High-dimensional statistical learning and inference

在科学研究和技术发展的许多前沿产生的许多当代统计问题都面临着高维性的挑战。在高维统计研究中，需要探索低维结构在适当参数化条件下的稀疏性，以避免噪声随维度累积的问题。该提案旨在面对基因组学、机器学习、健康研究、经济学和金融等一系列重要的高维统计问题。其中包括来自微阵列数据分析的各种新出现的问题，如归一化、显著性分析和疾病分类；基于高维统计学习的变量选择与特征提取基于高维特征空间的稀疏分类与聚类资产配置与投资组合管理的高维协方差矩阵估计时空研究和遗传网络的稀疏协方差估计。所有这些问题都有其独特的特点，从它们的应用环境来看，但它们都具有类似的高维挑战和稀疏性特征。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，这些高社会影响的新问题将得到解决。同时，PI还打算通过渐近分析和模拟研究，对这些问题及其相关的方法提供基本的理解，从而推动理论，方法和计算向前发展。由于技术的创新，如今在许多当代科学问题中，大规模和复杂的数据是广泛可用的。需要高维统计模型来处理这些科学工作。高维的挑战来自科学和人文学科的不同领域，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、稀疏度探索是知识发现的关键。在本提案中，我们建议从基因组研究、机器学习、健康科学、经济学和金融等方面发展前沿的统计理论和方法来解决这些问题。提出的技术和结果不仅有助于研究者解决其学科中出现的新问题，而且对统计思维、方法发展和理论研究都有很大的影响。

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.