A0888
Title: Local estimation and testing of latent network curvature
Authors: Steven Wilkins-Reeves - Univeristy of Washington (Austria)
Tyler McCormick - University of Washington (United States) [presenting]
Abstract: Network data, commonly used throughout the physical, social, and biological sciences, consists of nodes (individuals) and the edges (interactions) between them. One way to represent network data's complex, high-dimensional structure is to embed the graph into a low-dimensional geometric space. The curvature of this space, in particular, provides insights into the structure in the graph, such as the propensity to form triangles or present tree-like structures. An estimating function is derived for curvature based on triangle side lengths and the midpoints between sides where the only input is a distance matrix and also establishes asymptotic normality. Next, a novel latent distance matrix estimator has been introduced for networks and an efficient algorithm to compute the estimate via solving iterative quadratic programs. This method is applied to the Los Alamos National Laboratory Unified Network and Host dataset, and it is shown how curvature estimates can be used to detect a red-team attack faster than naive methods, as well as discover non-constant latent curvature in co-authorship networks in physics.
