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。大规模的网络数据和关系数据在基因组学和健康科学、经济、金融和社交媒体中经常遇到。拟议的项目将(1)加强网络和关系数据统计分析的方法和理论发展。(2)提高对社会网络社区结构的认识。这项拨款的研究将推动网络数据建模理论和方法的前沿。这些新的发展将为来自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，例如了解个人的社会行为和社会网络的动态性质。拟议的项目在大规模网络和关系数据的统计推断主题下有以下三个相互关联的目标。(1)提出了一种新的协变信息群落检测框架。已经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。这项研究的目的是研究协变量信息何时以及如何在社区发现准确性方面有所帮助。(2)提出了一种新的动态随机块模型框架及其在变点检测中的应用。随机区块模型及其变体通常是为静态网络定义的。这里的目标是定义一个动态版本的随机区块模型，清楚地解释网络如何随着时间的推移而演变。提出了一种通用的动态谱聚类方法，并建立了它的理论性质。对动态网络变点检测这一重要问题进行了详细研究。(3)引入条件依赖度量及其在无向图模型中的应用。确定支持网络依赖结构的变量或因素是非常重要的。其目标是引入一种灵活的条件依赖度量，该度量可以捕获范围广泛的不同依赖结构。PI将开发一种新的方法，通过使用所得到的条件依赖度量来生成具有所需特征的通用无向图。

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.