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  • 1.
    Lindsten, Fredrik
    et al.
    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.
    Bunch, Pete
    Särkkä, Simo
    Schön, Thomas B.
    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.
    Godsill, Simon J.
    Rao–Blackwellized particle smoothers for conditionally linear Gaussian models2016In: IEEE Journal on Selected Topics in Signal Processing, ISSN 1932-4553, E-ISSN 1941-0484, Vol. 10, no 2, p. 353-365Article in journal (Refereed)
  • 2.
    Lindsten, Fredrik
    et al.
    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.
    Johansen, A. M.
    Naesseth, C. A.
    Kirkpatrick, B.
    Schön, Thomas B.
    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.
    Aston, J. A. D.
    Bouchard-Côté, A.
    Divide-and-Conquer with sequential Monte Carlo2017In: Journal of Computational And Graphical Statistics, ISSN 1061-8600, E-ISSN 1537-2715, Vol. 26, no 2, p. 445-458Article in journal (Refereed)
  • 3. Rainforth, Tom
    et al.
    Naesseth, Christian A.
    Lindsten, Fredrik
    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.
    Paige, Brooks
    van de Meent, Jan-Willem
    Doucet, Arnaud
    Wood, Frank
    Interacting Particle Markov Chain Monte Carlo2016In: Proceedings of the 33rd International Conference on Machine Learning, 2016Conference paper (Refereed)
  • 4.
    Schön, Thomas B.
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Svensson, Andreas
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Murray, Lawrence
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Lindsten, Fredrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo2018In: Mechanical systems and signal processing, ISSN 0888-3270, E-ISSN 1096-1216, Vol. 104, p. 866-883Article in journal (Refereed)
    Abstract [en]

    Probabilistic modeling provides the capability to represent and manipulate uncertainty in data, models, predictions and decisions. We are concerned with the problem of learning probabilistic models of dynamical systems from measured data. Specifically, we consider learning of probabilistic nonlinear state-space models. There is no closed-form solution available for this problem, implying that we are forced to use approximations. In this tutorial we will provide a self-contained introduction to one of the state-of-the-art methods the particle Metropolis-Hastings algorithm which has proven to offer a practical approximation. This is a Monte Carlo based method, where the particle filter is used to guide a Markov chain Monte Carlo method through the parameter space. One of the key merits of the particle Metropolis-Hastings algorithm is that it is guaranteed to converge to the "true solution" under mild assumptions, despite being based on a particle filter with only a finite number of particles. We will also provide a motivating numerical example illustrating the method using a modeling language tailored for sequential Monte Carlo methods. The intention of modeling languages of this kind is to open up the power of sophisticated Monte Carlo methods including particle Metropolis-Hastings to a large group of users without requiring them to know all the underlying mathematical details.

  • 5.
    Singh, S. S.
    et al.
    Univ Cambridge, Dept Engn, Trumpington St, Cambridge CB2 1PZ, England..
    Lindsten, Fredrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Moulines, E.
    Ecole Polytech, Ctr Math Appl, Route Saclay, F-91128 Palaiseau, France..
    Blocking strategies and stability of particle Gibbs samplers2017In: Biometrika, ISSN 0006-3444, E-ISSN 1464-3510, Vol. 104, no 4, p. 953-969Article in journal (Refereed)
    Abstract [en]

    Sampling from the posterior probability distribution of the latent states of a hidden Markov model is nontrivial even in the context of Markov chain Monte Carlo. To address this, Andrieu et al. (2010) proposed a way of using a particle filter to construct a Markov kernel that leaves the posterior distribution invariant. Recent theoretical results have established the uniform ergodicity of this Markov kernel and shown that the mixing rate does not deteriorate provided the number of particles grows at least linearly with the number of latent states. However, this gives rise to a cost per application of the kernel that is quadratic in the number of latent states, which can be prohibitive for long observation sequences. Using blocking strategies, we devise samplers that have a stable mixing rate for a cost per iteration that is linear in the number of latent states and which are easily parallelizable.

  • 6.
    Singh, Sumeetpal S.
    et al.
    University of Cambridge.
    Lindsten, Fredrik
    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.
    Moulines, Eric
    Ecole Polytechnique, Paris.
    Blocking strategies and stability of particle Gibbs samplers2017In: Biometrika, ISSN 0006-3444, E-ISSN 1464-3510, Vol. 104, no 4, p. 953-969Article in journal (Refereed)
  • 7.
    Svensson, Andreas
    et al.
    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.
    Lindsten, Fredrik
    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.
    Learning dynamical systems with particle stochastic approximation EMIn: Article in journal (Refereed)
  • 8.
    Svensson, Andreas
    et al.
    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.
    Lindsten, Fredrik
    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.
    Schön, Thomas B.
    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.
    Learning nonlinear state-space models using smooth particle-filter-based likelihood approximations2018In: Proceedings of the 18th IFAC symposium on system identification, 2018, p. 652-657Conference paper (Refereed)
  • 9.
    Svensson, Andreas
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Schön, Thomas B.
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Lindsten, Fredrik
    Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.
    Learning of state-space models with highly informative observations: A tempered sequential Monte Carlo solution2018In: Mechanical systems and signal processing, ISSN 0888-3270, E-ISSN 1096-1216, Vol. 104, p. 915-928Article in journal (Refereed)
    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.

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