Big Data Program
High-dimensional multivariate data is commonly encountered nowadays in a variety of disciplines, including genomics, finance and economics, information technology systems, and biomedical engineering. Understanding the structure of and uncovering relationships among variables measured by these data will have crucial impacts in the corresponding scientific areas.
Though some heuristic algorithms and intuitive methods have been designed for and widely applied in both industrial and scientific applications, as of now, our understandings of them are still limited. The advances of random matrix theory provide a tool set for researchers to study behaviors of many practical algorithms. For example, establishing estimation rates of the algorithms of interest is very helpful in understanding when they should be used in practice.