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Abstract:
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Multiple network analysis has applications in a multitude of research settings including social network analysis and dynamical biological networks. 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 describe the bias it introduces when analyzing networks with different connectivity structure. In addition, we prove a Central Limit Theorem and study the bias-variance tradeoff inherent in this embedding approach. Finally, we provide simulation studies that verify our asymptotic theory in finite sample networks and demonstrate how this bias-variance tradeoff can lead to better estimation performance.
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