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Title: The importance of being correlated: Implications of dependence in joint spectral inference across multiple networks Authors:  Konstantinos Pantazis - University of Maryland (United States)
Avanti Athreya - Johns Hopkins University (United States)
Jesus Arroyo - Texas AM 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) [presenting]
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. Such inference procedures typically rely heavily on independence assumptions across the multiple network realizations, and even in this case, little attention has been paid to the induced network correlation in such joint embeddings. We present a generalized omnibus embedding methodology and provide a detailed analysis of this embedding across both independent and correlated networks, the latter of which significantly extends the reach of such procedures. We describe how this omnibus embedding can itself induce correlation, leading us to distinguish between inherent correlation -- the correlation that arises naturally in multisample network data -- and induced correlation, which is an artifice of the joint embedding methodology. 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. Further, we show how an appropriately calibrated generalized omnibus embedding can detect changes in real biological networks that previous embedding procedures could not discern.