Statistical Methods for Data with Network Structure

计算和测量技术的最新进展导致在所有应用领域收集的数据量呈爆炸式增长。这些数据中的许多具有复杂的结构，其形式为文本、图像、视频、音频、流数据等。本课题主要研究一类重要的问题，即网络结构的数据问题。这样的数据在不同的工程和科学领域很常见，如生物学、计算机科学、电气工程、经济学和社会学。虽然已经有了关于网络的广泛研究(主要是在统计领域之外)，但大部分研究都是仅使用链接信息来描述和建模网络结构。当前研究计划的目标是利用节点特征作为附加信息，并开发既考虑链路信息又考虑节点信息的统计方法。该研究计划将在统计学、生物学、计算机科学、电气工程、物理学、心理学和社会学等多个领域做出重大贡献。该教育计划还包括大量举措，让本科生和研究生参与到与该项目相关的主题中，让他们接触到最先进的研究。研究旨在开发新的统计方法和相关理论，利用数据中的网络结构。这样的数据在各个领域变得越来越常见。具体地说，研究者的目标是研究三个不同但相关的问题：a)部分观测网络的链接预测，它处理我们观察到的网络是具有观测误差的真实网络的情况；b)具有节点特征的网络中的社区检测，它结合网络链接信息和节点上的附加信息来改进社区检测；c)学习网络结构，它处理一个人有兴趣从数据中识别底层网络结构的情况。

Recent advances in computing and measurement technologies have led to an explosion in the amounts of data that are being collected in all areas of application. Much of these data have complex structure, in the form of text, images, video, audio, streaming data, and so on. This project focuses on one important class of problems, viz, data with network structure. Such data are common in diverse engineering and scientific areas, such as biology, computer science, electrical engineering, economics, and sociology. While there has been extensive research on networks (primarily outside the field of Statistics), much of it deals with characterizing and modeling network structures using link information only. The goal of the current research program is to exploit the node features as additional information and develop statistical methods that take into account both link and node information. The research program will make significant contributions in several areas, including Statistics, Biology, Computer Science, Electrical Engineering, Physics, Psychology, and Sociology. The educational program also includes substantial initiatives that will involve undergraduate and graduate students and expose them to state-of-the-art research in the topics related to the project.The research aims to develop new statistical methodologies and associated theory that exploit the network structure in the data. Such data are becoming increasingly common in various fields. Specifically, the investigator aims to study three different but related problems: a) link prediction for partially observed networks, which deals with the situation where the network we observe is the true network with observation errors; b) community detection in networks with node features, which combines network link information and additional information on the nodes to improve community detection; c) learning network structures, which deals with the situation where one is interested in identifying the underlying network structure from the data.