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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 of Bouchard-Côté et al. (J Am Stat Assoc 113(522):855-867, 2018) which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state-space models (Singh et al. in Biometrika 104(4):953-969, 2017) and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the resulting algorithm. 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 MCMC. The efficiency of our 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. (J R Stat Soc Ser B Stat Methodol 72(3):269-342, 2010), is illustrated numerically for both simulated data and a challenging real-world financial dataset.

Supplementary information

The online version supplementary material available at 10.1007/s11222-021-10034-6.

SUBMITTER: Goldman JV

PROVIDER: S-EPMC8408370 | biostudies-literature | 2021

REPOSITORIES: biostudies-literature

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

Goldman Jacob Vorstrup JV Singh Sumeetpal S SS

Statistics and computing 20210901 5

We propose a novel blocked version of the continuous-time bouncy particle sampler of Bouchard-Côté et al. (J Am Stat Assoc 113(522):855-867, 2018) which is applicable to any differentiable probability density. This alternative implementation is motivated by blocked Gibbs sampling for state-space models (Singh et al. in Biometrika 104(4):953-969, 2017) and leads to significant improvement in terms of effective sample size per second, and furthermore, allows for significant parallelization of the ...[more]

PMID: 34483502

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Project description:BackgroundOne of the goals of the Systems Biology community is to have a detailed map of all biological interactions in an organism. One small yet important step in this direction is the creation of biological networks from post-genomic data. Bayesian networks are a very promising model for the inference of regulatory networks in Systems Biology. Usually, Bayesian networks are sampled with a Markov Chain Monte Carlo (MCMC) sampler in the structure space. Unfortunately, conventional MCMC sampling schemes are often slow in mixing and convergence. To improve MCMC convergence, an alternative method is proposed and tested with different sets of data. Moreover, the proposed method is compared with the traditional MCMC sampling scheme.ResultsIn the proposed method, a simpler and faster method for the inference of regulatory networks, Graphical Gaussian Models (GGMs), is integrated into the Bayesian network inference, trough a Hierarchical Bayesian model. In this manner, information about the structure obtained from the data with GGMs is taken into account in the MCMC scheme, thus improving mixing and convergence. The proposed method is tested with three types of data, two from simulated models and one from real data. The results are compared with the results of the traditional MCMC sampling scheme in terms of network recovery accuracy and convergence. The results show that when compared with a traditional MCMC scheme, the proposed method presents improved convergence leading to better network reconstruction with less MCMC iterations.ConclusionsThe proposed method is a viable alternative to improve mixing and convergence of traditional MCMC schemes. It allows the use of Bayesian networks with an MCMC sampler with less iterations. The proposed method has always converged earlier than the traditional MCMC scheme. We observe an improvement in accuracy of the recovered networks for the Gaussian simulated data, but this improvement is absent for both real data and data simulated from ODE.

Dataset Information

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

Supplementary information

Publications

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

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