Network Structure Identification from Corrupt Data Streams

TL;DR

This paper investigates how data corruption affects the accuracy of network structure identification in linear time-invariant systems and Markov random fields, revealing that errors are localized around corrupted nodes.

Contribution

It provides an exact characterization of erroneous links caused by corrupt data and extends the analysis to Markov random fields, highlighting the impact of data corruption.

Findings

Erroneous links are restricted to neighborhoods of corrupted nodes in LTI systems.

Data corruption leads to spurious links in Markov random fields.

The analysis offers insights into robustness of network inference methods.

Abstract

Complex networked systems can be modeled as graphs with nodes representing the agents and links describing the dynamic coupling between them. Previous work on network identification has shown that the network structure of linear time-invariant (LTI) systems can be reconstructed from the joint power spectrum of the data streams. These results assumed that data is perfectly measured. However, real-world data is subject to many corruptions, such as inaccurate time-stamps, noise, and data loss. We show that identifying the structure of linear time-invariant systems using corrupt measurements results in the inference of erroneous links. We provide an exact characterization and prove that such erroneous links are restricted to the neighborhood of the perturbed node. We extend the analysis of LTI systems to the case of Markov random fields with corrupt measurements. We show that data corruption in Markov random fields results in spurious probabilistic relationships in precisely the locations where spurious links arise in LTI systems.