Smoothing With Couplings of Conditional Particle Filters

@article{Jacob2019SmoothingWC,
  title={Smoothing With Couplings of Conditional Particle Filters},
  author={Pierre E. Jacob and Fredrik Lindsten and Thomas Bo Sch{\"o}n},
  journal={Journal of the American Statistical Association},
  year={2019},
  volume={115},
  pages={721 - 729}
}
Abstract 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 CI 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… Expand
Unbiased Smoothing using Particle Independent Metropolis-Hastings
TLDR
A simple way of coupling two MCMC chains built using Particle Independent Metropolis–Hastings (PIMH) to produce unbiased smoothing estimators is proposed, which is easier to implement than recently proposed unbiased smoothers. Expand
On Unbiased Score Estimation for Partially Observed Diffusions
We consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiasedExpand
Importance sampling type estimators based on approximate marginal Markov chain Monte Carlo
TLDR
This work considers importance sampling (IS) type weighted estimators based on Markov chain Monte Carlo (MCMC) targeting an approximate marginal of the target distribution and shows that the IS type approach can provide substantial gains relative to an analogous DA scheme, and is often competitive even without parallelisation. Expand
Unbiased Estimation of the Gradient of the Log-Likelihood for a Class of Continuous-Time State-Space Models
TLDR
This paper applies a doubly randomized scheme that involves a novel coupled conditional particle filter (CCPF) on the second level of randomization to obtain an unbiased estimate of the gradient of the log-likelihood (score function) of a class of continuous-time state-space models. Expand
Unbiased Markov chain Monte Carlo methods with couplings
Markov chain Monte Carlo (MCMC) methods provide consistent approximations of integrals as the number of iterations goes to 1. MCMC estimators are generally biased after any fixed number ofExpand
Unbiased Markov chain Monte Carlo for intractable target distributions
Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models withExpand
Unbiased Markov chain Monte Carlo with couplings
TLDR
The theoretical validity of the proposed couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee (2014) is established and their efficiency relative to the underlying MCMC algorithms is studied. Expand
Probabilistic learning of nonlinear dynamical systems using sequential Monte Carlo
TLDR
This tutorial will provide a self-contained introduction to one of the state-of-the-art methods—the particle Metropolis-Hastings algorithm—which has proven to offer a practical approximation to the problem of learning probabilistic nonlinear state-space models. Expand
Bayesian identification of state-space models via adaptive thermostats
TLDR
Numerical results show a clear benefit of a new method based on simulating a stochastic differential equation constructed to have the posterior parameter distribution as its limiting distribution, compared to a direct application of particle-filter-based gradient estimates within the thermostat. Expand
Estimating Convergence of Markov chains with L-Lag Couplings
TLDR
L-lag couplings are introduced to generate computable, non-asymptotic upper bound estimates for the total variation or the Wasserstein distance of general Markov chains. Expand
...
1
2
3
4
...

References

SHOWING 1-10 OF 118 REFERENCES
Particle Smoothing for Hidden Diffusion Processes: Adaptive Path Integral Smoother
  • H. Ruiz, H. Kappen
  • Computer Science, Mathematics
  • IEEE Transactions on Signal Processing
  • 2017
TLDR
A novel algorithm based on path integral control theory is proposed to efficiently estimate the smoothing distribution of continuous-time diffusion processes from partial observations by using an adaptive importance sampling method to improve the effective sampling size of the posterior and the reliability of the estimation of the marginals. Expand
Sequential Monte Carlo smoothing for general state space hidden Markov models
Computing smoothing distributions, the distributions of one or more states conditional on past, present, and future observations is a recurring problem when operating on general hidden Markov models.Expand
Coupling of Particle Filters
Particle filters provide Monte Carlo approximations of intractable quantities such as point-wise evaluations of the likelihood in state space models. In many scenarios, the interest lies in theExpand
Sequential Monte Carlo smoothing with application to parameter estimation in nonlinear state space models
This paper concerns the use of sequential Monte Carlo methods (SMC) for smoothing in general state space models. A well-known problem when applying the standard SMC technique in the smoothing mode isExpand
Towards smooth particle filters for likelihood estimation with multivariate latent variables
In parametrized continuous state-space models, one can obtain estimates of the likelihood of the data for fixed parameters via the Sequential Monte Carlo methodology. Unfortunately, even if theExpand
Coupled conditional backward sampling particle filter
Unbiased estimation for hidden Markov models has been recently proposed by Jacob et al (to appear), using a coupling of two conditional particle filters (CPFs). Unbiased estimation has manyExpand
The Iterated Auxiliary Particle Filter
ABSTRACT We present an offline, iterated particle filter to facilitate statistical inference in general state space hidden Markov models. Given a model and a sequence of observations, the associatedExpand
Blocking strategies and stability of particle Gibbs samplers
Summary Sampling from the posterior probability distribution of the latent states of a hidden Markov model is nontrivial even in the context of Markov chain Monte Carlo. To address this, Andrieu etExpand
Unbiased Markov chain Monte Carlo with couplings
TLDR
The theoretical validity of the proposed couplings of Markov chains together with a telescopic sum argument of Glynn and Rhee (2014) is established and their efficiency relative to the underlying MCMC algorithms is studied. Expand
Smooth Particle Filters for Likelihood Evaluation and Maximisation
In this paper, a method is introduced for approximating the likelihood for the unknown parameters of a state space model. The approximation converges to the true likelihood as the simulation sizeExpand
...
1
2
3
4
5
...