Graph Learning Under Partial Observability

TL;DR

This paper explores how much information about a network's structure can be inferred from limited observations of node behavior, especially when only a subset of nodes can be probed, highlighting recent advances in this challenging inverse problem.

Contribution

It surveys recent progress on learning network topology from partial observations, addressing the challenges posed by large-scale networks with limited node probing.

Findings

Partial observations can still reveal significant information about network topology.

Limited node probing poses challenges but recent methods show promising results.

Understanding the influence of unobserved nodes improves decentralized processing strategies.

Abstract

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.