar 

  • Rasmussen CE, Williams CK (2006) Gaussian processes for machine learning. MIT Press, Cambridge

    MATH  Google Scholar 

  • Särkkä S (2013) Bayesian filtering and smoothing. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Särkkä S, Solin A, Hartikainen J (2013) Spatiotemporal learning via infinite-dimensional Bayesian filtering and smoothing. IEEE Sig Process Mag 30(4):51–61

    Article  Google Scholar 

  • Särkkä S, Álvarez MA, Lawrence ND (2019, to appear) Gaussian process latent force models for learning and stochastic control of physical systems. IEEE Trans Autom Control 64(7):2953–2960

    Article  Google Scholar 

  • Solin A, Särkkä S (2018) Hilbert space methods for reduced-rank Gaussian process regression. ArXiv: 1401.5508

    Google Scholar 

  • Svensson A, Solin A, Särkkä S, Schön T (2016) Machine Learning Research. In: Proceedings of the 19th International Conference on Artificial intelligence and statistics, Vol 51, pp 213–221

    Google Scholar 

  • Titsias M (2009) Machine Learning Research. In: Proceedings of the Twelth International Conference on Artificial intelligence and statistics, Vol 5, pp 567–574

    Google Scholar 

  • Turner R, Deisenroth M, Rasmussen C (2010) State-space inference and learning with Gaussian processes. In: Proceedings of the thirteenth international conference on artificial intelligence and statistics, pp 868–875

    Google Scholar 

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Author information

Authors and Affiliations

  1. Aalto University, Helsinki, Finland

    Simo Särkkä

Authors
  1. Simo Särkkä
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Correspondence to Simo Särkkä .

Editor information

Editors and Affiliations

  1. Electrical and Computer Engineering, Boston University, Boston, MA, USA

    John Baillieul

  2. Automation and Control Solutions, Honeywell, Golden Valley, MN, USA

    Tariq Samad

Section Editor information

  1. Division of Automatic Control, Department of Electrical Engineering, Linköping University, Linköping, Sweden

    Lennart Ljung

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Särkkä, S. (2019). The Use of Gaussian Processes in System Identification. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_100087-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_100087-1

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  • Publisher Name: Springer, London

  • Print ISBN: 978-1-4471-5102-9

  • Online ISBN: 978-1-4471-5102-9

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