Title: Semiblind subgraph reconstruction in Gaussian graphical models,
Abstract: Consider a social network where only a few nodes (agents) have meaningful
interactions in the sense that the conditional dependency graph over node
attribute variables (behaviors) is sparse. A company that can only observe the
interactions between its own customers will generally not be able to accurately
estimate its customers' dependency subgraph: it is blinded to any external
interactions of its customers and this blindness creates false edges in its
subgraph. In this paper we address the semiblind scenario where the company has
access to a noisy summary of the complementary subgraph connecting external
agents, e.g., provided by a consolidator. The proposed framework applies to
other applications as well, including field estimation from a network of awake
and sleeping sensors and privacy-constrained information sharing over social
subnetworks. We propose a penalized likelihood approach in the context of a
graph signal obeying a Gaussian graphical models (GGM). We use a convex-concave
iterative optimization algorithm to maximize the penalized likelihood.