Graph quilting: graphical model selection from partially observed covariances

Understand

Graphical model selection is a seemingly impossible task when many pairs of variables are never jointly observed; this requires inference of conditional dependencies with no observations of corresponding marginal dependencies.

• This under-explored statistical problem arises in neuroimaging, for example, when different partially overlapping subsets of neurons are recorded in non-simultaneous sessions.
• We call this statistical challenge the "Graph Quilting" problem.
• We study this problem in the context of sparse inverse covariance learning, and focus on Gaussian graphical models where we show that missing parts of the covariance matrix yields an unidentifiable precision matrix specifying the graph.