  We investigate the increasingly prominent task of jointly inferring multiple
networks from nodal observations. While most joint inference methods assume
that observations are available at all nodes, we consider the realistic and
more difficult scenario where a subset of nodes are hidden and cannot be
measured. Under the assumptions that the partially observed nodal signals are
graph stationary and the networks have similar connectivity patterns, we derive
structural characteristics of the connectivity between hidden and observed
nodes. This allows us to formulate an optimization problem for estimating
networks while accounting for the influence of hidden nodes. We identify
conditions under which a convex relaxation yields the sparsest solution, and we
formalize the performance of our proposed optimization problem with respect to
the effect of the hidden nodes. Finally, synthetic and real-world simulations
provide evaluations of our method in comparison with other baselines.
