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.

变量选择在当今许多科学研究中出现的高维统计模型中起着重要作用。研究人员研究基于高维统计建模正则化机制的变量选择技术，开发高维特征空间变量筛选的新方法，并探索这些技术在高维稀疏推理中的应用。提出了三个相互关联的研究课题进行调查。首先，研究者研究了一种具有惩罚似然的统一变量选择方法，该方法同时选择显着变量并估计其回归系数，并开发了适用于超高维特征空间的某些筛选技术。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，并且还研究了协方差选择。第三，研究者研究变量选择技术在函数数据分析中的应用，其中回归系数函数表现出各种稀疏性。现在在许多科学学科和工程问题中普遍出现的海量数据集的分析对统计理论和方法提出了许多挑战小规模研究中不存在这些。该提案的一个主要目标是为高维变量选择这一重要且具有挑战性的主题做出方法论和理论贡献。这些新进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增强的可解释性来分析高维数据。高维度的挑战来自科学和人文科学的各个领域，从基因组学和健康科学到经济学和金融学。拟议的高维度变量选择工作不仅有助于更好地识别对公共卫生或市场风险等重要的因素，而且将使各个领域的广泛科学家和研究人员受益。