Flexible Statistical Modelling for High Dimensional Data

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Scientific and technology innovations have made massive high-dimensional data ubiquitous in various fields, such as biological science, medical studies, public health, social sciences, e-commerce, finance, climate studies, and so on. During the past decade statisticians have developed a rich collection of new tools for high-dimensional statistical modeling. Despite these important advances, there are still many challenges and open problems to be dealt with in high-dimensional data analysis. Their solutions require innovative ideas and techniques to handle the methodological, computational and theoretical challenges. The goal of this research is to develop mathematically solid and computationally efficient methods to address these pressing and important inferential challenges. This research consists of three projects. The first project concerns measurement errors in high-dimensional M-estimation. The PI will study a new unified convex approach to solve the error-in-variables penalized M-regression including Huber regression, logistic regression, quantile regression, and the support vector machine. In the second project the PI will establish a new inference tool named composite M-estimation and demonstrate its applications in high-dimensional learning. In the third project the PI will study a flexible heterogeneity pursuit method for understanding the heterogeneity effects in high-dimensional data. Software packages will be created to make the new methods readily available to other researchers and practitioners.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.