Graph Learning Under Partial Observability
This addresses the challenge of graph learning in large-scale networks for researchers and practitioners in decentralized processing, but it is incremental as it surveys existing advances rather than presenting new results.
The paper surveys the inverse problem of inferring network topology from node behavior under partial observability, where only a limited fraction of nodes can be probed, and reviews recent advances on whether such partial observations are sufficient to discover the graph linking the probed nodes.
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among neighboring nodes. There is a large body of literature examining the effect of the graph structure on the performance of decentralized processing strategies. In this article, we examine the inverse problem and consider the reverse question: How much information does observing the behavior at the nodes of a graph convey about the underlying topology? For large-scale networks, the difficulty in addressing such inverse problems is compounded by the fact that usually only a limited fraction of the nodes can be probed, giving rise to a second important question: Despite the presence of unobserved nodes, can partial observations still be sufficient to discover the graph linking the probed nodes? The article surveys recent advances on this challenging learning problem and related questions.