Collaborative Research: New Statistical Methods and Theory for High-Dimensional Data

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High-dimensional data have become ubiquitous in this big-data era. In recent years, many statistical methods and theory have been developed for analyzing high-dimensional data with successful applications in practice. There are still many challenges and open problems to be addressed. Their solutions call for innovative ideas. The proposed research projects are motivated by real applications where the current state-of-the-art high-dimensional data analytic methods fail to deliver good solutions. The research results will be directly applicable in various fields such as genomics, medical imaging, public health, social networks, E-commerce, and among others. For example, methods developed in this proposal will enable us to better understand how a social network evolves and how brain functions change with age. The research results will be disseminated through journal publications, conference presentations and seminar talks. This proposal has an education program that contributes to the education and training of the next-generation statisticians.In this project novel statistical methods and theory are proposed to study three important topics of large-scale statistical inference: (a) dynamic graphical models and latent graphical models, (b) high-dimensional regression with noisy and corrupted data, and (c) profile matrix inference in structural pursuit. The investigators will develop innovative techniques to handle the methodological, computational and theoretical challenges. The research results will not only provide new powerful data analytic tools for solving open problems in (a), (b) and (c), but also shed light on general principles for statistical learning from complex high-dimensional data. In order to make the research outcomes readily available to other researchers and practitioners, the investigators will implement the methodology developed in this proposal into software packages that will be publicly distributed.