Abstract:
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Multiple network analysis has applications in a multitude of research settings including social network analysis, dynamical biological networks, and connectomics. Joint embedding techniques aim to represent these networks in a common, low dimensional space by mapping the vertices of the networks to points in Euclidean space. This representation enables researchers to employ statistical and machine learning techniques to address research problems in multiple network analysis. We study one such embedding, the Omnibus embedding, and prove a Central Limit Theorem which reveals a bias-variance tradeoff introduced when analyzing networks with different connectivity structure. We study the ramifications of this bias-variance tradeoff in subsequent statistical tasks including estimation performance, multiplex community detection, and network hypothesis testing. Finally, we provide simulation studies that verify our asymptotic theory in finite sample networks and demonstrate how this bias-variance tradeoff enables robust multiple network analysis.
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