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Title: High-dimensional Gaussian graphical model for network-linked data Authors:  Tianxi Li - University of Virginia (United States) [presenting]
Cheng Qian - University of Michigan, Ann Arbor (United States)
Liza Levina - University of Michigan (United States)
Ji Zhu - University of Michigan (United States)
Abstract: Graphical models are commonly used to represent conditional independence relationships between variables, and estimating them from high-dimensional data has been an active research area. However, almost all existing methods rely on the assumption that the observations share the same mean, and that they are independent. At the same time, datasets with observations connected by a network are becoming increasingly common, and tend to violate both these assumptions. We develop a Gaussian graphical model for settings where the observations are connected by a network and have potentially different mean vectors, varying smoothly over the network. We propose an efficient estimation method for this model and demonstrate its effectiveness in both simulated and real data, obtaining meaningful interpretable results on a statistician's coauthorship network. We also prove that our method estimates both the inverse covariance matrix and the corresponding graph structure correctly under the assumption of network cohesion, which refers to the empirically observed phenomenon of network neighbors sharing similar traits.