Joint Network Topology Inference in the Presence of Hidden Nodes

TL;DR

This paper proposes a method for jointly inferring multiple network topologies from nodal data when some nodes are hidden, using graph stationarity assumptions and convex optimization to handle hidden influences.

Contribution

It introduces a novel approach to infer network structures with hidden nodes by leveraging stationarity and similar connectivity, including conditions for convex relaxation and performance analysis.

Findings

Effective in identifying network structures with hidden nodes.

Outperforms baseline methods in synthetic and real-world tests.

Provides theoretical guarantees for the convex relaxation approach.

Abstract

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.