Identification of Gaussian Process State-Space Models with Particle Stochastic Approximation EM

Frigola, Roger; Lindsten, Fredrik; Schön, Thomas B.; Rasmussen, Carl Edward

doi:10.3182/20140824-6-za-1003.01843

Cited by 30 publications

(39 citation statements)

References 19 publications

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“…Finally, deriving a bound for the more advanced GP-based model as given in [2] and [28] would be very interesting as our future work.…”

Section: Discussionmentioning

confidence: 99%

“…The study of Gaussian process (GP)-based state-space models has been emerging in recent years. Dynamic models for the state formulated as Gaussian processes are introduced in [2]. There are also studies on Gaussian process-based measurement models, such as [3] and [4].…”

Section: A Motivations and Backgroundmentioning

confidence: 99%

“…However, in [2], [28], they assume no prior training data, and the GP model (namely the kernel hyperparameters) will be estimated jointly with the latent state in the GP system model. The estimation problem is very difficult.…”

Section: Some Implications To State Estimation and Assumptionsmentioning

confidence: 99%

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Cramér–Rao Bounds for Filtering Based on Gaussian Process State-Space Models

Zhao

Fritsche

Hendeby

et al. 2019

IEEE Trans. Signal Process.

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Posterior Cramér-Rao bounds (CRBs) are derived for the estimation performance of three Gaussian process-based state-space models. The parametric CRB is derived for the case with a parametric state transition and a Gaussian process-based measurement model. We illustrate the theory with a target tracking example and derive both parametric and posterior filtering CRBs for this specific application. Finally, the theory is illustrated with a positioning problem, with experimental data from an office environment where the obtained estimation performance is compared to the derived CRBs.

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“…Finally, deriving a bound for the more advanced GP-based model as given in [2] and [28] would be very interesting as our future work.…”

Section: Discussionmentioning

confidence: 99%

Section: A Motivations and Backgroundmentioning

confidence: 99%

See 1 more Smart Citation

Cramér–Rao Bounds for Filtering Based on Gaussian Process State-Space Models

Zhao

Fritsche

Hendeby

et al. 2019

IEEE Trans. Signal Process.

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“…Under mild regularity conditions, these iterations yield a sequence of parameter estimates that converges to a stationary point of the marginal likelihood of the data (under the condition that the number of particles M k at iteration k is such that that ∞ k=1 M −1 k = ∞; see [32]). Then, using the estimated hyperparameters, we can run a new Gibbs sampler and approximate the integrals in (17) with averages over the samples:…”

Section: Update the Parameters According To Corollarymentioning

confidence: 99%

Modeling and identification of uncertain-input systems

2019

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In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about the input or the linear system, we use Gaussian-process models. We estimate the model from data using the empirical Bayes approach: the input and the impulse responses of the linear system are estimated using the posterior means of the Gaussian-process models given the data, and the hyperparameters that characterize the Gaussian-process models are estimated from the marginal likelihood of the data. We propose an iterative algorithm to find the hyperparameters that relies on the EM method and results in simple update steps. In the most general formulation, neither the marginal likelihood nor the posterior distribution of the unknowns is tractable. Therefore, we propose two approximation approaches, one based on Markov-chain Monte Carlo techniques and one based on variational Bayes approximation. We also show special model structures for which the distributions are treatable exactly. Through numerical simulations, we study the application of the uncertain-input model to the identification of Hammerstein systems and cascaded linear systems. As part of the contribution of the paper, we show that this model structure encompasses many classical problems in system identification such as classical PEM, Hammerstein models, errors-in-variables problems, blind system identification, and cascaded linear systems. This allows us to build a systematic procedure to apply the algorithms proposed in this work to a wide class of classical problems.

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“…In practice, the ancestor sampling in the CSMC procedure gives rise to a considerable improvement over PG, comparable to that of backward simulation. The method has been successfully applied to challenging inference problems, such as Wiener system identification (Lindsten et al, 2013b) and learning of nonparametric, nonlinear SSMs (Frigola et al, 2013). We illustrate the PGAS method in the following example.…”

Section: Particle Gibbs With Ancestor Samplingmentioning

confidence: 99%

Particle filters and Markov chains for learning of dynamical systems

Lindsten

2013

Self Cite

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Sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC) methods provide computational tools for systematic inference and learning in complex dynamical systems, such as nonlinear and non-Gaussian state-space models. This thesis builds upon several methodological advances within these classes of Monte Carlo methods.Particular emphasis is placed on the combination of SMC and MCMC in so called particle MCMC algorithms. These algorithms rely on SMC for generating samples from the often highly autocorrelated state-trajectory. A specific particle MCMC algorithm, referred to as particle Gibbs with ancestor sampling (PGAS), is suggested. By making use of backward sampling ideas, albeit implemented in a forward-only fashion, PGAS enjoys good mixing even when using seemingly few particles in the underlying SMC sampler. This results in a computationally competitive particle MCMC algorithm. As illustrated in this thesis, PGAS is a useful tool for both Bayesian and frequentistic parameter inference as well as for state smoothing. The PGAS sampler is successfully applied to the classical problem of Wiener system identification, and it is also used for inference in the challenging class of non-Markovian latent variable models.Many nonlinear models encountered in practice contain some tractable substructure. As a second problem considered in this thesis, we develop Monte Carlo methods capable of exploiting such substructures to obtain more accurate estimators than what is provided otherwise. For the filtering problem, this can be done by using the well known RaoBlackwellized particle filter (RBPF). The RBPF is analysed in terms of asymptotic variance, resulting in an expression for the performance gain offered by Rao-Blackwellization. Furthermore, a Rao-Blackwellized particle smoother is derived, capable of addressing the smoothing problem in so called mixed linear/nonlinear state-space models. The idea of Rao-Blackwellization is also used to develop an online algorithm for Bayesian parameter inference in nonlinear state-space models with affine parameter dependencies.v Populärvetenskaplig sammanfattningMatematiska modeller av dynamiska förlopp används inom i stort sett alla tekniska och naturvetenskapliga discipliner. Till exempel, inom epidemiologi används modeller för att prediktera, dvs. förutsäga, spridningen av influensavirus inom en population. Antag att vi gör regelbundna observationer av hur många personer i populationen som är smittade. Baserat på denna information kan en modell användas för att prediktera antalet nya sjukdomsfall under, låt säga, nästkommande veckor. Den här typen av information möjliggör att en epidemi kan identifieras i ett tidigt skede, varpå åtgärder kan tas för att minska dess påverkan. Ett annat exempel är att prediktera hur hastigheten och orienteringen på ett flygplan påverkas då en viss styrsignal ställs ut på rodren, vilket är viktigt vid styrsystemdesign. Sådana prediktioner kräver en modell av flygplanets dynamik. Ytterligare ett exempel är att prediktera utvecklingen på e...

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Identification of Gaussian Process State-Space Models with Particle Stochastic Approximation EM

Cited by 30 publications

References 19 publications

Cramér–Rao Bounds for Filtering Based on Gaussian Process State-Space Models

Cramér–Rao Bounds for Filtering Based on Gaussian Process State-Space Models

Modeling and identification of uncertain-input systems

Particle filters and Markov chains for learning of dynamical systems

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