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

随着信息和技术的快速发展，大数据现在经常在科学研究和技术发展的许多前沿领域被收集。需要各种先进的技术来应对大数据中突出表现的计算、噪声积累和虚假关联等挑战。为了解决高维统计中的概率问题，出现了新的理论挑战。这一合作研究项目旨在结合两位研究人员在概率和统计方面的力量和专业知识，以解决高维数据分析中的一些新出现的和具有挑战性的问题。该项目将主要集中在两类问题上：(I)球面上的高维统计和(Ii)随机矩阵和多项式的零点的特征值的行为。这两个主题本质上是相关的，因为高维数据通常以矩阵的形式表示。该项目将为高维统计创造新的理论和方法，并将它们相互作用并应用于几个不同的学科，包括数学、统计物理、信息理论和计算机科学。该项目还包括培训顶尖的数学科学家和工程师，并通过在线媒体、会议和研讨会演示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.