CAREER: Statistical Learning from Data with Graph/Network Structures

职业：从具有图/网络结构的数据中进行统计学习

• 批准号: 0748389
• 负责人: Ji Zhu
• 金额: $ 40万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0748389&HistoricalAwards=false
• 关键词: CAREER; Statistical; Learning; Data; Graph

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.

该研究旨在开发新的统计方法和相关理论，将网络/图形结构纳入数据中。 这些数据在各个领域越来越普遍。 具体来说，研究者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，包括两个和多个类别的半监督分类，聚类和分类数据的分析; B）学习网络结构，处理人们有兴趣从数据中识别底层网络结构的情况; c）具有结构约束的变量选择，当变量或参数之间存在固有结构时处理变量选择。计算和测量技术的最新进展导致了在所有应用领域中收集的数据量的爆炸式增长。 这些数据大多具有复杂的结构，以文本、图像、视频、音频、流数据等形式存在，本文主要研究一类重要的问题，即具有网络或图结构的数据。 这些数据在不同的工程和科学领域中很常见，例如生物学、计算机科学、电子工程、经济学、社会学等。虽然对网络的研究已经很广泛（主要是在统计学领域之外），但其中大部分都涉及网络结构的表征和建模。 目前研究计划的目标是利用网络结构作为额外的信息，并开发考虑到数据之间关系结构的统计方法。 该研究计划将在几个领域做出重大贡献，包括统计学，生物学，计算机科学，电气工程，IOE，物理学，心理学和社会学。 教育计划还包括大量的举措，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先进的研究。 这些包括新课程，暑期研讨会，指导和软件开发。