liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Sequential Monte Carlo for inference in nonlinear state space models
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.ORCID iD: 0000-0002-9424-1272
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: urn:nbn:se:liu:diva-106752DOI: 10.3384/lic.diva-106752Local ID: LIU-TEK-LIC-2014:85ISBN: 978-91-7519-369-4 (print)OAI: oai:DiVA.org:liu-106752DiVA: diva2:718460
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
List of papers
1. Particle Metropolis-Hastings using gradient and Hessian information
Open this publication in new window or tab >>Particle Metropolis-Hastings using gradient and Hessian information
2015 (English)In: Statistics and computing, ISSN 0960-3174, E-ISSN 1573-1375, Vol. 25, no 1, 81-92 p.Article in journal (Other academic) Published
Abstract [en]

Particle Metropolis-Hastings (PMH) allows for Bayesian parameter inference in nonlinear state space models by combining MCMC and particle filtering. The latter is used to estimate the intractable likelihood. In its original formulation, PMH makes use of a marginal MCMC proposal for the parameters, typically a Gaussian random walk. However, this can lead to a poor exploration of the parameter space and an inefficient use of the generated particles.

We propose two alternative versions of PMH that incorporate gradient and Hessian information about the posterior into the proposal. This information is more or less obtained as a byproduct of the likelihood estimation. Indeed, we show how to estimate the required information using a fixed-lag particle smoother, with a computational cost growing linearly in the number of particles. We conclude that the proposed methods can: (i) decrease the length of the burn-in phase, (ii) increase the mixing of the Markov chain at the stationary phase, and (iii) make the proposal distribution scale invariant which simplifies tuning.

Place, publisher, year, edition, pages
Springer, 2015
National Category
Control Engineering Signal Processing Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-106749 (URN)10.1007/s11222-014-9510-0 (DOI)000349028500013 ()
Projects
Probabilistic modelling of dynamical systems
Funder
Swedish Research Council, 621-2013-5524
Note

On the day of the defence date the status of this article was Manuscript.

Available from: 2014-05-21 Created: 2014-05-21 Last updated: 2017-12-05Bibliographically approved
2. Particle filter-based Gaussian process optimisation for parameter inference
Open this publication in new window or tab >>Particle filter-based Gaussian process optimisation for parameter inference
2014 (English)In: Proceedings of the 19th IFAC World Congress, 2014 / [ed] Edward Boje and Xiaohua Xia, 2014, 8675-8680 p.Conference paper, Published paper (Refereed)
Abstract [en]

We propose a novel method for maximum-likelihood-based parameter inference in nonlinear and/or non-Gaussian state space models. The method is an iterative procedure with three steps. At each iteration a particle filter is used to estimate the value of the log-likelihood function at the current parameter iterate. Using these log-likelihood estimates, a surrogate objective function is created by utilizing a Gaussian process model. Finally, we use a heuristic procedure to obtain a revised parameter iterate, providing an automatic trade-off between exploration and exploitation of the surrogate model. The method is profiled on two state space models with good performance both considering accuracy and computational cost.

Series
World Congress,, ISSN 1474-6670 ; Volume 19, Part 1
Keyword
Particle filtering/Monte Carlo methods; Bayesian methods; Nonlinear system identification
National Category
Control Engineering Signal Processing Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-106750 (URN)10.3182/20140824-6-ZA-1003.00278 (DOI)978-3-902823-62-5 (ISBN)
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
3. Approximate inference in state space models with intractable likelihoods using Gaussian process optimisation
Open this publication in new window or tab >>Approximate inference in state space models with intractable likelihoods using Gaussian process optimisation
2014 (English)Report (Other academic)
Abstract [en]

We propose a novel method for MAP parameter inference in nonlinear state space models with intractable likelihoods. The method is based on a combination of Gaussian process optimisation (GPO), sequential Monte Carlo (SMC) and approximate Bayesian computations (ABC). SMC and ABC are used to approximate the intractable likelihood by using the similarity between simulated realisations from the model and the data obtained from the system. The GPO algorithm is used for the MAP parameter estimation given noisy estimates of the log-likelihood. The proposed parameter inference method is evaluated in three problems using both synthetic and real-world data. The results are promising, indicating that the proposed algorithm converges fast and with reasonable accuracy compared with existing methods.

