Estimation and Inference in Latent Structure Random Graphs

• Activity Number: 129 - Advances in Graph Inference and Network Analysis
• Type: Topic Contributed
• Date/Time: Monday, August 3, 2020 : 1:00 PM to 2:50 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Avanti Athreya* and Minh Tang and Youngser Park and Carey Priebe
• Companies: Johns Hopkins University and NC State University and Johns Hopkins University and Johns Hopkins University
• Keywords: Latent structure random graphs; Efficient estimation; bilateral homology

Abstract

We introduce the latent structure model (LSM) random graph, defined as a random dot product graph in which the latent position distribution incorporates both probabilistic and geometric constraints. To describe the latent position distribution, we specify both a family of underlying distributions on some fixed Euclidean space and a structural support submanifold from which the latent positions for the graph are drawn. Under mild conditions, we show how spectral estimates of the latent positions of an RDPG can be used for efficient estimation of the paramaters of the LSM, and we describe how to estimate or learn the structural support in cases where it is unknown, with an illustrative focus on graphs with latent positions along the Hardy-Weinberg curve. Finally, we use the latent structure model formulation to test bilateral homology in the Drosophila connectome.