An O(log2 N) SMC2 Algorithm on Distributed Memory with an Approx. Optimal L-Kernel

Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC 2 ) are two methods that use an unbiased estimate of the log-likelihood obtained fro...

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Bibliographic Details
Published in:IEEE/SICE/RSJ International Conference on Multisensor Fusion and Integration for Intelligent Systems pp. 1 - 8
Main Authors: Rosato, Conor, Varsi, Alessandro, Murphy, Joshua, Maskell, Simon
Format: Conference Proceeding
Language:English
Published: IEEE 27.11.2023
Subjects:
Bayes methods
Bayesian inference
biomedical applications
distributed memory
Markov processes
Monte Carlo methods
parallel algorithms
Parameter estimation
Particle filters
particle Markov Chain Monte Carlo
Program processors
Recycling
SMC 2
ISSN:2767-9357
Online Access:Get full text
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Summary:Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC 2 ) are two methods that use an unbiased estimate of the log-likelihood obtained from a particle filter (PF) to evaluate the target distribution. P-MCMC constructs a single Markov chain which is sequential by nature so cannot be readily parallelized using Distributed Memory (DM) architectures. This is in contrast to SMC 2 which includes processes, such as importance sampling, that are described as embarrassingly parallel. However, difficulties arise when attempting to parallelize resampling. None-the-less, the choice of backward kernel, recycling scheme and compatibility with DM architectures makes SMC 2 an attractive option when compared with p-MCMC. In this paper, we present an SMC 2 framework that includes the following features: an optimal (in terms of time complexity) \mathcal{O}(\log_2 N) parallelization for DM architectures, an approximately optimal (in terms of accuracy) backward kernel, and an efficient recycling scheme. On a cluster of 128 DM processors, the results on a biomedical application show that SMC 2 achieves up to a 70× speed-up vs its sequential implementation. It is also more accurate and roughly 54× faster than p-MCMC. A GitHub link is given which provides access to the code.
ISSN:2767-9357
DOI:10.1109/SDF-MFI59545.2023.10361452