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

随着最近科学数据的爆炸式增长及其前所未有的规模和复杂性，降维正在成为任何现代统计分析的核心要素。该项目旨在将降维方法与当前的统计学习技术相结合，为高维和复杂结构的现代数据提供一种全新的灵活有效的降维解决方案。从耦合，调查员建立了一个框架，降维，纳入有关变量之间的已知结构关系的先验信息。在此框架内，研究人员计划开发一系列降维解决方案，使结果更容易解释和准确。这样的框架将极大地促进神经成像，气候和基因组数据的分析，其中先前的结构信息通常是可用的。现代技术经常产生大量的数据，这样的数据洪流现在吞噬了科学和公共生活的每一个分支。因此，科学进步现在严重依赖于处理和分析复杂高维数据的能力。这些分析的核心是降低数据维度的方法，有时是显着的，通过识别一小部分重要的变量，或者获得原始测量的一些组合。该项目旨在开发一系列新颖的降维方法来解决高维数据分析中的这些紧迫挑战。这项研究预计将在两个方面做出重大贡献：使科学家能够快速有效地从海量数据中提取有用的信息，同时通过理论，方法和应用的进步使统计学科受益。

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.