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We investigate the increasingly prominent task of jointly inferring multiplenetworks from nodal observations. While most joint inference methods assumethat observations are available at all nodes, we consider the realistic andmore difficult scenario where a subset of nodes are hidden and cannot bemeasured. Under the assumptions that the partially observed nodal signals aregraph stationary and the networks have similar connectivity patterns, we derivestructural characteristics of the connectivity between hidden and observednodes. This allows us to formulate an optimization problem for estimatingnetworks while accounting for the influence of hidden nodes. We identifyconditions under which a convex relaxation yields the sparsest solution, and weformalize the performance of our proposed optimization problem with respect tothe effect of the hidden nodes. Finally, synthetic and real-world simulationsprovide evaluations of our method in comparison with other baselines.

Joint Network Topology Inference in the Presence of Hidden Nodes