CAREER: Statistical Learning from Data with Graph/Network Structures

这项研究的目的是开发新的统计方法和相关理论，将网络/图表结构纳入数据。这样的数据在各个领域变得越来越常见。具体地说，研究人员研究了三个不同但相关的问题：a)通过随机游走的网络统计学习，包括两类和多类的半监督分类、聚类和分类数据分析；b)学习网络结构，它处理人们对从数据中识别潜在网络结构的感兴趣的情况；c)结构约束变量选择，当变量或参数之间存在内在结构时，处理变量选择。最近计算和测量技术的进步导致了所有应用领域收集的数据量的爆炸性增长。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。这个建议集中在一类重要的问题上，即具有网络或图结构的数据。这样的数据在生物、计算机科学、电气工程、经济学、社会学等不同的工程和科学领域中很常见。虽然已经有了关于网络的广泛研究(主要是在统计学领域之外)，但其中大部分涉及网络结构的特征和建模。目前研究方案的目标是利用网络结构作为附加信息，并开发考虑到数据之间关系结构的统计方法。该研究计划将在统计学、生物学、计算机科学、电气工程、IOE、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的倡议，将涉及本科生和研究生，并使他们接触到与提案相关的主题的最新研究。其中包括新课程、暑期工作坊、指导和软件开发。

The research aims to develop new statistical methodologies and associated theory that incorporate the network/graph structure in the data. Such data are becoming increasingly common in various fields. Specifically, the investigator studies three different but related problems: a) statistical learning on networks via random walks, which includes semi-supervised classification for two and multiple classes, clustering, and analysis of categorical data; b) learning network structures, which deals with the situation where one is interested in identifying the underlying network structure from the data; c) variable selection with structural constraints, which deals with variable selection when there is inherent structure among the variables or parameters.Recent advances in computing and measurement technologies have led to an explosion in the amount 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 proposal focuses on one important class of problems, viz, data with network or graph structure. Such data are common in diverse engineering and scientific areas, such as biology, computer science, electrical engineering, economics, sociology and so on. While there has been extensive research on networks (primarily outside the field of Statistics), much of it deals with characterizing and modeling network structures. The goal of the current research program is to exploit the network structure as additional information and develop statistical methods that take into account the structure of relationships between the data. The research program will make significant contributions in several areas, including Statistics, Biology, Computer Science, Electrical Engineering, IOE, 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 proposal. These include new courses, summer workshops, mentoring, and software development.