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Smoothing With Couplings of Conditional Particle Filters

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posted on 24.08.2020 by Pierre E. Jacob, Fredrik Lindsten, Thomas B. Schön

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 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 for a realistic Lotka–Volterra model with an intractable transition density. Supplementary materials for this article are available online.

Funding

The authors gratefully acknowledge the Swedish Foundation for Strategic Research (SSF) via the projects Probabilistic Modeling and Inference for Machine Learning (contract number: ICA16-0015) and ASSEMBLE (contract number: RIT15-0012), the Swedish Research Council (VR) via the projects Learning of Large-Scale Probabilistic Dynamical Models (contract number: 2016-04278) and NewLEADS—New Directions in Learning Dynamical Systems (contract number: 621-2016-06079), and the National Science Foundation through grant DMS-1712872.

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