Random Matrix Theory and High Dimensional Statistics

随机矩阵理论和高维统计

• 批准号: 1209166
• 负责人: Tiefeng Jiang
• 金额: $ 18万
• 依托单位: University of Minnesota-Twin Cities
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1209166&HistoricalAwards=false
• 关键词: Random; Matrix; Theory; Dimensional; Statistics

High dimensional data are becoming increasingly available from a wide range of scientific investigations, including genomics, bioinformatics, engineering, and climate studies. Sound analysis of such datasets poses many statistical challenges. It calls for new statistical theory and methods as well as new technical tools. In this collaborative research project, the investigators will first develop results and technical tools in random matrix theory and then take a unified approach using the technical tools developed to study several important problems in high dimensional statistics as well as applications in signal processing, physics, and mathematics. The statistical and scientific objectives outlined in this proposal are interdisciplinary and will establish connections among different fields - random matrix theory, high dimensional statistics, signal processing, physics, and mathematics. The research will also provide technical tools as well as methodology, to researchers in other scientific fields who collect and analyze high dimensional data. These include, but are not limited to, genomics, biostatistics, and electrical engineering. The procedures and algorithms developed in this project will be implemented and softwares developed will be made freely and publicly available on the web as open sourcecode along with the associated research reports so as to facilitate the dissemination of knowledge.

高维数据越来越多地可从广泛的科学调查中获得，包括基因组学，生物信息学，工程和气候研究。对这类数据集的合理分析带来了许多统计挑战。它需要新的统计理论和方法以及新的技术工具。在这个合作研究项目中，研究人员将首先开发随机矩阵理论的结果和技术工具，然后使用开发的技术工具采取统一的方法来研究高维统计中的几个重要问题以及在信号处理，物理和数学中的应用。该提案中概述的统计和科学目标是跨学科的，并将在不同领域-随机矩阵理论，高维统计，信号处理，物理和数学之间建立联系。该研究还将为收集和分析高维数据的其他科学领域的研究人员提供技术工具和方法。这些包括，但不限于，基因组学，生物统计学和电气工程。该项目开发的程序和算法将得到实施，开发的软件将作为开放源代码沿着相关研究报告在网上免费公开，以促进知识的传播。