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Faster MCMC for Gaussian latent position network models

Published online by Cambridge University Press:  22 February 2022

Neil A. Spencer Open the ORCID record for Neil A. Spencer [Opens in a new window] ,
Brian W. Junker  and
Tracy M. Sweet Open the ORCID record for Tracy M. Sweet [Opens in a new window]
Neil A. Spencer*
Affiliation:
Harvard University, Boston, MA 02115, USA
Brian W. Junker
Affiliation:
Carnegie Mellon University, Pittsburgh, PA 15213, USA
Tracy M. Sweet
Affiliation:
University of Maryland College Park, College Park, MD 20742, USA
*
*Corresponding author. Email: [email protected]
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Abstract

Latent position network models are a versatile tool in network science; applications include clustering entities, controlling for causal confounders, and defining priors over unobserved graphs. Estimating each node’s latent position is typically framed as a Bayesian inference problem, with Metropolis within Gibbs being the most popular tool for approximating the posterior distribution. However, it is well-known that Metropolis within Gibbs is inefficient for large networks; the acceptance ratios are expensive to compute, and the resultant posterior draws are highly correlated. In this article, we propose an alternative Markov chain Monte Carlo strategy—defined using a combination of split Hamiltonian Monte Carlo and Firefly Monte Carlo—that leverages the posterior distribution’s functional form for more efficient posterior computation. We demonstrate that these strategies outperform Metropolis within Gibbs and other algorithms on synthetic networks, as well as on real information-sharing networks of teachers and staff in a school district.

Keywords

Hamiltonian Monte Carlonetwork datafirefly Monte Carlolatent space modellongitudinal network dataBayesian computation
Type
Research Article
Information
Network Science , Volume 10 , Issue 1 , March 2022 , pp. 20 - 45
Copyright
© The Author(s), 2022. Published by Cambridge University Press

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Footnotes

Action Editor: Stanley Wasserman

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