Statistical Network Models: Building the Foundation

有人可能会读这篇摘要有几个原因。这可能是由于这位读者偶然发现了这个摘要，或者我们有共同的研究兴趣。总的来说，必须认识到，不同的人首先有不同的天生倾向来阅读科学成果，这可能是由于好奇心、欲望或动机的差异。很长一段时间以来，我们一直很想了解这样的社会关系是如何形成的，是什么影响了它们的形成，以及在多大程度上影响了它们。统计网络分析是一门新兴的学科，其动机是基于概率建模的观点来描述网络中固有的各种随机现象。近年来，由于包括社交媒体和复杂系统在内的各种领域的网络数据呈指数级增长，这种需求变得越来越迫切。尽管在一些特定的模型上取得了进展，但缺乏一个统一的主题，许多基础网络模型缺乏统计或推理保证。该项目首次尝试建立p1模型的统计基础，p1模型是一个规范模型，可以描述网络的几个主要特征，包括稀疏性（与可能的总边数相比，网络的边相对较少）、同质性（相似的节点比不相似的节点更有可能连接）、差异异质性（节点描述建立连接的差异倾向）、互惠（在定向网络中，连接往往是相互的）。四十年前提出的这个模型催化了几个重要的统计网络模型，但仍然缺乏理解和研究。该项目旨在通过研究几个悬而未决的问题，包括其参数估计的存在性和大样本性质，以及测试感兴趣的假设的新结果，来推进p1模型的研究。在此基础上，我们将以解释变量的形式结合上下文信息来解释社会关系的形成。该项目将成为今后一个更大的研究方案的跳板，以发展一个统一的框架来处理网络中常见的各种依赖关系结构。

There are several reasons why someone may be reading this summary. It can be due to that this reader stumbles upon this summary by chance or that we share common research interests. Overall, it must be recognised that different individuals have different innate tendency to read scientific output in the first place, perhaps due to differences in curiosity, desire, or motivation. Understanding the mechanism on how social connections like this are formed, what affect their formation and to what extent has fascinated us for a very long time. Statistical network analysis is a nascent discipline motivated by the need to describe various stochastic phenomena inherent in networks based on a probabilistic modelling perspective. This need has become increasingly pressing in recent years due to an exponential surge of networked data in a wide variety of fields including social media and complex systems. Though progress has been made on some particular models, a unifying theme is lacking with many foundational network models lacking statistical or inferential guarantees.This project presents a first attempt in building the statistical foundation for the p1 model, a canonical model that can depict several major features of a network including sparsity (a network has relatively few edges in comparison to the total possible number of edges), homophily (similar nodes are more likely to connect than dissimilar ones), differential heterogeneity (nodes depict differential tendency to make connections), and reciprocity (connections tend to be mutual in directed networks). Proposed four decades ago, this model has catalysed several important statistical network models but remains poorly understood and studied. This project aims to advance the research on the p1 model by investigating several open questions including the existence and the large-sample properties of its parameter estimates, as well as novel results for testing hypotheses of interest. Built on this advance, we will incorporate contextual information in the form of explanatory variables for explaining the forming of social ties. The project will serve as the springboard for a larger research programme in the future to develop a unified framework to deal with various dependency structures commonly seen in networks.