Collaborative Research: Penalization Methods for Screening, Variable Selection and Dimension Reduction in High-Dimensional Regression via Multiple Index Models

合作研究：通过多指标模型进行高维回归筛选、变量选择和降维的惩罚方法

• 批准号: 1107047
• 负责人: Yu Michael Zhu
• 金额: $ 5万
• 依托单位: Purdue University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-15 至 2014-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1107047&HistoricalAwards=false
• 关键词: Collaborative; Research; Penalization; Methods; Screening

The project aims to develop effective penalization methods for screening, dimension reduction, and variable selection in high dimensional regression. The investigators focus mainly on multiple index models, because this type of models combines the strengths of linear and nonparametric regression while avoiding their drawbacks. A novel penalization approach is employed for model fitting, which regularizes both the parametric and nonparametric components of a multiple index model. A pilot study shows that this approach is more advantageous than other existing ones. When facing ultra-high dimensionality, the investigators use a forward variable screening procedure to reduce the dimension to a manageable size before applying the proposed penalization. The investigators plan to study the theoretical properties of this approach and develop fast and efficient computing algorithms for its implementation. The proposed approach is further extended to applications involving categorical responses or random effects.Advances in science and technology have led to an explosive growth of massive data across a variety of areas such as bioinformatics, climate research, internet, etc. Traditional statistical methods for clustering, regression and classification become ineffective when dealing with a large number of variables. Lately, a tremendous amount of research effort has been dedicated to the development of statistical methods such as dimension reduction and variable selection for analyzing this type of massive data. The investigators join the effort by proposing a novel penalization approach and developing efficient computing algorithms. The results from this project not only advance statistical research but also help other scientists and researchers better understand and analyze their massive data and hence enhance their scientific discovery.

该项目旨在在高维回归中开发有效的筛查，降低维度和可变选择的惩罚方法。研究人员主要关注多个索引模型，因为这种类型的模型结合了线性和非参数回归的优势，同时避免了它们的缺点。模型拟合采用了一种新颖的惩罚方法，该方法将多个索引模型的参数和非参数组件正规化。 一项试点研究表明，这种方法比其他现有方法更有利。在面对超高维度时，研究人员会使用远期变量筛选程序将维度降低到可管理的尺寸，然后再应用拟议的惩罚。研究人员计划研究这种方法的理论特性，并为其实施开发快速有效的计算算法。所提出的方法进一步扩展到涉及分类响应或随机效应的应用程序。科学和技术的预测导致在各种领域（例如生物信息学，气候研究，互联网等）爆炸性大量数据的爆炸性增长。在处理大量变量时，用于聚类，回归和分类的传统统计方法变得无效。最近，大量的研究工作专门用于开发统计方法，例如缩小维度和可变选择，用于分析这种大规模数据。研究人员通过提出一种新颖的惩罚方法并开发有效的计算算法来加入这项工作。该项目的结果不仅可以提高统计研究，还可以帮助其他科学家和研究人员更好地理解和分析其大量数据，从而增强了他们的科学发现。