CAREER: Statistical inference of network and relational data

技术创新是推动科学研究和社会进步的主要力量。在基因组学和健康科学、经济学、金融和社交媒体中经常遇到大规模网络数据和关系数据。拟议的项目将(1)加强网络和相关数据统计分析的方法和理论发展。(2)推进了对社会网络社区结构的认识。这项资助的研究将推动网络数据建模理论和方法的前沿。这些新进展将为不同科学和人文领域的研究人员提供对大规模网络数据的更好理解，例如，理解个体的社会行为和社会网络的动态性质。在大规模网络和相关数据的统计推断主题下，提出的项目有以下三个相互关联的目标。(1)引入一种基于协变量信息的社区检测新框架。已有许多现有的社区检测方法。然而，它们大多侧重于分析网络，而没有考虑协变量信息，这对于实现更高的社区检测精度是有价值的。本研究的目的是研究协变量信息何时以及如何帮助社区检测准确性。(2)建立一种新的动态随机块模型框架，并将其应用于变化点检测。随机块模型及其变体通常是针对静态网络定义的。这里的目标是定义随机块模型的动态版本，并清楚地解释网络如何随时间演变。提出了一种通用的动态谱聚类方法，并建立了该方法的理论性质。详细研究了动态网络变化点检测这一重要问题。(3)在无向图模型中引入一种条件依赖度量。确定强调网络依赖结构的变量或因素具有重要意义。我们的目标是引入一个灵活的条件依赖度量，它可以捕获各种不同的依赖结构。PI将开发一种新方法，通过使用所得到的条件依赖度量来生成具有理想特征的一般无向图。

Technological innovations have provided a primary force in advancement of scientific research and in social progress. Large scale network data and relational data are frequently encountered in genomics and health sciences, economics, finance and social media. The proposed project will (1) enhance methodological and theoretical developments for statistical analysis of network and relational data. (2) advance the understanding of the community structure of social network. The research emanating from this grant will advance the frontiers of theory and methods for network data modeling. The new developments will provide better understandings of large scale network data for researchers from diverse fields of sciences and humanities, e.g., understanding the social behavior of individuals and the dynamic nature of social network.The proposed project has the following three interrelated objectives under the theme of statistical inference for large scale network and relational data. (1) To introduce a new framework for community detection with covariate information. There have been many existing approaches to community detection. However, a majority of them focus on analyzing the network without considering the covariate information, which could be valuable for achieving greater accuracy of community detection. The goal of this research is to study when and how will covariate information help in terms of the community detection accuracy. (2) To develop a new dynamic stochastic block model framework with applications in change point detection. The stochastic block model along with its variants are usually defined for a static network. The goal here is to define a dynamic version of the stochastic block model, with a clear interpretation of how the network evolves over time. A general dynamic spectral clustering method will be proposed and its theoretical properties established. The important problem of change point detection of the dynamic network will be studied in details. (3) To introduce a conditional dependency measure with applications in undirected graphical models. It is of fundamental interest to ascertain variables or factors underlining the network dependency structure. The goal is to introduce a flexible conditional dependency measure, which can capture a wide range of different dependency structures. The PI will develop a new method for generating a general undirected graph with desirable features by making use of the resulting conditional dependency measure.