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A flexible state–space model for learning nonlinear dynamical systems
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Division of Systems and Control. Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.ORCID iD: 0000-0001-5183-234X
2017 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 80, 189-199 p.Article in journal (Refereed) Published
Abstract [en]

We consider a nonlinear state-space model with the state transition and observation functions expressed as basis function expansions. The coefficients in the basis function expansions are learned from data. Using a connection to Gaussian processes we also develop priors on the coefficients, for tuning the model flexibility and to prevent overfitting to data, akin to a Gaussian process state-space model. The priors can alternatively be seen as a regularization, and helps the model in generalizing the data without sacrificing the richness offered by the basis function expansion. To learn the coefficients and other unknown parameters efficiently, we tailor an algorithm using state-of-the-art sequential Monte Carlo methods, which comes with theoretical guarantees on the learning. Our approach indicates promising results when evaluated on a classical benchmark as well as real data.

Place, publisher, year, edition, pages
2017. Vol. 80, 189-199 p.
Keyword [en]
System identification, Nonlinear models, Regularization, Probabilistic models, Bayesian learning, Gaussian processes, Monte Carlo methods
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:uu:diva-311584DOI: 10.1016/j.automatica.2017.02.030ISI: 000401391800023OAI: oai:DiVA.org:uu-311584DiVA: diva2:1060732
Funder
Swedish Research Council, 621-2013-5524Swedish Foundation for Strategic Research
Note

The material in this paper was partially presented at the 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), December 13-16, 2015, Cancun, Mexico and at the 19th International Conference on Artificial Intelligence and Statistics (AISTATS), May 9-11, 2016, Cadiz, Spain.

Available from: 2017-03-28 Created: 2016-12-29 Last updated: 2017-06-13Bibliographically approved
In thesis
1. Learning probabilistic models of dynamical phenomena using particle filters
Open this publication in new window or tab >>Learning probabilistic models of dynamical phenomena using particle filters
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Dynamical behavior can be seen in many real-life phenomena, typically as a dependence over time. This thesis studies and develops methods and probabilistic models for statistical learning of such dynamical phenomena.

A probabilistic model is a mathematical model expressed using probability theory. Statistical learning amounts to constructing such models, as well as adjusting them to data recorded from real-life phenomena. The resulting models can be used for, e.g., drawing conclusions about the phenomena under study and making predictions.

The methods in this thesis are primarily based on the particle filter and its generalizations, sequential Monte Carlo (SMC) and particle Markov chain Monte Carlo (PMCMC). The model classes considered are nonlinear state-space models and Gaussian processes.

The following contributions are included. Starting with a Gaussian-process state-space model, a general, flexible and computationally feasible nonlinear state-space model is derived in Paper I. In Paper II, a benchmark is performed between the two alternative state-of-the-art methods SMCs and PMCMC. Paper III considers PMCMC for solving the state-space smoothing problem, in particular for an indoor positioning application. In Paper IV, SMC is used for marginalizing the hyperparameters in the Gaussian-process state-space model, and Paper V is concerned with learning of jump Markov linear state-space models. In addition, the thesis also contains an introductory overview covering statistical inference, state-space models, Gaussian processes and some advanced Monte Carlo methods, as well as two appendices summarizing some useful technical results.

Place, publisher, year, edition, pages
Uppsala University, 2016
Series
Information technology licentiate theses: Licentiate theses from the Department of Information Technology, ISSN 1404-5117 ; 2016-011
National Category
Control Engineering
Research subject
Electrical Engineering with specialization in Automatic Control
Identifiers
urn:nbn:se:uu:diva-311585 (URN)
Supervisors
Available from: 2016-11-18 Created: 2016-12-29 Last updated: 2016-12-29Bibliographically approved

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