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

拟议的项目旨在开发新的统计学习理论和方法，用于分析具有复杂结构的高维数据。中心问题是如何有效地结合数据结构的先验信息，以减少高维学习中的统计不确定性。特别是，PI将研究：a)基于正则化Boosting的新的通用框架，用于适应数据结构的灵活的高维建模，以及相关的学习理论；b)新的正则化Boost方法，在预测器中存在分组结构的情况下执行双层变量选择；c)在预测器中存在图形结构的情况下，用于函数估计和子网络选择的新Boost方法。随着技术的进步，高维数据分析在各种科学领域中变得越来越重要，包括基因组学、医学、工程学、环境研究和经济学。传统的统计方法存在高维、低样本量以及这些数据之间的高度相关性的问题。对于这类不适定问题，将互补的先验结构知识结合到数据分析中是至关重要的，以实现更健壮的模型和更一致的发现。例如，在许多基因组研究中，关于数据结构的信息，如基因的分组或图形结构，以基因通路和调控网络的形式广泛存在。研究人员的工作将以自由软件的形式贡献新的统计方法和计算工具，以有效地将这些结构信息整合到高维建模中。它将促进对高维数据的分析，以实现预测精度的大幅提高，以及建立更稳定和更可解释的模型。它还将促进统计学家和其他领域科学家之间的合作。此外，拟议的项目包括一项教育计划，涉及开发新课程，指导本科生和研究生，并让他们接触到该项目中最先进的研究成果。

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.