Integrative Multivariate Analysis of Multi-View Data

多视图数据，或测量与单一主题相关的几个不同但相互关联的特征集，可能从一系列来源收集，在工程和科学研究领域变得越来越普遍。该项目创新了新的方法、统计理论和可扩展的计算工具，以解决多视图数据的一系列统计学习问题。该项目对多视角数据生成机制进行综合统计分析，将使我们能够利用从不同镜头和不同角度获得的信息，获得对现实世界现象的非凡见解。PI将开发几种降阶矩阵结构的推广，以实现多视图学习的多元统计方法。约秩估计的一般方法是现代多变量分析中最关键的组成部分之一。然而，对于处理多视图数据，降阶方法的潜力还远远没有被充分实现或理解。本项目提出了以下总体目标：(1)开发用于联合学习的综合多元回归，这需要利用多组特征来构建多元响应的综合预测模型；(2)通过探索多组特征之间的共享低维关联结构和开发多元响应的连贯预测模型，发展共享学习的综合典型相关分析；(3)通过利用高维矩阵对象的子矩阵之间的全局和局部低维结构，发展多尺度学习的综合降维；(4)制定稳健学习的诊断措施，这将实现可靠的多视图数据集成和数据质量评估。

Multi-view data, or the measuring of several distinct yet interrelated sets of characteristics pertaining to a single set of subjects and possibly collected from an array of sources, has become increasingly common in the fields of engineering and scientific research. This project innovates new methodologies, statistical theories, and scalable computational tools to tackle a range of statistical learning problems with multi-view data. An integrated statistical analysis of the multi-view data generation mechanisms, enabled by this project, will allow us to gain extraordinary insight of real-world phenomena by utilizing information obtained from different lenses and from different angles. The PI will develop several generalizations of the reduced-rank matrix structure, to enable a spectrum of multivariate statistical methods for multi-view learning. The general methodology of reduced-rank estimation is one of the most critical ingredients in modern multivariate analysis. However, for handling multi-view data, the potential of the reduced-rank methodology is far from being fully realized or understood. This project presents the following overarching objectives: (1) develop integrative multivariate regression for joint learning, which entails the exploitation of multiple sets of features to build an integrated predictive model of multivariate response; (2) develop integrative canonical correlation analysis for shared learning, by combining the exploration of shared low-dimensional association structures between multiple sets of features and the development of coherent predictive models for multivariate response; (3) develop integrative dimension reduction for multi-scale learning, by utilizing both the global and local low-dimensional structures among sub-matrices of a high-dimensional matrix object; (4) develop diagnostic measures for robust learning, which would enable reliable multi-view data integration and data quality assessment.