# Local Tomography of Large Networks under the Low-Observability Regime

arXiv: https://arxiv.org/abs/1805.09081 · HTML: https://mlsanity.com/paper/1805.09081/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 May 2018.

## Built on by (most cited first, 5 of 5)

- [Learning the Causal Structure of Networked Dynamical Systems under Latent Nodes and Structured Noise](https://mlsanity.com/paper/2312.05974/) (2023)
- [An Unbiased Symmetric Matrix Estimator for Topology Inference under Partial Observability](https://mlsanity.com/paper/2203.15500/) (2022)
- [Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach](https://mlsanity.com/paper/2208.04405/) (2022)
- [Inferring the Graph of Networked Dynamical Systems under Partial Observability and Spatially Colored Noise](https://mlsanity.com/paper/2312.11324/) (2023)
- [Online Network Inference from Graph-Stationary Signals with Hidden Nodes](https://mlsanity.com/paper/2409.08760/) (2024)

## Abstract (arXiv)

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"os-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.