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Title: The importance of being correlated: Implications of dependence in joint spectral inference across multiple networks Authors:  Konstantinos Pantazis - Johns Hopkins University (United States) [presenting]
Avanti Athreya - Johns Hopkins University (United States)
Jesus Arroyo - Texas A&M University (United States)
William Frost - Rosalind Franklin University (United States)
Evan Hill - Rosalind Franklin University (United States)
Vince Lyzinski - University of Maryland, College Park (United States)
Abstract: Spectral inference on multiple networks is a rapidly-developing subfield of graph statistics. Recent work has demonstrated that joint, or simultaneous, spectral embedding of multiple independent networks can deliver more accurate estimation than individual spectral decompositions of those same networks. Little attention has been paid, however, to considering multiple networks with inherent correlation, and even less, to the network correlation that such joint embedding procedures naturally induce. We present a generalized omnibus embedding methodology and we provide a detailed analysis of this embedding across both independent and correlated networks. We also describe how this omnibus embedding can itself induce correlation which leads us to distinguish between inherent correlation---that is, the correlation that arises naturally in multisample network data---and induced correlation, which is an artifice of the joint embedding methodology. 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 provide network analogues of classical questions such as the effective sample size for more generally correlated data. We construct an appropriately calibrated omnibus embedding that can detect changes in real biological networks that previous embedding procedures could not discern.