Improving particle approximations of the joint smoothing distribution with linear computational cost

Dubarry, Cyrille; Douc, Randal

doi:10.1109/ssp.2011.5967661

Cited by 7 publications

(13 citation statements)

References 9 publications

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“…The initial state is modeled asp0 ∼ N (x0, P0). Since a k is not available until after RS-iteration k + 1, we make one step ahead predictions p k|k−1 , which are used in place ofp k in the stopping rule (6). The additional steps for Algorithm 3, required by the adaptive stopping rule, are given in Algorithm 4.…”

Section: Adaptive Stoppingmentioning

confidence: 99%

“…Several SMC-based smoothing algorithms, i.e., particle smoothers (PS), have been presented in the literature. These include forward filtering/backward smoothing (FFBSm) [3], two-filter smoothing [4,5] and Markov chain Monte Carlo (MCMC) smoothing [6,7,8]. However, it remains a major challenge to develop accurate and computationally efficient methods for particle smoothing.…”

Section: Introductionmentioning

confidence: 99%

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Adaptive stopping for fast particle smoothing

Taghavi

Lindsten

Svensson

et al. 2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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Particle smoothing is useful for offline state inference and parameter learning in nonlinear/non-Gaussian state-space models. However, many particle smoothers, such as the popular forward filter/backward simulator (FFBS), are plagued by a quadratic computational complexity in the number of particles. One approach to tackle this issue is to use rejection-sampling-based FFBS (RS-FFBS), which asymptotically reaches linear complexity. In practice, however, the constants can be quite large and the actual gain in computational time limited. In this contribution, we develop a hybrid method, governed by an adaptive stopping rule, in order to exploit the benefits, but avoid the drawbacks, of RS-FFBS. The resulting particle smoother is shown in a simulation study to be considerably more computationally efficient than both FFBS and RS-FFBS.

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Section: Adaptive Stoppingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Adaptive stopping for fast particle smoothing

Taghavi

Lindsten

Svensson

et al. 2013

2013 IEEE International Conference on Acoustics, Speech and Signal Processing

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“…A method which is related to MH-FFBP is the Metropolis-Hastings improved particle smoother (MH-IPS), suggested by Dubarry and Douc (2011). The method is also reminiscent of the resample-move algorithm ).…”

Section: Metropolis-hastings Improved Particle Smoothermentioning

confidence: 99%

“…In the simulation studies conducted by Dubarry and Douc (2011), only a few MCMC Algorithm 9 Metropolis-Hastings improved particle smoother (Dubarry and Douc, 2011) Input: Forward filter particle trajectories {x…”

Section: Dubarry and Doucmentioning

confidence: 99%

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Particle filters and Markov chains for learning of dynamical systems

Lindsten

2013

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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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Computation of Gaussian orthant probabilities in high dimension

Ridgway

2015

Stat Comput

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We study the computation of Gaussian orthant probabilities, i.e. the probability that a Gaussian variable falls inside a quadrant. The Geweke-Hajivassiliou-Keane (GHK) algorithm [Genz, 1992;Geweke, 1991;Hajivassiliou et al., 1996;Keane, 1993], is currently used for integrals of dimension greater than 10. In this paper we show that for Markovian covariances GHK can be interpreted as the estimator of the normalizing constant of a state space model using sequential importance sampling (SIS). We show for an AR(1) the variance of the GHK, properly normalized, diverges exponentially fast with the dimension. As an improvement we propose using a particle filter (PF). We then generalize this idea to arbitrary covariance matrices using Sequential Monte Carlo (SMC) with properly tailored MCMC moves. We show empirically that this can lead to drastic improvements on currently used algorithms.We also extend the framework to orthants of mixture of Gaussians (Student, Cauchy etc.), and to the simulation of truncated Gaussians.

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Improving particle approximations of the joint smoothing distribution with linear computational cost

Cited by 7 publications

References 9 publications

Adaptive stopping for fast particle smoothing

Adaptive stopping for fast particle smoothing

Particle filters and Markov chains for learning of dynamical systems

Computation of Gaussian orthant probabilities in high dimension

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