Smoothing algorithms for state–space models

Briers, Mark; Doucet, Arnaud; Maskell, Simon

doi:10.1007/s10463-009-0236-2

Cited by 235 publications

(288 citation statements)

References 39 publications

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“…The estimation of the latent state distribution conditioned on the observations is a computationally intractable problem. There are in principle two types of approaches to approximate this computation: one can use one of many variations of particle filtering-smoothing methods, see [6,10,24]. The advantage of these methods is that they can in principle represent the latent state distribution with arbitrary accuracy, given sufficient computational resources.…”

Section: Bayesian System Identification: Potential For Neuroscience Dmentioning

confidence: 99%

Adaptive Importance Sampling for Control and Inference

Kappen

Ruiz

2016

J Stat Phys

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Path integral (PI) control problems are a restricted class of non-linear control problems that can be solved formally as a Feynman-Kac PI and can be estimated using Monte Carlo sampling. In this contribution we review PI control theory in the finite horizon case. We subsequently focus on the problem how to compute and represent control solutions. We review the most commonly used methods in robotics and control. Within the PI theory, the question of how to compute becomes the question of importance sampling. Efficient importance samplers are state feedback controllers and the use of these requires an efficient representation. Learning and representing effective state-feedback controllers for non-linear stochastic control problems is a very challenging, and largely unsolved, problem. We show how to learn and represent such controllers using ideas from the cross entropy method. We derive a gradient descent method that allows to learn feed-back controllers using an arbitrary parametrisation. We refer to this method as the path integral cross entropy method or PICE. We illustrate this method for some simple examples. The PI control methods can be used to estimate the posterior distribution in latent state models. In neuroscience these problems arise when estimating connectivity from neural recording data using EM. We demonstrate the PI control method as an accurate alternative to particle filtering.

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Section: Bayesian System Identification: Potential For Neuroscience Dmentioning

confidence: 99%

Adaptive Importance Sampling for Control and Inference

Kappen

Ruiz

2016

J Stat Phys

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“…It is demonstrated experimentally in [7] that this procedure outperforms significantly the forward filtering-backward smoothing approach.…”

Section: Smc Smoothingmentioning

confidence: 96%

“…Although this is not an issue when p θ ( y n:T | x n ) can be computed exactly, it does preclude the direct use of SMC methods to estimate this integral. To address this problem, a generalized version of the two-filter formula was proposed in [7]. It relies on the introduction of a set of artificial probability densities { p θ,n (x n )} T n=1 and the joint densities (27) which are constructed such that their marginal densities,…”

Section: Smc Smoothingmentioning

confidence: 99%

An Overview of Sequential Monte Carlo Methods for Parameter Estimation in General State-Space Models

Kantas

Doucet

Singh

et al. 2009

IFAC Proceedings Volumes

200

198

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Nonlinear non-Gaussian state-space models arise in numerous applications in control and signal processing. Sequential Monte Carlo (SMC) methods, also known as Particle Filters, provide very good numerical approximations to the associated optimal state estimation problems. However, in many scenarios, the state-space model of interest also depends on unknown static parameters that need to be estimated from the data. In this context, standard SMC methods fail and it is necessary to rely on more sophisticated algorithms. The aim of this paper is to present a comprehensive overview of SMC methods that have been proposed to perform static parameter estimation in general state-space models. We discuss the advantages and limitations of these methods.

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“…For this reason, various alternative particle smoothers have been proposed. One possible approach is to approximate the two-filter formula using particle methods [Kitagawa, 1996, Briers et al, 2010, Fearnhead et al, 2010. The disadvantage of such two-filter type smoothers is that the construction of the backward filter can be quite troublesome.…”

Section: Particle Filters and Smoothersmentioning

confidence: 99%

“…Another possible approach for the RBPS is to use the two-filter formula, and form the smoothing solution by combining two RBPFs, one running forward and one backwards in time [Briers et al, 2010, Fearnhead et al, 2010.…”

Section: Rao-blackwellized Particle Filters and Smoothersmentioning

confidence: 99%