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.