Estimating Latent Space Geometry of Network Formation Models

• Activity Number: 69 - Network Analysis
• Type: Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Shane Lubold* and Tyler McCormick and Arun Chandrasekhar
• Companies: Department of Statistics, University of Washington and University of Washington and Stanford University
• Keywords: Latent Space Models; Curvature Estimation; Bootstrapping for Hypothesis Tests; Rank Estimation

Abstract

In a latent space (LS) network model, nodes have corresponding locations in some "latent" or "social" space, and the closer the nodes are in this space, the more likely they are to form an edge. Typically, researchers select a LS geometry (the manifold class, dimension, and curvature) by assumption and not in a data-driven way. In this work, we present a method to consistently estimate the manifold type, dimension, and curvature. Our approach is based on the clique structure of the network, which provides information about LS positions on the unknown manifold. We use this information to conduct hypothesis tests about the manifold type and to estimate the manifold's dimension and curvature. We explore the accuracy of our approach with simulations and then apply our approach to datasets from economics and sociology.