Spectral embedding methods and subsequent inference tasks on dynamic multiplex graphs

所提出的研究集中在动态多路图(DMPGs)的统计分析上。从数学上讲，图也称为网络，可以被解释为节点的集合，边出现在节点之间。网络数据被收集在许多领域，如医疗保健、生物和网络安全，并且它们正变得越来越丰富，不断产生新的研究问题。特别是，动态多路传输网络正在成为现实世界应用中日益常见的数据结构。在DMPG中，边可以有不同的类型，并且随着时间的推移而演变。例如，在企业计算机网络中，节点可以由主机表示，而边对应于它们之间的连接，随着时间的推移在不同的端口上动态发生。由于这类对象的复杂性，对DMPG的统计建模研究只触及了皮毛。因此，需要开发新的统计方法，本研究旨在弥补这一差距，为DMPG开发现实的统计模型。本研究方案的目的是开发原则性和可扩展性的统计模型，以表示动态多路复用图的全部多层复杂性。这一目标将通过利用从光谱方法到主题建模的一系列统计技术来实现。特别是，这项研究建议集中在发现网络中的低维子结构的技术，即众所周知的嵌入方法。这样的技术还有帮助后续推理任务的额外好处，例如具有相似行为的节点的集群。将仔细评估为DMPG提出的新嵌入方法的统计特性，并将利用所提出的方法来改进和扩展现有的用于聚类、链接预测和异常检测的模型。此外，拟议的模型将具有灵活性，可以包含以协变量形式提供的关于节点和边的额外信息。特别是，这项研究提案将侧重于将文本等非结构化数据纳入拟议的建模框架，结合网络分析和自然语言处理的各个方面。

The proposed research is centred around statistical analysis of dynamic multiplex graphs (DMPGs). Mathematically, a graph, also known as network, can be interpreted as a collection of nodes, with edges occurring between them. Network data are collected in many domains, such as healthcare, biology, and cyber-security, and they are becoming increasingly rich, continuously generating new research questions. In particular, dynamic multiplex networks are emerging as increasingly common data structures observed in real-world applications. In DMPGs, edges could have different types, and evolve in time. For example, in an enterprise computer network, nodes could be represented by hosts, and edges correspond to connections between them, occurring dynamically over time on different ports. Because of the complexity of such objects, research has only scratched the surface with statistical modelling for DMPGs. Therefore, the development of novel statistical methodology is required, and this research intends to bridge this gap, developing realistic statistical models for DMPGs.The aim of this research proposal is to develop principled and scalable statistical models which represent the full multi-layered complexity of dynamic multiplex graphs. This goal will be achieved by exploiting an array of statistical techniques, spanning from spectral methods to topic modelling. In particular, this research proposal focusses on techniques for discovering low-dimensional substructure in networks, known as embedding methods. Such techniques have the added benefit of aiding subsequent inference tasks, such as clustering of nodes with similar behaviour. The statistical properties of novel embedding methods proposed for DMPGs will be carefully assessed, and the proposed methods will be utilised to improve and extend existing models for clustering, link prediction, and anomaly detection. In addition, the proposed models will have the flexibility to encompass additional information on nodes and edges, available in the form of covariates. In particular, this research proposal will focus on incorporating unstructured data, such as text, within the proposed modelling frameworks, combining aspects from network analysis and natural language processing.