Consider a social network where only a few nodes (agents) have meaningfulinteractions in the sense that the conditional dependency graph over nodeattribute variables (behaviors) is sparse. A company that can only observe theinteractions between its own customers will generally not be able to accuratelyestimate its customers' dependency subgraph: it is blinded to any externalinteractions of its customers and this blindness creates false edges in itssubgraph. In this paper we address the semiblind scenario where the company hasaccess to a noisy summary of the complementary subgraph connecting externalagents, e.g., provided by a consolidator. The proposed framework applies toother applications as well, including field estimation from a network of awakeand sleeping sensors and privacy-constrained information sharing over socialsubnetworks. We propose a penalized likelihood approach in the context of agraph signal obeying a Gaussian graphical models (GGM). We use a convex-concaveiterative optimization algorithm to maximize the penalized likelihood.
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