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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
Abstract #317882
Title: The Importance of Being Correlated: Implications of Dependence in Joint Spectral Inference Across Multiple Networks
Author(s): Konstantinos Pantazis* and Avanti Athreya and Vince Lyzinski and Jesus Arroyo ReliĆ³n 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

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.

Authors who are presenting talks have a * after their name.

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