Online detection of changes in the latent structure of network models

网络值数据，也就是说可以由连接节点的集合表示的数据，在许多领域中遇到，例如在社交网络、消息服务或计算机网络的建模中。人们可以用这种模型来模拟城市地区可租赁自行车的使用。通过一个节点，我们只是指一个感兴趣的对象。例如，在社交网络中，一个节点可能代表用户的个人资料页面，或者在可租赁自行车的设置中，一个节点可能是一个下车/集合点。例如，考虑使用公司网络流量的网络模型来检测黑客攻击的任务，其中节点表示物理计算机，而边表示这些计算机之间的连接。一个潜在的，但关键是未观察到的群体结构将存在于这些节点之间，决定它们如何相互作用。由于这种结构是未观察到的，我们不能获得描述它的直接数据，而是必须从相互作用中推断出它。随着网络流量随时间的推移而演变，我们希望能够动态观察节点的推断潜在组结构的变化，因为变化将反映节点或节点的行为变化，这可以用作恶意行为的警告信号。我们把这种群体结构的演变称为变化点。存在着对网络价值数据建模的方法，而且，也有在这些网络中寻找变化点的工作。然而，目前还没有关于在线检测网络数据中的变点的文献，也就是说，实时检测。在这个项目中，我们提出了一种新颖的方法来检测这些未观察到的变化，在飞行中的网络模型，在一个approsticallyrobust和计算效率的方式。我们的目标是了解网络值数据结构变化的数学特性，并根据检测到的变化调整我们的算法。该项目福尔斯EPSRC数学科学研究领域。

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.