Identifying the Latent Space Geometry of Network Models Through Analysis of Curvature

• Activity Number: 334 - Network Data and Models
• Type: Contributed
• Date/Time: Tuesday, August 9, 2022 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Shane Lubold* and Arun Chandrasekhar and Tyler McCormick
• Companies: University of Washington and Stanford University and University of Washington
• Keywords: Latent space models; curvature estimation; statistical geometry; Aggregated relational data; partial network data

Abstract

Modeling networks is fundamentally challenging because of high-order dependence between connections. A common approach assigns each person in the graph to a position on a low-dimensional manifold. Distance between individuals in this latent space is inversely proportional to the likelihood of forming a connection. The choice of the latent geometry (the manifold class, dimension, and curvature) has consequential impacts on the substantive conclusions of the model. More positive curvature in the manifold, for example, encourages more and tighter communities; negative curvature induces repulsion among nodes. Currently, however, the choice of the latent geometry is an a priori modeling assumption and there is limited guidance about how to make these choices in a data-driven way. In this work, we present a method to consistently estimate the manifold type, dimension, and curvature from an empirically relevant class of latent spaces. We explore the accuracy of our approach with simulations and then apply our approach to data-sets from economics, sociology, and neuroscience. Finally, we show how to adopt this estimation procedure to cases where only partial network data is available.