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 Erdős-Rényi random graph, while the observable subnetwork is left arbitrary. The main result of this work is to establish 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.

中文翻译：

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低可观察性机制下大型网络的局部断层扫描

本文研究了通过观察代理的状态演变来重建交互代理网络的拓扑结构的问题。我们专注于具有局部观察附加约束的大规模网络设置，其中只有一小部分代理可以被切实观察到。目标是推断交互的底层子网络，我们将这个问题称为局部断层扫描。为了研究大规模设置，我们采用了适当的随机公式，其中网络的不可观察部分被建模为 Erdős-Rényi 随机图，而可观察的子网络则是任意的。这项工作的主要结果是确定，在这种情况下，局部断层扫描实际上很有可能，前提是满足网络模型的某些条件（如网络组合矩阵的稳定性和对称性）。值得注意的是，这样的结论是在低可观察性的情况下建立的，其中可观察子网的基数是固定的，而整个网络的规模扩展到无穷大。