Local Tomography of Large Networks under the Low-Observability Regime

TL;DR

This paper demonstrates that it is possible to reconstruct the local structure of large, partially observable networks with high probability, even when only a small fraction of agents are observed, under certain conditions.

Contribution

The work introduces a stochastic framework for local network tomography in large-scale networks with partial observations, proving high-probability recoverability under low-observability conditions.

Findings

Local tomography is feasible with high probability in large networks.

Reconstruction is possible under stability and symmetry conditions.

The approach works even when the observable subnetwork size is fixed as total network size grows.

Abstract

This article studies the problem of reconstructing the topology of a network of interacting agents via observations of the state-evolution of the agents. We focus on the large-scale network setting with the additional constraint of $partial$ observations, where only a small fraction of the agents can be feasibly observed. The goal is to infer the underlying subnetwork of interactions and we refer to this problem as $local$ $tomography$. In order to study the large-scale setting, we adopt a proper stochastic formulation where the unobserved part of the network is modeled as an Erd\"{o}s-R\'enyi random graph, while the observable subnetwork is left arbitrary. The main result of this work is establishing that, under this setting, local tomography is actually possible with high probability, provided that certain conditions on the network model are met (such as stability and symmetry of the network combination matrix). Remarkably, such conclusion is established under the $low$-$observability$ $regime$, where the cardinality of the observable subnetwork is fixed, while the size of the overall network scales to infinity.