Statistical learning with high-dimensional structured data: a regularized boosting approach

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The proposed project aims to develop new statistical learning theories and methodologies for the analysis of high-dimensional data with complex structures. The central problem is how to effectively incorporate the a priori information on data structures to reduce statistical uncertainty in high-dimensional learning. In particular, the PI will investigate: a) a novel general framework based on regularized boosting for flexible high-dimensional modeling adaptive to data structures, and the associated learning theory; b) a new regularized boosting method that performs bi-level variable selection in presence of grouping structures in the predictors; c) a new boosting method for function estimation and subnetwork selection in presence of graphical structures in the predictors.With advances of technology, high-dimensional data analysis becomes increasingly important in various scientific disciplines, including genomics, medicine, engineering, environmental studies, and economics. Conventional statistical methods suffer from the high-dimension, low sample size, as well as the high correlation among these data. For such ill-posed problems, it is crucial to incorporate the complementary a priori structural knowledge in data analysis in order to achieve more robust models and more consistent discoveries. For example, in many genomic researches, the information on data structures, such as grouping or graphical structures of the genes, are widely available in forms of gene pathways and regulatory networks. The investigator's work will contribute new statistical methods and computational tools, in forms of free software, to efficiently integrate these structural information in high-dimensional modeling. It will facilitate the analysis of high-dimensional data to achieve a substantial improvement on predictive accuracy, as well as to build more stable and interpretable models. It will also promote collaborations between statisticians and scientists from other fields. Moreover, the proposed project includes an educational program that involves development of new courses, mentoring undergraduate and graduate students and exposing them to the state-of-the-art research in this project.