Divide-and-Conquer With Sequential Monte Carlo

• Published in: Journal of computational and graphical statistics Vol. 26; no. 2; pp. 445 - 458
• Main Authors: Lindsten, F., Johansen, A. M., Naesseth, C. A., Kirkpatrick, B., Schön, T. B., Aston, J. A. D., Bouchard-Côté, A.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03.04.2017; American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America; Taylor & Francis Ltd
• Subjects: Algorithms; Approximation; Bayesian methods; Collection; Computer simulation; Decomposition; Graphical models; Hierarchical models; Markov analysis; Markov processes; Mathematical models; Monte Carlo simulation; Particle filters; Populations; Probabilistic inference; Probabilistic methods; Probability distribution; Probability theory; Regression; Regression analysis; Studies; Graphical models; Particle filters; Bayesian methods; Hierarchical models
• ISSN: 1061-8600; 1537-2715; 1537-2715
• DOI: 10.1080/10618600.2016.1237363

We propose a novel class of Sequential Monte Carlo (SMC) algorithms, appropriate for inference in probabilistic graphical models. This class of algorithms adopts a divide-and-conquer approach based upon an auxiliary tree-structured decomposition of the model of interest, turning the overall inferential task into a collection of recursively solved subproblems. The proposed method is applicable to a broad class of probabilistic graphical models, including models with loops. Unlike a standard SMC sampler, the proposed divide-and-conquer SMC employs multiple independent populations of weighted particles, which are resampled, merged, and propagated as the method progresses. We illustrate empirically that this approach can outperform standard methods in terms of the accuracy of the posterior expectation and marginal likelihood approximations. Divide-and-conquer SMC also opens up novel parallel implementation options and the possibility of concentrating the computational effort on the most challenging subproblems. We demonstrate its performance on a Markov random field and on a hierarchical logistic regression problem. Supplementary materials including proofs and additional numerical results are available online.