New Dimension Reduction Approaches for Modern Scientific Data with High Dimensionality and Complex Structure

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With the recent explosion of scientific data, and its unprecedented size and complexity, dimension reduction is becoming a central ingredient in any modern statistical analysis. This project aims to couple dimension reduction methodology with current statistical learning techniques, which results in an entirely new class of flexible and effective dimension reduction solutions for modern data with both high dimensionality and complex structure. From the coupling, the investigator establishes a framework for dimension reduction that incorporates prior information regarding the known structural relationships between the variables. Within this framework, the investigator plans to develop a family of dimension reduction solutions so that the results are more readily interpretable and accurate. Such a framework is to greatly facilitate the analysis of neuroimaging, climate, and genomic data where prior structural information is often available. Modern technologies routinely produce massive amounts of data and such a data deluge now engulfs every branch of science and public life. As a result, scientific progress now heavily depends on the ability to process and analyze complex high-dimensional data. At the heart of these analyses are methods that reduce the dimensionality of the data, sometimes dramatically, by identifying a small set of variables that are important, or obtaining a few combinations of the original measurements. This project aims to develop a host of novel dimension reduction methods to address these pressing challenges in high-dimensional data analysis. The proposed research is expected to make significant contributions on two fronts: enabling scientists to quickly and effectively extract useful information from massive data, and at the same time, benefiting the discipline of statistics with advances in theory, methods and applications.