Fast Variational Inference of Latent Space Models for Dynamic Networks Using Bayesian P-Splines

TL;DR

This paper introduces a fast Bayesian variational inference method for continuous-time latent space models in dynamic networks, enabling scalable analysis of large datasets with theoretical error bounds.

Contribution

It proposes a novel Bayesian P-spline prior and a stochastic variational inference algorithm that is scalable and provides non-asymptotic error bounds for continuous-time LSMs.

Findings

Algorithm is linear in the number of edges, enabling large-scale analysis.

Established non-asymptotic error bounds for Bayesian estimators.

Successfully analyzed a large international conflict dataset with over 4 million relations.

Abstract

Latent space models (LSMs) are often used to analyze dynamic (time-varying) networks that evolve in continuous time. Existing approaches to Bayesian inference for these models rely on Markov chain Monte Carlo algorithms, which cannot handle modern large-scale networks. To overcome this limitation, we introduce a new prior for continuous-time LSMs based on Bayesian P-splines that allows the posterior to adapt to the dimension of the latent space and the temporal variation in each latent position. We propose a stochastic variational inference algorithm to estimate the model parameters. We use stochastic optimization to subsample both dyads and observed time points to design a fast algorithm that is linear in the number of edges in the dynamic network. Furthermore, we establish non-asymptotic error bounds for point estimates derived from the variational posterior. To our knowledge, this is the first such result for Bayesian estimators of continuous-time LSMs. Lastly, we use the method to analyze a large data set of international conflicts consisting of 4,456,095 relations from 2018 to 2022.