Estimation and Inference with High-Dimensional Data

高维数据是在广泛的学科中收集的，从生物学和医学研究、自然科学、工程学到社会科学、经济学和金融学。利用这些数据进行统计推断已变得越来越重要。本研究计划的目标是发展改进的统计方法、演算法和理论，以估计和推断高维数据。该项目将在几个应用中实现这些新方法，以证明它们的可行性、有效性和实用性。该项目还将开展全面的数值实验，以验证新算法的计算效率，并证明相关理论在现实环境中的相关性。数值工作的目的是产生具体的证据的效用的方法在广泛的背景下。这项工作将促进具有不同专业知识的研究人员之间的合作，使学生和年轻研究人员能够迅速与前沿研究保持一致，并鼓励他们着手开展一系列令人兴奋的研究课题。将特别努力招收和鼓励来自代表性不足群体的学生。向公众提供软件和其他工具，加强科学和数据驱动决策的实际应用。高维数据是统计学研究的一个热点领域，因为它在现代一些最广泛使用的统计方法的发展和理论理解中发挥了核心作用。本研究项目旨在为基于微分的统计推断方法和近似消息传递的收敛性及其与经验贝叶斯方法的联系所产生的新兴主题的未来工作奠定坚实的基础。旨在发展Stein无偏风险估计的中心极限定理，正则化估计的新方法和理论，包括置信区间和区域在内的去偏统计推断的新方法和理论，以及近似按摩传递中的经验贝叶斯方法。该项目旨在为此类统计推断提供丰富的新工具，研究新开发方法的理论和经验性质，并为其在社会学、经济学、神经成像、信号处理、通信、社会网络、生物信息学和文本分析等重要领域的应用奠定基础。预计该项目的研究结果也将对统计的其他领域产生影响，包括因果推理、缺失数据、生存分析、压缩感知、信息检索和信号处理，从而显著推进统计和数据科学的研究。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

High-dimensional data are collected in a wide range of disciplines, from biology and medical research, natural sciences, and engineering to social sciences, economics, and finance. Statistical inference with such data has become increasingly important. The objective of this research project is to develop improved statistical methods, algorithms, and theory for estimation and inference with high-dimensional data. The project will implement the new methods in several applications that demonstrate their feasibility, effectiveness, and usefulness. The project will also carry out comprehensive numerical experiments to verify the computational efficiency of the new algorithms and to prove the relevance of the related theory in realistic settings. The numerical work aims to produce concrete evidence of the utility of the approach in wide contexts. The work will foster collaborations between researchers with different expertise, allow students and young researchers to align quickly with cutting edge research, and encourage them to embark on a host of exciting research topics. Special efforts will be devoted to recruiting and encouraging students from underrepresented groups. Software and other tools will be made available to the public, enhancing scientific and data-driven decision making in practical applications.High-dimensional data is an intense area of research in statistics due to its central role in the development and theoretical understanding of some of the most widely used statistical methods in modern time. This research project intends to establish a solid foundation for future work in the emerging topic arising from the convergence of differential-based statistical inference methods and approximate message passing, and their connection to empirical Bayesian methods. It aims to develop the central limit theorem for Stein's unbiased risk estimate, new methods and theory for regularized estimation, new methods and theory for de-biased statistical inference including confidence intervals and regions, and empirical Bayes methods in approximate massage passing. The project intends to produce a rich collection of new tools for such statistical inference, study the theoretical and empirical properties of the newly developed methods, and set the scene for their application in important fields including sociology, economics, neural imaging, signal processing, communications, social networks, bioinformatics, and text analysis. The project findings are expected to have impact as well in other fields of statistics, including causal inference, missing data, survival analysis, compressed sensing, information retrieval, and signal processing, significantly advancing statistics and data science research in general.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.