CAREER: High Dimensional Variable Selection and Risk Properties

职业：高维变量选择和风险属性

• 批准号: 0955316
• 负责人: Jinchi Lv
• 金额: $ 40万
• 依托单位: University of Southern California
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0955316&HistoricalAwards=false
• 关键词: CAREER; Dimensional; Variable; Selection; Risk

High dimensional variable selection plays a pivotal role in contemporary statistical modeling, learning and scientific discoveries. Long-standing theoretical questions in the literature include how high dimensionality regularization methods with general penalties can handle, what the role of penalty functions is, and how to characterize the optimality of variable selection procedures. The investigator proposes to study four interrelated research topics. First, the investigator studies penalized likelihood methods with general penalties, which are widely applied for simultaneously selecting important variables and estimating their effects in high dimensional statistical inference, where the dimensionality can be much larger than sample size. Second, various contexts of high dimensional variable selection beyond penalized likelihood methods including penalized empirical risk and hunting for interactions are investigated. Third, the investigator proposes new principles for model selection when models are possibly misspecified and studies the robustness of various regularization methods for high dimensional variable selection under model misspecification. Fourth, the risk properties and optimality of various high dimensional regularization methods in the contexts of penalized least squares and penalized likelihood are further investigated.The analysis of vast data sets now commonly arises in diverse fields of sciences, engineering and humanities ranging from genomics and health sciences to economics, finance and machine learning. High dimensional data analysis poses numerous challenges to statistical theory, methods and implementations that are not present in smaller scale studies. A major goal of this proposal is to make theoretical and methodological contributions to the important and challenging topic of high dimensional variable selection and statistical inference. These new developments provide unified and systematic understandings of various regularization methods in high dimensions, and allow scientists to analyze high dimensional data with increased efficiency, expediency and interpretability. The proposed work is incorporated into new courses on the state-of-the-art high dimensional statistical learning, and will benefit the training and learning of undergraduates, graduate students, and underrepresented minorities. The proposed work on variable selection in high dimensions will not only help better identify factors that are important to, for example, public health and market risk, but also benefit a broad range of scientists and researchers in various fields.

高维变量选择在当代统计建模，学习和科学发现中起关键作用。文献中长期存在的理论问题包括具有一般性惩罚能够处理的高维度正则化方法，惩罚功能的作用是什么以及如何表征可变选择程序的最佳性。研究人员建议研究四个相互关联的研究主题。首先，研究人员的研究对一般惩罚的可能性方法进行了惩罚，这些方法被广泛应用于同时选择重要变量并在高维统计推断中估算其效果，其中维度可以比样本量大得多。其次，研究了高维变量选择的各种背景，包括受惩罚的似然方法，包括受惩罚的经验风险和狩猎相互作用。第三，研究者提出了模型选择的新原则，当模型可能被错误指定时，并研究了模型错误指定下的各种正则化方法的鲁棒性，用于高维变量选择。第四，进一步研究了受惩罚最小二乘和受惩罚可能性的各种高维正规化方法的风险特性和最佳性。进一步研究了对大量数据集的分析，现在通常在科学领域，工程和人文科学领域，基因组学以及基因组学和健康等等的分析经济学，金融和机器学习的科学。高维数据分析对较小规模研究中不存在的统计理论，方法和实施提出了许多挑战。该提案的主要目标是对高维变量选择和统计推断的重要且具有挑战性的主题做出理论和方法论贡献。这些新的发展提供了对高维度各种正则化方法的统一和系统的理解，并允许科学家以提高效率，便捷性和可解释性来分析高维数据。拟议的工作纳入了有关最先进的高维统计学习的新课程中，并将受益于本科生，研究生和代表性不足的少数民族的培训和学习。在高维度中选择可变选择的拟议工作不仅将有助于更好地确定对例如公共卫生和市场风险重要的因素，而且使各个领域中广泛的科学家和研究人员受益。