Faster MCMC for Gaussian Latent Position Network Models
This work addresses computational bottlenecks in Bayesian inference for network science, offering incremental improvements for researchers analyzing large networks.
The authors tackled the inefficiency of Metropolis within Gibbs for estimating latent positions in network models by proposing a new MCMC strategy combining split Hamiltonian Monte Carlo and Firefly Monte Carlo, which outperformed existing methods on synthetic and real-world school district networks.
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.