High-dimensional statistical learning and inference

高维挑战是科学研究和技术发展许多前沿领域产生的许多当代统计问题的特征。在高维统计研究中，需要探索低维结构，在适当的参数化下需要稀疏性，以避免维度噪声积累的问题。该提案旨在解决基因组学、机器学习、健康研究、经济学和金融学中的一些重要的高维统计问题。其中包括微阵列数据分析中出现的各种新问题，例如归一化、显着性分析和疾病分类；高维统计学习中的变量选择和特征提取；高维特征空间的稀疏分类和聚类；用于资产配置和投资组合管理的高维协方差矩阵估计；用于空间和时间研究以及遗传网络的稀疏协方差估计。所有这些问题在其应用环境中都有其独特的特征，但仍然面临着相似的高维挑战并具有稀疏性特征。这些新出现的具有高社会影响的问题将通过开发新的统计方法来解决，以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还打算通过渐进分析和模拟研究，对这些问题及其相关方法论提供基本的理解，从而推动理论、方法和计算的发展。由于技术创新，大规模和复杂的数据在当今许多当代科学问题中得到了广泛的应用。需要高维统计模型来解决这些科学工作。高维度的挑战来自科学和人文科学的不同领域，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、稀疏性探索对于知识发现至关重要。在本提案中，我们建议开发尖端的统计理论和方法来解决基因组研究、机器学习、健康科学、经济学和金融学中的这些问题。 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、方法论发展和理论研究产生强烈影响。

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.