Latent Space Network Modelling with Hyperbolic and Spherical Geometries

TL;DR

This paper investigates the inference of latent features in network models based on spherical and hyperbolic geometries, developing Bayesian estimation methods and validating them on real-world data.

Contribution

It introduces a Bayesian inference framework for non-Euclidean latent space network models with spherical and hyperbolic geometries, addressing identifiability and computational challenges.

Findings

Effective Bayesian estimation schemes for non-Euclidean latent spaces

Models fit well to real network data, capturing geometric properties

Addresses identifiability issues in latent space models

Abstract

A rich class of network models associate each node with a low-dimensional latent coordinate that controls the propensity for connections to form. Models of this type are well established in the network analysis literature, where it is typical to assume that the underlying geometry is Euclidean. Recent work has explored the consequences of this choice and has motivated the study of models which rely on non-Euclidean latent geometries, with a primary focus on spherical and hyperbolic geometry. In this paper, we examine to what extent latent features can be inferred from the observable links in the network, considering network models which rely on spherical and hyperbolic geometries. For each geometry, we describe a latent space network model, detail constraints on the latent coordinates which remove the well-known identifiability issues, and present Bayesian estimation schemes. Thus, we develop computational procedures to perform inference for network models in which the properties of the underlying geometry play a vital role. Finally, we assess the validity of these models on real data.