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A graph/particle-based method for experiment design in nonlinear systems
Dept. of Automatic Control, KTH, Royal Institute of Technology, Stockholm, Sweden.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9424-1272
Dept. of Automatic Control, KTH, Royal Institute of Technology, Stockholm, Sweden.
Dept. of Information Technology, Uppsala University, Uppsala, Sweden.
2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Edward Boje and Xiaohua Xia, International Federation of Automatic Control , 2014, 1404-1409 p.Conference paper, Published paper (Refereed)
Abstract [en]

We propose an extended method for experiment design in nonlinear state space models. The proposed input design technique optimizes a scalar cost function of the information matrix, by computing the optimal stationary probability mass function (pmf) from which an input sequence is sampled. The feasible set of the stationary pmf is a polytope, allowing it to be expressed as a convex combination of its extreme points. The extreme points in the feasible set of pmf’s can be computed using graph theory. Therefore, the final information matrix can be approximated as a convex combination of the information matrices associated with each extreme point. For nonlinear systems, the information matrices for each extreme point can be computed by using particle methods. Numerical examples show that the proposed techniquecan be successfully employed for experiment design in nonlinear systems.

Place, publisher, year, edition, pages
International Federation of Automatic Control , 2014. 1404-1409 p.
Series
World Congress, ISSN 1474-6670 ; Volumen 19, Part 1
National Category
Control Engineering Signal Processing Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:liu:diva-106751DOI: 10.3182/20140824-6-ZA-1003.00361ISBN: 978-3-902823-62-5 (print)OAI: oai:DiVA.org:liu-106751DiVA: diva2:718421
Conference
19th IFAC World Congress, Cape Town, South Africa, August 24-29
Projects
Probabilistic modelling of dynamical systems
Funder
Swedish Research Council, 621-2013-5524
Available from: 2014-05-21 Created: 2014-05-21 Last updated: 2016-05-04Bibliographically approved
In thesis
1. Sequential Monte Carlo for inference in nonlinear state space models
Open this publication in new window or tab >>Sequential Monte Carlo for inference in nonlinear state space models
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Nonlinear state space models (SSMs) are a useful class of models to describe many different kinds of systems. Some examples of its applications are to model; the volatility in financial markets, the number of infected persons during an influenza epidemic and the annual number of major earthquakes around the world. In this thesis, we are concerned with state inference, parameter inference and input design for nonlinear SSMs based on sequential Monte Carlo (SMC) methods.

The state inference problem consists of estimating some latent variable that is not directly observable in the output from the system. The parameter inference problem is concerned with fitting a pre-specified model structure to the observed output from the system. In input design, we are interested in constructing an input to the system, which maximises the information that is available about the parameters in the system output. All of these problems are analytically intractable for nonlinear SSMs. Instead, we make use of SMC to approximate the solution to the state inference problem and to solve the input design problem. Furthermore, we make use of Markov chain Monte Carlo (MCMC) and Bayesian optimisation (BO) to solve the parameter inference problem.

In this thesis, we propose new methods for parameter inference in SSMs using both Bayesian and maximum likelihood inference. More specifically, we propose a new proposal for the particle Metropolis-Hastings algorithm, which includes gradient and Hessian information about the target distribution. We demonstrate that the use of this proposal can reduce the length of the burn-in phase and improve the mixing of the Markov chain.

Furthermore, we develop a novel parameter inference method based on the combination of BO and SMC. We demonstrate that this method requires a relatively small amount of samples from the analytically intractable likelihood, which are computationally costly to obtain. Therefore, it could be a good alternative to other optimisation based parameter inference methods. The proposed BO and SMC combination is also extended for parameter inference in nonlinear SSMs with intractable likelihoods using approximate Bayesian computations. This method is used for parameter inference in a stochastic volatility model with -stable returns using real-world financial data.

Finally, we develop a novel method for input design in nonlinear SSMs which makes use of SMC methods to estimate the expected information matrix. This information is used in combination with graph theory and convex optimisation to estimate optimal inputs with amplitude constraints. We also consider parameter estimation in ARX models with Student-t innovations and unknown model orders. Two different algorithms are used for this inference: reversible Jump Markov chain Monte Carlo and Gibbs sampling with sparseness priors. These methods are used to model real-world EEG data with promising results.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2014. 118 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1652
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-106752 (URN)10.3384/lic.diva-106752 (DOI)LIU-TEK-LIC-2014:85 (Local ID)978-91-7519-369-4 (ISBN)LIU-TEK-LIC-2014:85 (Archive number)LIU-TEK-LIC-2014:85 (OAI)
Presentation
2014-05-28, Visionen, B-building, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2014-05-21 Created: 2014-05-21 Last updated: 2016-05-04Bibliographically approved

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Dahlin, JohanSchön, Thomas

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Citation style
  • apa
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