A Bayesian Dynamic Latent Space Model for Weighted Networks

TL;DR

This paper introduces a Bayesian dynamic latent space eigenmodel for weighted temporal networks, capturing complex dependencies and improving inference efficiency with novel sampling techniques.

Contribution

It develops a new dynamic latent space eigenmodel that handles weighted networks with time-varying features and introduces efficient Bayesian inference methods.

Findings

The model effectively captures integer-valued weights and network sparsity.

The auxiliary-mixture sampler improves computational efficiency and chain mixing.

The approach is adaptable to various network types and weight distributions.

Abstract

A new dynamic latent space eigenmodel (LSM) is proposed for weighted temporal networks. The model accommodates integer-valued weights, excess of zeros, time-varying node positions (features), and time-varying network sparsity. The latent positions evolve according to a vector autoregressive process that accounts for lagged and contemporaneous dependence across nodes and features, a characteristic neglected in the LSM literature. A Bayesian approach is used to address two of the primary sources of inference intractability in dynamic LSMs: latent feature estimation and the choice of latent space dimension. We employ an efficient auxiliary-mixture sampler that performs data augmentation and supports conditionally conjugate prior distributions. A point-process representation of the network weights and the finite-dimensional distribution of the latent processes are used to derive a multi-move sampler in which each feature trajectory is drawn in a single block, without recursions. This sampling strategy is new to the network literature and can significantly reduce computational time while improving chain mixing. To avoid trans-dimensional samplers, a Laplace approximation of the partial marginal likelihood is used to design a partially collapsed Gibbs sampler. Overall, our procedure is general, as it can be easily adapted to static and dynamic settings, as well as to other discrete or continuous weight distributions.