Li, Tianxi (2018). High-Dimensional Guassian Graphical Model for Network-linked data.
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 thesame mean, and that they are independent. At the same time, datasets with observations connected by a network are becoming increasinglycommon, and tend to violate both these assumptions. We develop a Gaussian graphical model for settings where the observations are connectedby a network and have potentially different mean vectors, varying smoothly over the network. We propose an efficient estimation method for thismodel and demonstrate its effectiveness in both simulated and real data, obtaining meaningful interpretable results on a statistician’s coauthorshipnetwork. We also prove that our method estimates both the inverse covariance matrix and the corresponding graph structure correctly under theassumption of network cohesion, which refers to the empirically observed phenomenon of network neighbors sharing similar traits.
11th International Conference of the ERCIM WG on Computational and Methodological Statistics (CMStatistics 2018)
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