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。 大规模网络数据和关系数据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。 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)促进对社会网络社区结构的理解。这项资助的研究将推进网络数据建模理论和方法的前沿。 新的发展将为来自不同科学和人文领域的研究人员提供更好的大规模网络数据理解，例如，理解个人的社会行为和社会网络的动态本质。在大规模网络和关系数据的统计推断的主题下，拟议的项目有以下三个相互关联的目标。(1)介绍一种新的基于协变量信息的社区发现框架。有许多现有的社区检测方法。然而，他们中的大多数人专注于分析网络，而不考虑协变量信息，这可能是有价值的，以实现更高的准确性社区检测。本研究的目标是研究协变量信息何时以及如何有助于社区检测准确性。 (2)发展一种新的动态随机块模型框架，并应用于变点检测。随机块模型沿着及其变体通常是针对静态网络定义的。这里的目标是定义一个动态版本的随机块模型，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深入研究。 (3)介绍了一种条件依赖测度及其在无向图模型中的应用。确定网络依赖结构的变量或因素具有根本意义。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将开发一种新的方法，通过使用所产生的条件依赖性度量来生成具有所需特征的一般无向图。

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.