Online detection of changes in the latent structure of network models

网络价值数据，也就是可以由一组连接节点表示的数据，在许多领域都会遇到，比如在社交网络、消息传递服务或计算机网络的建模中。我们可以用这样的框架来模拟城市地区出租自行车的使用。通过节点，我们简单地引用感兴趣的对象。例如，在社交网络的上下文中，节点可能代表用户的个人资料页面，或者在可租赁自行车设置中，节点将是下车/收集点。通常，在这些网络中存在一个潜在的、未被观察到的动态结构。例如，考虑使用公司网络流量的网络模型来检测黑客行为的任务，其中节点表示物理计算机，而边缘表示这些计算机之间的连接。这些节点之间存在着一种潜在的、但关键是未被观察到的群体结构，它决定了它们如何相互作用。由于这种结构是未观察到的，我们无法获得描述它的直接数据，而必须从相互作用中推断出来。随着网络流量随着时间的推移而变化，我们希望能够动态地观察节点的推断潜在组结构的变化，因为这些变化将反映一个或多个节点的行为变化，这些变化可以作为恶意行为的警告信号。我们把群体结构中的这种进化称为变化点。存在建模网络价值数据的方法，此外，还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即实时检测网络数据变化点的文献。在这个项目中，我们提出了一种新的方法，用于以统计鲁棒性和计算效率高的方式动态检测网络模型中这些未观察到的变化。我们的目标是了解网络价值数据结构变化的数学性质，并根据我们对这种检测到的变化的实时置信度调整我们的算法。该项目属于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.