Joint inference of multiple graphs with hidden variables from stationary graph signals

TL;DR

This paper introduces a joint inference method for multiple related graphs with hidden variables, leveraging stationarity and graph similarity to improve topology estimation from partial observations.

Contribution

It proposes a novel approach to jointly infer multiple related graphs accounting for hidden nodes, enhancing accuracy over existing single-network methods.

Findings

Improved graph inference accuracy demonstrated on synthetic data.

Effective modeling of hidden variables reduces their negative impact.

Method validated on real-world graph data.

Abstract

Learning graphs from sets of nodal observations represents a prominent problem formally known as graph topology inference. However, current approaches are limited by typically focusing on inferring single networks, and they assume that observations from all nodes are available. First, many contemporary setups involve multiple related networks, and second, it is often the case that only a subset of nodes is observed while the rest remain hidden. Motivated by these facts, we introduce a joint graph topology inference method that models the influence of the hidden variables. Under the assumptions that the observed signals are stationary on the sought graphs and the graphs are closely related, the joint estimation of multiple networks allows us to exploit such relationships to improve the quality of the learned graphs. Moreover, we confront the challenging problem of modeling the influence of the hidden nodes to minimize their detrimental effect. To obtain an amenable approach, we take advantage of the particular structure of the setup at hand and leverage the similarity between the different graphs, which affects both the observed and the hidden nodes. To test the proposed method, numerical simulations over synthetic and real-world graphs are provided.