Spatiotemporal blocking of the bouncy particle sampler for efficient inference in state space models

Abstract

We propose a novel blocked version of the continuous-time bouncy particle sampler Bouchard-Côté et al. [2018] applicable to any differentiable probability density. Motivated by Singh et al.[2017], we also introduce an alternative implementation that leads to significant improvement in terms of effective sample size per second, and furthermore allows for parallelization at the cost of an extra logarithmic factor. The new algorithms are particularly efficient for latent state inference in high-dimensional state space models, where blocking in both space and time is necessary to avoid degeneracy of the proposal kernel. The efficiency of the blocked bouncy particle sampler, in comparison with both the standard implementation of the bouncy particle sampler and the particle Gibbs algorithm of Andrieu et al. [2010], is illustrated numerically for both simulated data and a challenging real-world financial dataset.

Iterated Block Particle Filter for High-dimensional Parameter Learning: Beating the Curse of Dimensionality

“…However, the beautiful work of Rebeschini and Van Handel (2015) is theoretical in nature and was not anticipated to be applicable to real highdimensional problems (page 2812 therein). In recent years, many efforts have been undertaken to develop practical methods for these problems by developing the "block" concept, include but are not limited to, the following: Johansen (2015) proposed a method for systems identification based on both the block sampling idea and the annealed importance sampling approach; Singh et al (2017) applied the particle Gibbs algorithm inside a generic Gibbs sampler over temporal blocks to handle long time series; Park and Ionides (2020) proposed a twisted particle filter model (Whiteley and Lee (2014)) with iterated auxiliary PFs (Guarniero et al (2017)) to infer on moderately high-dimensional spatiotemporal models where its particle filtering corresponds to an adapted version of the block sampling method; Goldman and Singh (2021) proposed a blocked sampling scheme for latent state inference in high-dimensional state space models; Ionides et al (2021) proposed the bagged filter for partially observed interacting systems and showed that BPF can perform well on practical scientific models.…”