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  • 1.
    Olsson, Jimmy
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    An efficient particle-based online EM algorithm for general state-space models2015In: IFAC-PapersOnLine, ISSN 2405-8963, Vol. 48, no 28, p. 963-968Article in journal (Refereed)
    Abstract [en]

    Estimating the parameters of general state-space models is a topic of importance for many scientific and engineering disciplines. In this paper we present an online parameter estimation algorithm obtained by casting our recently proposed particle-based, rapid incremental smoother (PaRIS) into the framework of online expectation-maximization (EM) for state-space models proposed by Cappé (2011). Previous such particle-based implementations of online EM suffer typically from either the well-known degeneracy of the genealogical particle paths or a quadratic complexity in the number of particles. However, by using the computationally efficient and numerically stable PaRIS algorithm for estimating smoothed expectations of timeaveraged sufficient statistics of the model we obtain a fast algorithm with very limited memory requirements and a computational complexity that grows only linearly with the number of particles. The efficiency of the algorithm is illustrated in a simulation study.

  • 2.
    Olsson, Jimmy
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    An efficient particle-based online EM algorithm for general state-space modelsManuscript (preprint) (Other academic)
  • 3.
    Olsson, Jimmy
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Efficient parameter inference in general hidden Markov models using the filter derivatives2016In: ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings, Institute of Electrical and Electronics Engineers (IEEE), 2016, p. 3984-3988Conference paper (Refereed)
    Abstract [en]

    Estimating online the parameters of general state-space hidden Markov models is a topic of importance in many scientific and engineering disciplines. In this paper we present an online parameter estimation algorithm obtained by casting our recently proposed particle-based, rapid incremental smoother (Paris) into the framework of recursive maximum likelihood estimation for general hidden Markov models. Previous such particle implementations suffer from either quadratic complexity in the number of particles or from the well-known degeneracy of the genealogical particle paths. By using the computational efficient and numerically stable Paris algorithm for estimating the needed prediction filter derivatives we obtain a fast algorithm with a computational complexity that grows only linearly with the number of particles. The efficiency and stability of the proposed algorithm are illustrated in a simulation study.

  • 4.
    Olsson, Jimmy
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Efficient particle-based online smoothing in general hidden Markov models: The PaRIS algorithm2017In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 23, no 3, p. 1951-1996Article in journal (Refereed)
    Abstract [en]

    This paper presents a novel algorithm, the particle-based, rapid incremental smoother (PaRIS), for efficient online approximation of smoothed expectations of additive state functionals in general hidden Markov models. The algorithm, which has a linear computational complexity under weak assumptions and very limited memory requirements, is furnished with a number of convergence results, including a central limit theorem. An interesting feature of PaRIS, which samples on-the-fly from the retrospective dynamics induced by the particle filter, is that it requires two or more backward draws per particle in order to cope with degeneracy of the sampled trajectories and to stay numerically stable in the long run with an asymptotic variance that grows only linearly with time.

  • 5.
    Olsson, Jimmy
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Efficient particle-based online smoothing in general hidden Markov models: the PaRIS algorithmManuscript (preprint) (Other academic)
  • 6.
    Olsson, Jimmy
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Particle-based adaptive-lag online marginal smoothing in general state-space modelsManuscript (preprint) (Other academic)
  • 7.
    Olsson, Jimmy
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    Particle-based, online estimation of tangent filters with application to parameter estimation in nonlinear state-space modelsManuscript (preprint) (Other academic)
  • 8.
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    On particle-based online smoothing and parameter inference in general hidden Markov models2015Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of two papers studying online inference in general hidden Markov models using sequential Monte Carlo methods.

    The first paper present an novel algorithm, the particle-based, rapid incremental smoother (PaRIS), aimed at efficiently perform online approximation of smoothed expectations of additive state functionals in general hidden Markov models. The algorithm has, under weak assumptions, linear computational complexity and very limited memory requirements. The algorithm is also furnished with a number of convergence results, including a central limit theorem.

    The second paper focuses on the problem of online estimation of parameters in a general hidden Markov model. The algorithm is based on a forward implementation of the classical expectation-maximization algorithm. The algorithm uses the PaRIS algorithm to achieve an efficient algorithm.

  • 9.
    Westerborn, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
    On particle-based online smoothing and parameter inference in general state-space models2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of 4 papers, presented in Paper A-D, on particle- based online smoothing and parameter inference in general state-space hidden Markov models.

    In Paper A a novel algorithm, the particle-based, rapid incremental smoother (PaRIS), aimed at efficiently performing online approxima- tion of smoothed expectations of additive state functionals in general hidden Markov models, is presented. The algorithm has, under weak assumptions, linear computational complexity and very limited mem- ory requirements. The algorithm is also furnished with a number of convergence results, including a central limit theorem.

    In Paper B the problem of marginal smoothing in general hidden Markov models is tackled. A novel, PaRIS-based algorithm is presented where the marginal smoothing distributions are approximated using a lagged estimator where the lag is set adaptively.

    In Paper C an estimator of the tangent filter is constructed, yield- ing in turn an estimator of the score function. The resulting algorithm is furnished with theoretical results, including a central limit theorem with a uniformly bounded variance. The resulting estimator is applied to online parameter estimation via recursive maximum liklihood.

    Paper D focuses on the problem of online estimation of parameters in general hidden Markov models. The algorithm is based on a for- ward implementation of the classical expectation-maximization algo- rithm. The algorithm uses the PaRIS algorithm to achieve an efficient algorithm. 

  • 10.
    Westerborn, Johan
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Olsson, Jimmy
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    EFFICIENT PARTICLE-BASED ONLINE SMOOTHING IN GENERAL HIDDEN MARKOV MODELS2014In: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, ISSN 1520-6149Article in journal (Refereed)
    Abstract [en]

    This paper deals with the problem of estimating expectations of sums of additive functionals under the joint smoothing distribution in general hidden Markov models. Computing such expectations is a key ingredient in any kind of expectation-maximization-based parameter inference in models of this sort. The paper presents a computationally efficient algorithm for online estimation of these expectations in a forward manner. The proposed algorithm has a linear computational complexity in the number of particles and does not require old particles and weights to be stored during the computations. The algorithm avoids completely the well-known particle path degeneracy problem of the standard forward smoother. This makes it highly applicable within the framework of online expectation-maximization methods. The simulations show that the proposed algorithm provides the same precision as existing algorithms at a considerably lower computational cost.

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