Joint Network Topology Inference in the Presence of Hidden Nodes

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.

References in corpus (17)

• The Emerging Field of Signal Processing on Graphs: Extending High-Dimensional Data Analysis to Networks and Other Irregular Domains
• High-dimensional graphs and variable selection with the Lasso
• Discrete Signal Processing on Graphs
• Graph Learning: A Survey
• Latent variable graphical model selection via convex optimization
• Connecting the Dots: Identifying Network Structure via Graph Signal Processing
• Stationary signal processing on graphs
• Stationary Graph Processes and Spectral Estimation
• Group Lasso with Overlaps: the Latent Group Lasso approach
• Blind Identification of Graph Filters
• Multilayer weighted social network model
• One condition for solution uniqueness and robustness of both l1-synthesis and l1-analysis minimizations
• Network Inference from Consensus Dynamics with Unknown Parameters
• Joint Inference of Multiple Graphs from Matrix Polynomials
• SILVar: Single Index Latent Variable Models
• Robust Graph Filter Identification and Graph Denoising from Signal Observations
• Joint Network Topology Inference via a Shared Graphon Model