Statistical Theory and Methods to Transform our Understanding of Network Data

这项研究的主要主题是将网络作为统计数据对象进行研究。网络是我们现代世界的基础：它们出现在整个科学和社会中，并在规模、复杂性和重要性上继续增长。每当我们观察实体和它们之间的关系时，我们就有效地定义了某种网络。作为由节点和链接组成的结构对象，网络在数学、科学和工程中发挥着强大而明确的作用。然而，作为由测量集合组成的统计对象，网络数据集需要在数学知识方面取得重大进展，才能实现基本理解。问题的关键在于在复杂性和简约性之间找到适当的平衡。目前，我们完全从数学角度理解的网络模型过于简单，无法准确描述现代数据。与此同时，丰富到足以提供准确描述的模型目前超出了我们的数学理解范围，这意味着我们不能使用它们从数据中得出可靠和可重复的结论。这种根本性的缺乏理解减缓了科学进步，并影响到每一个依赖于网络数据分析的经济、社会或其他决策。因此，这项研究的主要目标有两个：第一，发展将网络作为数据对象正确看待和解释所需的新统计理论；第二，将该理论转化为新的统计方法，使我们能够对现实世界中的网络数据进行建模和推断。这些目标反映了这样一个事实，即网络建模和推理是一个具有重大国家重要性的领域。它跨越了许多不同的领域和背景，在这些领域和背景下，必须根据对实体及其之间的关系或相互作用的衡量来得出和证实推论。随着网络的规模和复杂性的增长，我们使用现代统计方法对其进行分析的能力面临着跟不上步伐的严重风险。研究金申请者最近的理论突破在回答这一领域长期悬而未决的问题方面取得了初步进展，创造了一个直接和直接的机会，弥合我们了解网络数据的需求和我们做到这一点的能力之间的根本和日益扩大的差距。这样做将为英国提供独特的能力，在这一领域的国际前沿引领研究发展。这项研究将提供一套核心的统计基础，为彻底改革网络建模和推理提供强大的理论基础和实践工具。这项工作将在伦敦大学学院统计科学系进行，并将与来自大学内部以及学术界和业界伙伴的专题专家合作。所开发的方法将应用于一系列重要的实际问题，以便在开发过程中对其进行评估、改进和改进。这将提供一条直接影响的途径，并在即将取得的数学进步和这些进步将受益的重要实际问题之间建立紧密的耦合。它还将开辟与网络发挥关键作用的其他学科的新的数学联系，如生命科学，并直接导致新技术，这些新技术在一系列重要的实际应用中影响研究用户，这些应用直接影响英国民众的健康、安全和经济竞争力。

The principal subject of this research is the study of networks as statistical data objects. Networks are fundamental to our modern world: they appear throughout science and society, and continue to grow in size, complexity and importance. Whenever we observe entities and relationships between them, we effectively define a network of some sort. As structural objects composed of nodes and links, networks play a strong and well defined role across mathematics, science and engineering. As statistical objects made up of collections of measurements, however, network datasets require significant advances to be made in mathematical knowledge if we are to achieve fundamental understanding.The crux of the problem, and the essence of the approach to be undertaken in this research, lies in finding the right balance between complexity and parsimony. Currently, the network models that we understand fully from a mathematical viewpoint are too simple to accurately describe modern data. At the same time, models sufficiently rich to provide accurate descriptions are presently beyond our mathematical comprehension, meaning that we cannot use them to draw sound and repeatable conclusions from data. This fundamental lack of understanding slows scientific progress and affects every single economic, social or other policy decision that relies on the analysis of network data.The main objectives of this research are therefore twofold: first, to develop the new statistical theory needed to view and interpret networks properly as data objects; and second, to transform this theory into new statistical methods that will allow us to model and draw inferences from network data in the real world. These objectives reflect the fact that network modelling and inference is an area of significant national importance. It spans the many diverse fields and contexts where inferences must be drawn and substantiated based on measurements of entities and the relationships or interactions between them.As networks grow in size and complexity, our ability to analyse them using modern statistical methods is at severe risk of failing to keep pace. Recent theoretical breakthroughs by the fellowship applicant have provided initial headway towards answering longstanding open questions in this area, creating an immediate and direct opportunity to close the fundamental and growing gap between our need to understand network data and our ability to do so. Doing so will provide the UK with a unique capability to lead research developments at the international forefront of this area.This research will deliver a core set of statistical fundamentals that provide both the strong theoretical underpinnings and the practical tools required to revolutionise network modelling and inference. The work will be carried out in the Department of Statistical Science, University College London, and will involve collaborations with subject matter experts drawn both from within the University and from across the academic community and industry partners.The methods developed will be applied to a range of important practical problems, so that they may be assessed, refined and improved while under development. This will provide a direct pathway to impact and establish a tight coupling between the mathematical advancements to be achieved and the important practical problems that these advancements will benefit. It will also open up new mathematical connections with other disciplines where networks play a key role, such as the life sciences, and lead directly to new techniques that impact research users across a range of important practical applications that directly affect the health, security and economic competitiveness of the UK populace.