Faster MCMC for Gaussian Latent Position Network Models

TL;DR

This paper introduces a new MCMC method combining split Hamiltonian Monte Carlo and Firefly Monte Carlo to efficiently estimate latent positions in large Gaussian network models, outperforming traditional methods.

Contribution

It proposes a novel MCMC strategy that leverages the posterior's structure, improving efficiency in large-scale Gaussian latent position network models.

Findings

Outperforms Metropolis within Gibbs on synthetic networks

More efficient posterior computation demonstrated on real networks

Reduces correlation between samples for better inference

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.