Unbiased Smoothing using Particle Independent Metropolis-Hastings

Lawrece Middleton, George Deligiannidis, Arnaud Doucet, Pierre E. Jacob
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:2378-2387, 2019.

Abstract

We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run for a finite time. We propose a simple way of coupling two MCMC chains built using Particle Independent Metropolis-Hastings (PIMH) to produce unbiased smoothing estimators. Unbiased estimators are appealing in the context of parallel computing, and facilitate the construction of confidence intervals. The proposed scheme only requires access to off-the-shelf Particle Filters (PF) and is thus easier to implement than recently proposed unbiased smoothers. The approach is demonstrated on a Lévy-driven stochastic volatility model and a stochastic kinetic model.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-middleton19a, title = {Unbiased Smoothing using Particle Independent Metropolis-Hastings}, author = {Middleton, Lawrece and Deligiannidis, George and Doucet, Arnaud and Jacob, Pierre E.}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {2378--2387}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/middleton19a/middleton19a.pdf}, url = {https://proceedings.mlr.press/v89/middleton19a.html}, abstract = {We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run for a finite time. We propose a simple way of coupling two MCMC chains built using Particle Independent Metropolis-Hastings (PIMH) to produce unbiased smoothing estimators. Unbiased estimators are appealing in the context of parallel computing, and facilitate the construction of confidence intervals. The proposed scheme only requires access to off-the-shelf Particle Filters (PF) and is thus easier to implement than recently proposed unbiased smoothers. The approach is demonstrated on a Lévy-driven stochastic volatility model and a stochastic kinetic model.} }
Endnote
%0 Conference Paper %T Unbiased Smoothing using Particle Independent Metropolis-Hastings %A Lawrece Middleton %A George Deligiannidis %A Arnaud Doucet %A Pierre E. Jacob %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-middleton19a %I PMLR %P 2378--2387 %U https://proceedings.mlr.press/v89/middleton19a.html %V 89 %X We consider the approximation of expectations with respect to the distribution of a latent Markov process given noisy measurements. This is known as the smoothing problem and is often approached with particle and Markov chain Monte Carlo (MCMC) methods. These methods provide consistent but biased estimators when run for a finite time. We propose a simple way of coupling two MCMC chains built using Particle Independent Metropolis-Hastings (PIMH) to produce unbiased smoothing estimators. Unbiased estimators are appealing in the context of parallel computing, and facilitate the construction of confidence intervals. The proposed scheme only requires access to off-the-shelf Particle Filters (PF) and is thus easier to implement than recently proposed unbiased smoothers. The approach is demonstrated on a Lévy-driven stochastic volatility model and a stochastic kinetic model.
APA
Middleton, L., Deligiannidis, G., Doucet, A. & Jacob, P.E.. (2019). Unbiased Smoothing using Particle Independent Metropolis-Hastings. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:2378-2387 Available from https://proceedings.mlr.press/v89/middleton19a.html.

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