Publisher
25 p.
Series
LiTH-ISY-R, ISSN 1400-3902 ; 3075
Keyword
Approximate Bayesian computations, Gaussian process optimisation, Bayesian parameter inference, alpha-stable distribution
National Category
Probability Theory and Statistics Control Engineering Signal Processing
Identifiers
urn:nbn:se:liu:diva-106198 (URN)LiTH-ISY-R-3075 (ISRN)
Funder
Swedish Research Council, 621-2013-5524
Available from: 2014-04-28 Created: 2014-04-28 Last updated: 2016-05-04Bibliographically approved
4. A graph/particle-based method for experiment design in nonlinear systems
Open this publication in new window or tab >>A graph/particle-based method for experiment design in nonlinear systems
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
Series
World Congress, ISSN 1474-6670 ; Volumen 19, Part 1
National Category
Control Engineering Signal Processing Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-106751 (URN)10.3182/20140824-6-ZA-1003.00361 (DOI)978-3-902823-62-5 (ISBN)
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
5. Hierarchical Bayesian approaches for robust inference in ARX models
Open this publication in new window or tab >>Hierarchical Bayesian approaches for robust inference in ARX models
2012 (English)In: Proceedings from the 16th IFAC Symposium on System Identification, 2012 / [ed] Michel Kinnaert, International Federation of Automatic Control , 2012, Vol. 16 Part 1, 131-136 p.Conference paper, Oral presentation only (Refereed)
Abstract [en]

Gaussian innovations are the typical choice in most ARX models but using other distributions such as the Student's t could be useful. We demonstrate that this choice of distribution for the innovations provides an increased robustness to data anomalies, such as outliers and missing observations. We consider these models in a Bayesian setting and perform inference using numerical procedures based on Markov Chain Monte Carlo methods. These models include automatic order determination by two alternative methods, based on a parametric model order and a sparseness prior, respectively. The methods and the advantage of our choice of innovations are illustrated in three numerical studies using both simulated data and real EEG data.

Place, publisher, year, edition, pages
International Federation of Automatic Control, 2012
Series
IFAC papers online, ISSN 1474-6670 ; 2012
Keyword
Particle Filtering/Monte Carlo Methods; Bayesian Methods
National Category
Signal Processing
Identifiers
urn:nbn:se:liu:diva-81258 (URN)10.3182/20120711-3-BE-2027.00318 (DOI)978-3-902823-06-9 (ISBN)
Conference
The 16th IFAC Symposium on System Identification, July 11-13, Brussels, Belgium
Projects
CADICSCNDS
Funder
Swedish Research Council
Available from: 2012-09-10 Created: 2012-09-10 Last updated: 2016-05-04Bibliographically approved

Open Access in DiVA

Sequential Monte Carlo for inference in nonlinear state space models(2168 kB)623 downloads
File information
File name FULLTEXT01.pdfFile size 2168 kBChecksum SHA-512
6dfa7730cb86e54dbe0229dfe1e2fbd6776e9701d3262370c9a5ba0f1ac61dc654869794be60effbc07cc03fe1135f4a06e48ccfae8132615f9235a51a33c587
Type fulltextMimetype application/pdf
omslag(34 kB)18 downloads
File information
File name COVER01.pdfFile size 34 kBChecksum SHA-512
0c28bd8826602ba84df47df3398ba8bcb7876bc8b7f5b6d7531a5ff18516a16fc41fed3c602ac51b2e8872200620103415a251a17404dc983a8bb49e35b6046f
Type coverMimetype application/pdf

Other links

Publisher's full text

Authority records BETA

Dahlin, Johan

Search in DiVA

By author/editor
Dahlin, Johan
By organisation
Automatic ControlThe Institute of Technology
Control Engineering

Search outside of DiVA

GoogleGoogle Scholar
Total: 623 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

doi
isbn
urn-nbn

Altmetric score

doi
isbn
urn-nbn
Total: 1673 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf