Online detection of changes in the latent structure of network models

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Network-valued data, which is to say data that can be represented by a collection of connectednodes, are encountered in many domains, such as in the modeling of social networks, messagingservices, or computer networks. One can model the use of rentable bikes in urban areas using such aframework. By a node, we simply refer to an object of interest. In the context of social networks, forexample, a node may represent a user's profile page, or in the rentable bikes setup, a node would bea drop-off/collection point.Often, there exists an underlying, unobserved, and dynamic structure within these networks. Forexample, consider the task of detecting hacking using a network model of a company's networktraffic, where nodes represent physical computers, and edges represent connections between thosecomputers. An underlying, but crucially unobserved, group structure will exist between those nodes,dictating how they interact. As this structure is unobserved, we cannot obtain direct data describingit but must instead infer it from the interactions. As the network traffic evolves over time, we wantto be able to dynamically observe changes in the inferred latent group structure of the nodes, aschanges will reflect behavioral changes of a node or nodes, which could be used as a warning signof malicious behavior. We refer to such evolution in the group structure as a change point.Methodology exists for modeling network-value data, and furthermore, there is work on findingchange points within these networks. However, there is no existing literature on detecting changepoints in network data online, that is to say, in real-time. In this project, we propose a novelmethodology for detecting these unobserved changes in network models on the fly in a statisticallyrobust and computationally efficient manner. We aim to understand the mathematical properties ofchanges to the structure of network-valued data, and to adjust our algorithm inline with our real timeconfidence in such a detected change.This project falls within the EPSRC Mathematical Sciences research area.