Nested exemplar latent space models for dimension reduction in dynamic networks

TL;DR

This paper introduces a nested exemplar latent space model that significantly reduces dimensionality in dynamic network analysis by representing node attributes as dependent on low-dimensional exemplars, improving computational efficiency.

Contribution

The paper proposes a novel low-rank tensor decomposition approach for dynamic latent space models, enabling scalable analysis of large, sparse networks with temporal evolution.

Findings

Enhanced scalability in dynamic network modeling

Effective dimensionality reduction in ecological network data

Improved inference efficiency with Bayesian algorithms

Abstract

Dynamic latent space models are widely used for characterizing changes in networks and relational data over time. These models assign to each node latent attributes that characterize connectivity with other nodes, with these latent attributes dynamically changing over time. Node attributes can be organized as a three-way tensor with modes corresponding to nodes, latent space dimension, and time. Unfortunately, as the number of nodes and time points increases, the number of elements of this tensor becomes enormous, leading to computational and statistical challenges, particularly when data are sparse. We propose a new approach for massively reducing dimensionality by expressing the latent node attribute tensor as low rank. This leads to an interesting new nested exemplar latent space model, which characterizes the node attribute tensor as dependent on low-dimensional exemplar traits for each node, weights for each latent space dimension, and exemplar curves characterizing time variation. We study properties of this framework, including expressivity, and develop efficient Bayesian inference algorithms. The approach leads to substantial advantages in simulations and applications to ecological networks.