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

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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.