Variable Selection in High Dimensional Feature Space with Applications to Covariance Matrix Estimation and Functional Data Analysis

高维特征空间中的变量选择及其在协方差矩阵估计和函数数据分析中的应用

• 批准号: 0806030
• 负责人: Jinchi Lv
• 金额: $ 8.03万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-06-01 至 2011-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0806030&HistoricalAwards=false
• 关键词: Variable; Selection; Dimensional; Feature; Space

Variable selection plays an important role in high dimensional statistical modeling which nowadays arises in many scientific investigations. The investigator studies variable selection techniques built upon the machinery of regularization for high dimensional statistical modeling, develops new approaches to variable screening for high dimensional feature space, and explores the applications of these techniques to high dimensional sparse inference. Three interrelated research topics are proposed for investigation. First, the investigator studies a unified approach to variable selection with penalized likelihood which simultaneously selects significant variables and estimates their regression coefficients, and develops sure screening techniques applicable to ultra-high dimensional feature space. Second, factor models are proposed to estimate large scale covariance matrices while variable selection techniques are invoked to construct the factors, and covariance selection is also investigated. Third, the investigator studies the applications of variable selection techniques to functional data analysis where the regression coefficient functions exhibit various kinds of sparsity.The analysis of vast data sets now commonly arising in many scientific disciplines and engineering problems poses numerous challenges to statistical theory and methodology that are not present in smaller scale studies. A major goal of this proposal is to make methodological and theoretical contributions to the important and challenging topic of high dimensional variable selection. These new developments provide further understanding of various regularization methods in high dimensions, and allow scientists to analyze high dimensional data with efficient dimension reduction and increased interpretability. The challenges of high dimensionality arise from diverse fields of sciences and humanities ranging from genomics and health sciences to economics and finance. The proposed work on variable selection in high dimensions will not only help better identify factors that are important to, for instance, public health or market risk, but also benefit a broad range of scientists and researchers in various fields.

变量选择在高维统计建模中起着重要的作用，目前许多科学研究中都出现了高维统计建模。研究人员研究了建立在高维统计建模的正则化机制基础上的变量选择技术，发展了高维特征空间变量筛选的新方法，并探索了这些技术在高维稀疏推理中的应用。提出了三个相关的研究课题以供研究。首先，研究了惩罚似然变量选择的统一方法，即同时选择有意义的变量并估计其回归系数，发展了适用于超高维特征空间的确定性筛选技术。其次，提出了因子模型来估计大规模协方差矩阵，同时调用变量选择技术来构造因子，并对协方差选择进行了研究。第三，研究了变量选择技术在泛函数据分析中的应用，其中回归系数函数表现出各种稀疏性。分析目前在许多科学学科和工程问题中普遍出现的海量数据集给统计理论和方法带来了许多在较小规模研究中不存在的挑战。这一建议的一个主要目标是为高维变量选择这一重要而具有挑战性的主题做出方法论和理论贡献。这些新的发展提供了对高维中各种正则化方法的进一步理解，并使科学家能够通过有效的降维和更高的可解释性来分析高维数据。从基因组学和卫生科学到经济和金融，高维的挑战来自不同的科学和人文领域。拟议的高维变量选择工作不仅将有助于更好地确定对公共卫生或市场风险等重要因素，而且还将使各个领域的广泛科学家和研究人员受益。