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

随着信息技术的快速发展，大数据已经成为许多科学研究和技术发展前沿的常规数据。需要各种先进技术来解决大数据中突出的计算、噪声积累和伪相关等挑战。为了解决高维统计中的概率问题，出现了新的理论挑战。该合作研究项目旨在结合双方研究人员在概率和统计学方面的优势和专业知识，解决高维数据分析中出现的一些新兴和具有挑战性的问题。该项目将主要关注两类问题：(i)球面上的高维统计和（ii）随机矩阵和多项式零的特征值的行为。这两个主题天生相关，因为高维数据通常用矩阵表示。该项目将为高维统计创造新的理论和方法，相互作用并将其应用于几个不同的学科，包括数学、统计物理、信息论和计算机科学。该项目还包括培训顶尖的数学科学家和工程师，并通过网络媒体、会议和研讨会报告广泛传播研究成果和产品。

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.