# Smoothing with Couplings of Conditional Particle Filters

arXiv: https://arxiv.org/abs/1701.02002 · HTML: https://mlsanity.com/paper/1701.02002/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jan 2017.

## Built on by (most cited first, 2 of 2)

- [De-Sequentialized Monte Carlo: a parallel-in-time particle smoother](https://mlsanity.com/paper/2202.02264/) (2022)
- [Unbiased Estimation of the Gradient of the Log-Likelihood for a Class of Continuous-Time State-Space Models](https://mlsanity.com/paper/2105.11522/) (2021)

## Abstract (arXiv)

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.