FRG: Collaborative Research: Statistical Modeling and Inference of Vast Matrices for Complex Problems

技术进步使以相对较低的成本收集和存储大量数据成为可能。因此，广泛领域的科学研究通常会产生大量数据。通常情况下，我们获得测量数据的能力超过了从中获取有用信息的能力。这些紧迫的挑战是拟议研究的最终动机。特别是，这项合作提案为一系列涉及从协方差矩阵、波动矩阵、密度矩阵到关系矩阵的大型矩阵的统计理论和方法的发展以及计算技术的发展提出了新的研究计划。过去几年，由于科学和技术的进步，数据呈爆炸式增长。随着数据存储成本的持续下降，这些大数据的关注点不可避免地从数据管理过渡到从数据中获取可操作的见解。迫切需要应对这些挑战，了解大数据对科学研究和知识发现的深刻影响。拟议的研究项目涉及在系统生物学、高频金融和量子计算等众多科技领域的前沿自然出现的新问题。因此，拟议的研究努力不仅将推动大型矩阵统计理解的最新水平，而且还将促进各个科学领域的进步和对数字革命的拥抱。

Technological advances make it possible to collect and store large data with relatively low costs. As a result, scientific studies in a wide range of fields routinely generate a massive amount of data. Oftentimes, our ability to obtain measurements outpaces our ability to derive useful information from them. These pressing challenges serve as the ultimate motivation for the proposed research. In particular, this collaborative proposal presents novel research plans on the development of statistical theory and methodologies as well as computational techniques for a host of problems involving large matrices ranging from covariance matrices, volatility matrices, density matrices to relational matrices.The past few years have witnessed an explosion of data as a result of scientific and technological advances. As data storage cost continues to fall, the focal point on these big data has been transitioning inevitably from data management towards deriving actionable insights from them. There is a pressing need to respond to these challenges and understand the profound impact of large data on scientific research and knowledge discovery. The proposed research project deals with emerging problems that arise naturally at the frontier of a multitude of scientific and technological fields such as systems biology, high-frequency finance, and quantum computing among others. As a consequence, the proposed research effort will not only push forward the state-of-the-art of statistical understanding of large matrices, but also facilitate the advancement of various scientific fields and their embracement of the digital revolution.