Identifying Latent Space Geometry in Network Models Using Analysis of Curvature

• Activity Number: 387 - New Advances in Network and Relational Data Analysis
• Type: Invited
• Date/Time: Wednesday, August 5, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Section on Statistical Graphics
• Author(s): Tyler McCormick and Shane Lubold*
• Companies: University of Washington and Department of Statistics, University of Washington

Abstract

Networks are frequently modeled using latent space models. Nodes are points on a manifold and the probability of a link forming between two points is conditionally independent of anything else and declines in distance in the manifold. Typically, researchers select a latent space geometry---the manifold class and dimension---by assumption and not in a data-driven way. We develop a framework and provide a method wherein a researcher can estimate the latent space manifold out of an empirically relevant class (simply connected, complete Riemannian manifolds) given network data. The estimation of the manifold class, dimension, and curvature is consistent. The network model parameters are consistently estimable as well. Our argument may be of more general interest in statistical geometry: we can estimate the underlying geometry in such a context when a researcher observes a noisy estimate of a distance matrix generated by a collection of points on some manifold.