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
Machine learning with state-space models, Gaussian processes and Monte Carlo methods
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: 0000-0002-5601-1687
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 [en]
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: urn:nbn:se:uu:diva-357611ISBN: 978-91-513-0417-5 (print)OAI: oai:DiVA.org:uu-357611DiVA, id: diva2:1240418
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
List of papers
1. A flexible state–space model for learning nonlinear dynamical systems
Open this publication in new window or tab >>A flexible state–space model for learning nonlinear dynamical systems
2017 (English)In: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 80, p. 189-199Article 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.

Keywords
System identification, Nonlinear models, Regularization, Probabilistic models, Bayesian learning, Gaussian processes, Monte Carlo methods
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-311584 (URN)10.1016/j.automatica.2017.02.030 (DOI)000401391800023 ()
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: 2018-08-21Bibliographically approved
2. Data Consistency Approach to Model Validation
Open this publication in new window or tab >>Data Consistency Approach to Model Validation
(English)In: Article in journal (Refereed) Submitted
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-357607 (URN)
Funder
Swedish Foundation for Strategic Research Swedish Research Council
Available from: 2018-08-17 Created: 2018-08-17 Last updated: 2018-10-01
3. Learning dynamical systems with particle stochastic approximation EM
Open this publication in new window or tab >>Learning dynamical systems with particle stochastic approximation EM
(English)In: Article in journal (Refereed) Submitted
National Category
Signal Processing
Identifiers
urn:nbn:se:uu:diva-357505 (URN)
Funder
Swedish Research CouncilSwedish Foundation for Strategic Research
Available from: 2018-08-16 Created: 2018-08-16 Last updated: 2018-08-21
4. Identification of jump Markov linear models using particle filters
Open this publication in new window or tab >>Identification of jump Markov linear models using particle filters
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
National Category
Control Engineering
Identifiers
urn:nbn:se:uu:diva-234396 (URN)10.1109/CDC.2014.7040409 (DOI)978-1-4673-6090-6 (ISBN)
Conference
CDC 2014, December 15–17, Los Angeles, CA
Funder
Swedish Research Council, 621-2013-5524Swedish Research Council, 637-2014-466
Available from: 2015-02-12 Created: 2014-10-17 Last updated: 2018-08-21Bibliographically approved
5. Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution
Open this publication in new window or tab >>Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution
2018 (English)In: Mechanical systems and signal processing, ISSN 0888-3270, E-ISSN 1096-1216, Vol. 104, p. 915-928Article in journal (Refereed) Published
Abstract [en]

Probabilistic (or Bayesian) modeling and learning offers interesting possibilities for systematic representation of uncertainty using probability theory. However, probabilistic learning often leads to computationally challenging problems. Some problems of this type that were previously intractable can now be solved on standard personal computers thanks to recent advances in Monte Carlo methods. In particular, for learning of unknown parameters in nonlinear state-space models, methods based on the particle filter (a Monte Carlo method) have proven very useful. A notoriously challenging problem, however, still occurs when the observations in the state-space model are highly informative, i.e. when there is very little or no measurement noise present, relative to the amount of process noise. The particle filter will then struggle in estimating one of the basic components for probabilistic learning, namely the likelihood p(datalparameters). To this end we suggest an algorithm which initially assumes that there is substantial amount of artificial measurement noise present. The variance of this noise is sequentially decreased in an adaptive fashion such that we, in the end, recover the original problem or possibly a very close approximation of it. The main component in our algorithm is a sequential Monte Carlo (SMC) sampler, which gives our proposed method a clear resemblance to the SMC2 method. Another natural link is also made to the ideas underlying the approximate Bayesian computation (ABC). We illustrate it with numerical examples, and in particular show promising results for a challenging Wiener-Hammerstein benchmark problem.

Place, publisher, year, edition, pages
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD, 2018
Keywords
Probabilistic modelling, Bayesian methods, Nonlinear system identification, Sequential Monte Carlo, Particle filter, Approximate Bayesian computations, Highly informative observations, Tempering, Wiener-Hammerstein model
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:uu:diva-350269 (URN)10.1016/j.ymssp.2017.09.016 (DOI)000423652800057 ()
Funder
Swedish Research Council, 621-2013-5524, 2016-04278, 621-2016-06079Swedish Foundation for Strategic Research , RIT15-0012
Available from: 2018-05-15 Created: 2018-05-15 Last updated: 2018-08-21Bibliographically approved
6. Learning nonlinear state-space models using smooth particle-filter-based likelihood approximations
Open this publication in new window or tab >>Learning nonlinear state-space models using smooth particle-filter-based likelihood approximations
2018 (English)Conference paper, Published paper (Refereed)
Abstract [en]

When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The key idea in this paper is to run a particle filter based on a current parameter estimate, but then use the output from this particle filter to re-evaluate the likelihood function approximation also for other parameter values. This results in a (local) deterministic approximation of the likelihood and any standard optimization routine can be applied to find the maximum of this approximation. By iterating this procedure we eventually arrive at a final parameter estimate.

Series
IFAC-PapersOnLine, ISSN 2405-8963 ; 51:15
National Category
Signal Processing Control Engineering
Identifiers
urn:nbn:se:uu:diva-357504 (URN)10.1016/j.ifacol.2018.09.216 (DOI)000446599200111 ()
Conference
SYSID 2018, July 9–11, Stockholm, Sweden
Funder
Swedish Foundation for Strategic Research , RT15-0012, ICA16-0015Swedish Research Council, 621-2016-06079, 2016-04278
Available from: 2018-10-08 Created: 2018-08-16 Last updated: 2018-12-14Bibliographically approved
7. Marginalizing Gaussian process hyperparameters using sequential Monte Carlo
Open this publication in new window or tab >>Marginalizing Gaussian process hyperparameters using sequential Monte Carlo
2015 (English)In: Proc. 6th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, Piscataway, NJ: IEEE, 2015, p. 477-480Conference paper, Published paper (Refereed)
Place, publisher, year, edition, pages
Piscataway, NJ: IEEE, 2015
National Category
Signal Processing
Identifiers
urn:nbn:se:uu:diva-265654 (URN)10.1109/CAMSAP.2015.7383840 (DOI)000380473300124 ()978-1-4799-1963-5 (ISBN)
Conference
CAMSAP 2015, December 13–16, Cancún, Mexico
Funder
Swedish Research Council, 621-2013-5524
Available from: 2016-01-21 Created: 2015-11-02 Last updated: 2018-08-21Bibliographically approved

Open Access in DiVA

fulltext(3567 kB)292 downloads
File information
File name FULLTEXT01.pdfFile size 3567 kBChecksum SHA-512
8336be16b7d968835dd862aac1953bde6b83c647dc052b41e2043bdb0b957f887c550c5048ef5fb6222cd6fcbf665c2f5652774a65dabd92a721492c17d42e06
Type fulltextMimetype application/pdf
Buy this publication >>

Authority records BETA

Svensson, Andreas

Search in DiVA

By author/editor
Svensson, Andreas
By organisation
Division of Systems and ControlAutomatic control
Signal ProcessingProbability Theory and Statistics

Search outside of DiVA

GoogleGoogle Scholar
Total: 292 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

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 1103 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