The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference Across Multiple Networks

• Activity Number: 444 - Recent Advances in Statistical Methodology for Big Data
• Type: Contributed
• Date/Time: Thursday, August 12, 2021 : 4:00 PM to 5:50 PM
• Sponsor: IMS
• Author(s): Konstantinos Pantazis* and Avanti Athreya and Vince Lyzinski and Jesus Arroyo Relión and William N. Frost and Evan S. Hill
• Companies: Department of Mathematics and Department of Applied Mathematics and Statistics and University of Maryland and Texas A&M University, Department of Statitics and Cell Biology and Anatomy, and Center for Brain Function and Repair and Cell Biology and Anatomy, and Center for Brain Function and Repair
• Keywords: Joint graph embeddings; Induced correlation; Latent space models; Multiscale correlated network inference; Time series of networks; Biological networks

Abstract

Spectral inference on multiple networks is a rapidly-developing subfield of graph statistics. Recent work has demonstrated that joint, spectral embedding of multiple independent networks can deliver more accurate estimation than individual spectral decompositions of those same networks. Such inference procedures typically rely heavily on independence assumptions across the network realizations, and even in this case, little attention has been paid to the induced network correlation that can be a consequence of such joint embeddings. We present a generalized omnibus embedding methodology and we provide a detailed analysis of this embedding across both independent and correlated networks, and we further describe how this joint embedding can itself induce correlation. We show that the generalized embedding procedure is flexible and robust, and we prove both consistency and a central limit theorem for the embedded points. We examine how induced and inherent correlation can impact inference for network time series data, and we construct an appropriately calibrated omnibus embedding that can detect changes in real biological networks that previous embedding procedures could not discern.