Collaborative Research: Interface of Probability and Statistics for High-dimensional Inference

合作研究：高维推理的概率统计接口

• 批准号: 1406279
• 负责人: Tiefeng Jiang
• 金额: $ 28万
• 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: 2014
• 资助国家: 美国
• 起止时间: 2014-08-01 至 2019-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1406279&HistoricalAwards=false
• 关键词: Collaborative; Research; Interface; Probability; Statistics

With rapid advances in information and technology, big data are now routinely collected in many frontiers of scientific research and technological developments. Various advanced techniques are needed to address the challenges such as computation, noise accumulation, and spurious correlations prominently featured in big data. New theoretical challenges arise in order to address probabilistic problems in high-dimensional statistics. This collaborative research project intends to combine the strength and expertise on probability and statistics of both investigators to address a number of emerging and challenging issues in high-dimensional data analysis. The project will focus on primarily two types of problems: (i) high-dimensional statistics on spheres and (ii) behaviors of eigenvalues of random matrices and zeroes of polynomials. The two topics are innately related since high-dimensional data are often expressed in terms of matrices. The project would create new theories and methods for high-dimensional statistics, interact and apply them to several different disciplines including mathematics, statistical physics, information theory, and computer science. The project also involves training of top notch mathematical scientists and engineers and to disseminate the research results and products broadly via the online media, conferences and seminar presentations.

随着信息和技术的快速发展，大数据现在在科学研究和技术发展的许多前沿领域都被定期收集。需要各种先进的技术来解决大数据中突出的计算、噪声积累和虚假相关等挑战。为了解决高维统计中的概率问题，出现了新的理论挑战。这个合作研究项目旨在结合联合收割机的力量和专业知识的概率和统计的调查，以解决一些新兴的和具有挑战性的问题，在高维数据分析。该项目将主要关注两类问题：（i）球面上的高维统计和（ii）随机矩阵的特征值和多项式零点的行为。这两个主题是天生相关的，因为高维数据通常用矩阵表示。该项目将为高维统计创建新的理论和方法，并将其应用于包括数学，统计物理，信息论和计算机科学在内的几个不同学科。该项目还包括培训顶尖的数学科学家和工程师，并通过在线媒体、会议和研讨会演讲广泛传播研究成果和产品。