Stability properties of some particle filters

Whiteley, Nick

doi:10.1214/12-aap909

Cited by 61 publications

(133 citation statements)

References 26 publications

(53 reference statements)

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“…Favetto [48] proves results on the tightness of asymptotic variances for bounded test functions, while Douc et al [50] and Whitley [49] derive time-uniform bounds. It would be interesting to incorporate these convergence results into our model of gossip-based distributed particle filters and explore the implications.…”

Section: Discussion and Related Workmentioning

confidence: 95%

Error Propagation in Gossip-Based Distributed Particle Filters

Gupta

Coates

Rabbat

2015

IEEE Trans. on Signal and Inf. Process. over Networks

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This paper examines the impact of the gossip procedure on distributed particle filters that employ averaging to estimate the global likelihood function. We consider a model where a gossip-driven algorithm leads to the use of a slightly distorted version of the likelihood function, in lieu of its true value. Under standard regularity conditions, and a mild assumption on the true likelihood function, we derive a time-uniform bound on the weaksense Lp error of the filter. Furthermore, we present an associated exponential inequality for the large deviations of the filter. These bounds capture the combined effects of sampling and consensusbased approximation. The results allow us to evaluate the impact of such approximations on the overall performance of the distributed particle filter, and analyze its stability. Finally, through numerical experiments, we demonstrate the practical implications of these results and explore the relationship of the performance of the filter with these theoretical error bounds.

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Section: Discussion and Related Workmentioning

confidence: 95%

Error Propagation in Gossip-Based Distributed Particle Filters

Gupta

Coates

Rabbat

2015

IEEE Trans. on Signal and Inf. Process. over Networks

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“…Following (17) , one would call Algorithm 5 (ν i ) times, once to set each ancestor index in A j n−1 : j ∈ (ν i ) . These special cases also exemplify a more general phenomenon: sampling according to (17) using Algorithm 5 does not require the explicit computation of α n−1 . In Section 4.4 we address the issue of how a forest can be chosen adaptively.…”

Section: Forest Resamplingmentioning

confidence: 97%

Forest resampling for distributed sequential Monte Carlo

Lee

Whiteley

2015

Statistical Analysis

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This paper brings explicit considerations of distributed computing architectures and data structures into the rigorous design of Sequential Monte Carlo (SMC) methods. A theoretical result established recently by the authors shows that adapting interaction between particles to suitably control the effective sample size (ESS) is sufficient to guarantee stability of SMC algorithms. Our objective is to leverage this result and devise algorithms which are thus guaranteed to work well in a distributed setting. We make three main contributions to achieve this. First, we study mathematical properties of the ESS as a function of matrices and graphs that parameterize the interaction among particles. Secondly, we show how these graphs can be induced by tree data structures which model the logical network topology of an abstract distributed computing environment. Finally, we present efficient distributed algorithms that achieve the desired ESS control, perform resampling and operate on forests associated with these trees. © 2015 Wiley Periodicals, Inc. Statistical Analysis and Data Mining: The ASA Data Science Journal, 2015

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“…It turns out that the resampling step takes care of this and prevents the rapid accumulation of errors to occur. For more stability results, see Chopin (2004) and Whiteley (2013).…”

Section: Statistical Propertiesmentioning

confidence: 99%

Accelerating Monte Carlo methods for Bayesian inference in dynamical models

Dahlin

2016

Linköping Studies in Science and Technology. Dissertations

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Cover illustration: A Markov chain generated by the Metropolis-Hastings algorithm with an autoregressive proposal on a manifold given by a parametric function.This thesis was typeset using the L A T E X typesetting system originally developed by Leslie Lamport, based on T E X created by Donald Knuth. The text is set in Garamond and Cabin. The source code is set in Inconso ata. All plots are made using R (R Core together with colors from the RColorBrewer package (Neuwirth, 2014 Denna avhandling tillägnas min familj! AbstractMaking decisions and predictions from noisy observations are two important and challenging problems in many areas of society. Some examples of applications are recommendation systems for online shopping and streaming services, connecting genes with certain diseases and modelling climate change. In this thesis, we make use of Bayesian statistics to construct probabilistic models given prior information and historical data, which can be used for decision support and predictions. The main obstacle with this approach is that it often results in mathematical problems lacking analytical solutions. To cope with this, we make use of statistical simulation algorithms known as Monte Carlo methods to approximate the intractable solution. These methods enjoy well-understood statistical properties but are often computational prohibitive to employ.The main contribution of this thesis is the exploration of different strategies for accelerating inference methods based on sequential Monte Carlo ( smc) and Markov chain Monte Carlo ( mcmc). That is, strategies for reducing the computational effort while keeping or improving the accuracy. A major part of the thesis is devoted to proposing such strategies for the mcmc method known as the particle Metropolis-Hastings ( pmh) algorithm. We investigate two strategies: (i) introducing estimates of the gradient and Hessian of the target to better tailor the algorithm to the problem and (ii) introducing a positive correlation between the point-wise estimates of the target.Furthermore, we propose an algorithm based on the combination of s m c and Gaussian process optimisation, which can provide reasonable estimates of the posterior but with a significant decrease in computational effort compared with pmh. Moreover, we explore the use of sparseness priors for approximate inference in over-parametrised mixed effects models and autoregressive processes. This can potentially be a practical strategy for inference in the big data era. Finally, we propose a general method for increasing the accuracy of the parameter estimates in non-linear state space models by applying a designed input signal.v Populärvetenskaplig sammanfattningBorde Riksbanken höja eller sänka reporäntan vid sitt nästa möte för att nå inflationsmålet? Vilka gener är förknippade med en viss sjukdom? Hur kan Netflix och Spotify veta vilka filmer och vilken musik som jag vill lyssna på härnäst?Dessa tre problem är exempel på frågor där statistiska modeller kan vara användbara för att ge hjälp och underlag för be...

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Stability properties of some particle filters

Cited by 61 publications

References 26 publications

Error Propagation in Gossip-Based Distributed Particle Filters

Error Propagation in Gossip-Based Distributed Particle Filters

Forest resampling for distributed sequential Monte Carlo

Accelerating Monte Carlo methods for Bayesian inference in dynamical models

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