Coupling of Particle Filters

Jacob, Pierre E.; Lindsten, Fredrik; Schön, Thomas B.

doi:10.48550/arxiv.1606.01156

Cited by 6 publications

(7 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This allows for computing an approximate solution of large transportation problems and has proved useful for many problems where no computationally feasible method previously exists. Examples include computing multi-marginal optimal transport problems and barycenters (centroids) [7] and sampling from multivariate probability distribution [40]. For quadratic cost functions this approach can also be seen as the solution to a Schrödinger bridge problem [21].…”

mentioning

confidence: 99%

Generalized Sinkhorn Iterations for Regularizing Inverse Problems Using Optimal Mass Transport

Karlsson¹,

Ringh²

2017

SIAM J. Imaging Sci.

View full text Add to dashboard Cite

The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be formulated as a linear programming problem, it is in many cases intractable for large problems due to the vast number of variables. A recent development to address this builds on an approximation with an entropic barrier term and solves the resulting optimization problem using Sinkhorn iterations. In this work we extend this methodology to a class of inverse problems. In particular we show that Sinkhorn-type iterations can be used to compute the proximal operator of the transport problem for large problems. A splitting framework is then used to solve inverse problems where the optimal mass transport cost is used for incorporating a priori information. We illustrate the method on problems in computerized tomography. In particular we consider a limited-angle computerized tomography problem, where a priori information is used to compensate for missing measurements.

show abstract

mentioning

confidence: 99%

Generalized Sinkhorn Iterations for Regularizing Inverse Problems Using Optimal Mass Transport

Karlsson¹,

Ringh²

2017

SIAM J. Imaging Sci.

View full text Add to dashboard Cite

show abstract

“…In order to keep the complexity of sampling N pairs from P linear in N , we focus on a particular choice. Other choices of coupled resampling schemes are given in Deligiannidis et al (2018); Jacob et al (2016); Sen et al (2018), following earlier works such as Pitt (2002); Lee (2008).…”

Section: Coupled Resamplingmentioning

confidence: 99%

“…We consider the index-coupled resampling scheme, used by Chopin and Singh (2015) in their theoretical analysis of the CPF, and by Jasra et al (2017) in a multilevel Monte Carlo context, see also Section 2.4 in Jacob et al (2016). The scheme amounts to a maximal coupling of discrete distributions on {1, .…”

Section: Coupled Resamplingmentioning

confidence: 99%

Smoothing With Couplings of Conditional Particle Filters

Jacob

Lindsten

Schön

2019

Journal of the American Statistical Association

Self Cite

View full text Add to dashboard Cite

In state space models, smoothing refers to the task of estimating a latent stochastic process given noisy measurements related to the process. We propose an unbiased estimator of smoothing expectations. The lack-of-bias property has methodological benefits: independent estimators can be generated in parallel, and confidence intervals can be constructed from the central limit theorem to quantify the approximation error. To design unbiased estimators, we combine a generic debiasing technique for Markov chains with a Markov chain Monte Carlo algorithm for smoothing. The resulting procedure is widely applicable and we show in numerical experiments that the removal of the bias comes at a manageable increase in variance. We establish the validity of the proposed estimators under mild assumptions. Numerical experiments are provided on toy models, including a setting of highly-informative observations, and a realistic Lotka-Volterra model with an intractable transition density.

show abstract

“…This would reduce the variance in the ratio of likelihood estimates that appear in the acceptance probability, and hence improve the acceptance rate. Simulating such coupled particle filters is challenging, but see Sen et al (2017) and Jacob et al (2016) for recent approaches. 7.2.2.…”

Section: Particle Mcmcmentioning

confidence: 99%

Particle Filters and Data Assimilation

Fearnhead

Künsch

2018

Annu. Rev. Stat. Appl.

View full text Add to dashboard Cite

State-space models can be used to incorporate subject knowledge on the underlying dynamics of a time series by the introduction of a latent Markov state-process. A user can specify the dynamics of this process together with how the state relates to partial and noisy observations that have been made. Inference and prediction then involves solving a challenging inverse problem: calculating the conditional distribution of quantities of interest given the observations. This article reviews Monte Carlo algorithms for solving this inverse problem, covering methods based on the particle filter and the ensemble Kalman filter. We discuss the challenges posed by models with high-dimensional states, joint estimation of parameters and the state, and inference for the history of the state process. We also point out some potential new developments which will be important for tackling cutting-edge filtering applications.Comment: To appear in `Annual Review of Statistics and Its Application

show abstract

Coupling of Particle Filters

Cited by 6 publications

References 35 publications

Generalized Sinkhorn Iterations for Regularizing Inverse Problems Using Optimal Mass Transport

Generalized Sinkhorn Iterations for Regularizing Inverse Problems Using Optimal Mass Transport

Smoothing With Couplings of Conditional Particle Filters

Particle Filters and Data Assimilation

Contact Info

Product

Resources

About