CAREER: New Statistical Methodology and Theory for Mining High-Dimensional Data

高维建模领域发展迅速。本研究旨在推动这些发展，以应对不同领域出现的新挑战。特别是，研究人员研究（a）。用于将高维数据集映射到具有低得多的维度的空间上同时确保最小失真的新统计方法和理论;（B）.半参数模型中的有效和稳健的变量选择;（c）.一种新的正则化方法，用于非参数模型选择和估计。现代计算能力和科学创新使科学家能够轻松收集各个学科的高维数据。高维数据的分析给统计人员带来了许多挑战，也提供了巨大的机遇。高维数据的可用性重塑了统计建模。该提案侧重于从高维数据中进行知识发现和信息检索的新统计方法和理论。调查人员计划开发便于使用的计算机程序供公众使用。该研究也将对统计学以外的领域做出重大贡献，包括生物学、计算机科学、生物医学工程、医学信息学、经济学等。综合教育计划包括大量的举措，将涉及本科生和研究生，并使他们接触到与提案相关的主题的最先进的研究。其中包括新的课程、讲习班和辅导。研究成果将被整合到K-12教育中，并应用于工业研究。

The area of high-dimensional modeling is developing rapidly. This research aims to push these developments forward to meet new challenges arising in different fields. In particular, the investigator studies (a). new statistical methodology and theory for mapping high-dimensional datasets onto a space with much-lower dimensions while assuring minimum distortion; (b). efficient and robust variable selection in semiparametic models; (c). a novel regularization approach to nonparametric model selection and estimation.Modern computing power and scientific innovations allow scientists to easily collect high-dimensional data in various disciplines. Analysis of high-dimensional data poses many challenges and offers great opportunities to statisticians. The availability of high-dimensional data has reshaped statistical modeling. This proposal focuses on new statistical methodology and theory for knowledge discovery and information retrieval from high-dimensional data. The investigator plans to develop User-friendly computer programs for public use. The research will make significant contributions to areas outside statistics as well, including biology, computer science, biomedical engineering, medical informatics, economics, and so on. The integrated educational program includes substantial initiatives that will involve undergraduate and graduate students and expose them to state-of-the-art research in the topics related to the proposal. These include new courses, workshops and mentoring. The research results will be integrated into K-12 education and be applied to industrial research.