uu.seUppsala University Publications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • 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
Identification of jump Markov linear models using particle filters
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.
2014 (English)In: Proc. 53rd Conference on Decision and Control, Piscataway, NJ: IEEE, 2014, p. 6504-6509Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Piscataway, NJ: IEEE, 2014. p. 6504-6509
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:uu:diva-234396DOI: 10.1109/CDC.2014.7040409ISBN: 978-1-4673-6090-6 (print)OAI: oai:DiVA.org:uu-234396DiVA, id: diva2:756540
Conference
CDC 2014, December 15–17, Los Angeles, CA
Funder
Swedish Research Council, 621-2013-5524Swedish Research Council, 637-2014-466Available from: 2015-02-12 Created: 2014-10-17 Last updated: 2018-08-21Bibliographically 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
2. Machine learning with state-space models, Gaussian processes and Monte Carlo methods
Open this publication in new window or tab >>Machine learning with state-space models, Gaussian processes and Monte Carlo methods
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Numbers are present everywhere, and when they are collected and recorded we refer to them as data. Machine learning is the science of learning mathematical models from data. Such models, once learned from data, can be used to draw conclusions, understand behavior, predict future evolution, and make decisions. This thesis is mainly concerned with two particular statistical models for this purpose: the state-space model and the Gaussian process model, as well as a combination thereof. To learn these models from data, Monte Carlo methods are used, and in particular sequential Monte Carlo (SMC) or particle filters.

The thesis starts with an introductory background on state-space models, Gaussian processes and Monte Carlo methods. The main contribution lies in seven scientific papers. Several contributions are made on the topic of learning nonlinear state-space models with the use of SMC. An existing SMC method is tailored for learning in state-space models with little or no measurement noise. The SMC-based method particle Gibbs with ancestor sampling (PGAS) is used for learning an approximation of the Gaussian process state-space model. PGAS is also combined with stochastic approximation expectation maximization (EM). This  method, which we refer to as particle stochastic approximation EM, is a general method for learning parameters in nonlinear state-space models. It is later applied to the particular problem of maximum likelihood estimation in jump Markov linear models. An alternative and non-standard approach for how to use SMC to estimate parameters in nonlinear state-space models is also presented.

There are also two contributions not related to learning state-space models. One is how SMC can be used also for learning hyperparameters in Gaussian process regression models. The second is a method for assessing consistency between model and data. By using the model to simulate new data, and compare how similar that data is to the observed one, a general criterion is obtained which follows directly from the model specification. All methods are implemented and illustrated, and several are also applied to various real-world examples.

Place, publisher, year, edition, pages
Uppsala: Acta Universitatis Upsaliensis, 2018. p. 74
Series
Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology, ISSN 1651-6214 ; 1709
Keywords
Machine learning, State-space models, Gaussian processes
National Category
Signal Processing Probability Theory and Statistics
Research subject
Electrical Engineering with specialization in Automatic Control
Identifiers
urn:nbn:se:uu:diva-357611 (URN)978-91-513-0417-5 (ISBN)
Public defence
2018-10-12, ITC 2446, Lägerhyddsvägen 2, Uppsala, 10:15 (English)
Opponent
Supervisors
Available from: 2018-09-18 Created: 2018-08-21 Last updated: 2018-10-02

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Authority records BETA

Svensson, AndreasSchön, Thomas B.

Search in DiVA

By author/editor
Svensson, AndreasSchön, Thomas B.
By organisation
Division of Systems and ControlAutomatic control
Control Engineering

Search outside of DiVA

GoogleGoogle Scholar

doi
isbn
urn-nbn

Altmetric score

doi
isbn
urn-nbn
Total: 385 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association
  • vancouver
  • 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