An efficient stochastic approximation EM algorithm using conditional particle filters

Lindsten, Fredrik

doi:10.1109/icassp.2013.6638872

Cited by 39 publications

(66 citation statements)

References 36 publications

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“…Other approaches to maximum likelihood estimation in nonlinear state-space models include the combination of the popular Expectation Maximization (EM) algorithm and particle filters (Lindsten, 2013;Schön et al, 2011;Olsson et al, 2008).…”

Section: Related Workmentioning

confidence: 99%

Learning Nonlinear State-Space Models Using Smooth Particle-Filter-Based Likelihood Approximations

2018

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When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear statespace 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 local approximation. By iterating this procedure we eventually arrive at a final parameter estimate.

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Section: Related Workmentioning

confidence: 99%

Learning Nonlinear State-Space Models Using Smooth Particle-Filter-Based Likelihood Approximations

2018

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“…In most cases the E-step is difficult to perform, while the M-step can be considered relatively straightforward, meaning that standard optimization procedures for the M-step can be implemented, or closed form solutions are possible. Important strategies for dealing with an intractable E-step are MCEM (Wei and Tanner, 1990) and SAEM (Delyon et al, 1999), see also Lindsten (2013) for a synthetic review. In SAEM the integral in Q(θ|θ (k−1) ) is approximated using a stochastic procedure.…”

Section: The Standard Saem Algorithmmentioning

confidence: 99%

Likelihood-free stochastic approximation EM for inference in complex models

Picchini

2018

Communications in Statistics - Simulation and Computation

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A maximum likelihood methodology for the parameters of models with an intractable likelihood is introduced. We produce a likelihood-free version of the stochastic approximation expectation-maximization (SAEM) algorithm to maximize the likelihood function of model parameters. While SAEM is best suited for models having a tractable "complete likelihood" function, its application to moderately complex models is a difficult or even impossible task. We show how to construct a likelihood-free version of SAEM by using the "synthetic likelihood" paradigm. Our method is completely plug-and-play, requires almost no tuning and can be applied to both static and dynamic models. Four simulation studies illustrate the method, including a stochastic differential equation model, a stochastic Lotka-Volterra model and data from g-and-k distributions. MATLAB code is available as supplementary material.

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“…Stochastic approximation EM (SAEM) was introduced and analysed by Delyon et al [1999] and it was later realised that it is possible to use MCMC kernels within SAEM [Andrieu et al, 2005] (see also Benveniste et al [1990]). The aforementioned particle SAEM algorithm for nonlinear system identification was presented by Lindsten [2013] and it is summarised in Algorithm 4. …”

Section: Expectation Maximisation Revisitedmentioning

confidence: 99%

Sequential Monte Carlo Methods for System Identification**This work was supported by the projects Learning of complex dynamical systems (Contract number: 637-2014-466) and Probabilistic modeling of dynamical systems (Contract number: 621-2013-5524), both funded by the Swedish Research Council.

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One of the key challenges in identifying nonlinear and possibly nonGaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estimation problems arising in SSMs. When combined with additional identification techniques, these algorithms provide solid solutions to the nonlinear system identification problem. We describe two general strategies for creating such combinations and discuss why SMC is a natural tool for implementing these strategies. Abstract One of the key challenges in identifying nonlinear and possibly nonGaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estimation problems arising in SSMs. When combined with additional identification techniques, these algorithms provide solid solutions to the nonlinear system identification problem. We describe two general strategies for creating such combinations and discuss why SMC is a natural tool for implementing these strategies.

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An efficient stochastic approximation EM algorithm using conditional particle filters

Cited by 39 publications

References 36 publications

Learning Nonlinear State-Space Models Using Smooth Particle-Filter-Based Likelihood Approximations

Learning Nonlinear State-Space Models Using Smooth Particle-Filter-Based Likelihood Approximations

Likelihood-free stochastic approximation EM for inference in complex models

Sequential Monte Carlo Methods for System Identification**This work was supported by the projects Learning of complex dynamical systems (Contract number: 637-2014-466) and Probabilistic modeling of dynamical systems (Contract number: 621-2013-5524), both funded by the Swedish Research Council.

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