High-dimensional statistical learning and inference

高维统计学习和推理

• 批准号: 0704337
• 负责人: Jianqing Fan
• 金额: $ 92万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-06-15 至 2014-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0704337&HistoricalAwards=false
• 关键词: dimensional; statistical; learning; inference

The challenge of high-dimensionality characterizes many contemporary statistical problems arising frommany frontiers of scientific research and technological development. In high-dimensional statistical research, low-dimensional structures, which entail sparsity under suitable parametrization, are needed to be explored in order to circumvent the issue of noise accumulation with dimensionality. This proposal intends to confront a number of important high-dimensional statistical problems from genomics, machine learning, health studies, economics, and finance. These include various emerging issues from the analysis of microarray data such as normalization, significance analysis, and disease classification; variable selection and feature extraction from high-dimensional statistical learning; sparse classification and clustering from high-dimensional feature spaces; high-dimensional covariance matrix estimation for asset allocation and portfolio management; sparse covariance estimation for spatial and temporal studies and genetic networks. All of these problems have their distinguished characters from the context of their applications, but nevertheless share similar challenges with high dimensionality and admit features of sparsity. These emerging problems of high societal impacts will be confronted via developing new statistical methods to address the features and challenges associated with high-dimensionality, from statistical computation, feature selection, to noise reduction. At the same time, the PI also intends to provide fundamental understanding, via asymptotic analysis and simulation studies, to these problems and their associated methodologies that push theory, methods, and computation forward.Thanks to technological innovation, the availability of large-scale and complex data are widely available nowadays in many contemporary scientific problems. High-dimensional statistical models are required to address these scientific endeavors. The challenges of high-dimensionality arise from diverse fields of sciences and the humanities, ranging from genomics and health sciences to economics and finance. In these fields, variable selection, feature extraction, sparsity explorations are crucial for knowledge discovery. In this proposal, we propose to develop cutting-edge statistical theory and methods to address these problems from genomic studies, machine learning, health science, economics, and finance. The proposed techniques and results will not only help researchers to solve emerging problems in their disciplines, but also have strong impact on statistical thinking, methodological development, and theoretical studies.

高维性的挑战是当代许多科学研究和技术发展前沿所产生的统计问题的特征。在高维统计研究中，需要探索在适当的参数化下具有稀疏性的低维结构，以避免维数噪声累积的问题。该提案旨在面对来自基因组学，机器学习，健康研究，经济学和金融学的一些重要的高维统计问题。这些包括各种新出现的问题，从分析微阵列数据，如归一化，显着性分析和疾病分类;变量选择和特征提取从高维统计学习;稀疏分类和聚类从高维特征空间;高维协方差矩阵估计的资产分配和投资组合管理;稀疏协方差估计的空间和时间的研究和遗传网络。所有这些问题都有其独特的特点，从他们的应用背景，但仍然有类似的挑战，高维和稀疏性的特点。这些新出现的高社会影响的问题将通过开发新的统计方法来解决与高维相关的特征和挑战，从统计计算，特征选择到降噪。同时，PI还通过渐近分析和模拟研究，对这些问题及其相关方法进行基本理解，推动理论、方法和计算向前发展。由于技术创新，大规模和复杂数据的可用性在当今许多科学问题中广泛存在。需要高维统计模型来解决这些科学问题。高维度的挑战来自不同的科学和人文领域，从基因组学和健康科学到经济学和金融学。在这些领域中，变量选择、特征提取、稀疏性探索是知识发现的关键。在这项提案中，我们建议开发尖端的统计理论和方法，以解决来自基因组研究，机器学习，健康科学，经济学和金融学的这些问题。 所提出的技术和结果不仅有助于研究人员解决其学科中出现的问题，而且对统计思维，方法发展和理论研究产生了强烈的影响。