RI: Medium: Collaborative Research:Algorithmic High-Dimensional Statistics: Optimality, Computtional Barriers, and High-Dimensional Corrections

本研究旨在解决从大维度数据中学习和推断的紧迫挑战。当代传感和数据采集技术以前所未有的速度产生数据。因此，现代数据应用程序中普遍存在的挑战是从大量数据中高效可靠地提取相关信息和相关见解。与此同时，需要推理的相关特征的空前增长加剧了这一挑战，这些特征的增长有时甚至超过了数据样本的增长。经典的统计推理范式，要么只在大量数据样本存在的情况下有效，要么根本忽略了估计器的计算成本，对于许多新兴的机器学习和大数据分析应用来说，变得非常不充分，甚至不可靠。为了在高维中解决上述紧迫问题，需要引入新的理论工具，以便全面了解各种算法和任务的性能限制。该项目的目标有四个方面：首先，发展一种现代理论，以表征经典统计算法在高维上的精确性能。第二，建议对经典统计推断程序进行适当的修正，以适应样本匮乏的情况。第三，如果可能的话，开发计算效率高的算法，可以证明达到基本的统计极限。最后，第四，如果不能满足基本的统计限制，确定潜在的计算障碍。拟议研究计划的变革潜力在于通过统计学，近似理论，统计物理，数学优化和信息论的新组合发展基础统计数据分析理论，提供可扩展的统计推断和学习算法。在这个项目中开发的理论和算法将对各种工程和科学应用产生直接影响，如大规模机器学习、DNA测序、遗传疾病分析和自然语言处理。这一合作项目为学生培训提供了跨大学的机会，我们致力于通过长期指导和外展活动，吸引和帮助STEM领域代表性不足的学生和女性学生。本研究旨在解决从大维度数据中学习和推断的紧迫挑战。当代传感和数据采集技术以前所未有的速度产生数据。因此，现代数据应用程序中普遍存在的挑战是从大量数据中高效可靠地提取相关信息和相关见解。与此同时，需要推理的相关特征的空前增长加剧了这一挑战，这些特征的增长有时甚至超过了数据样本的增长。经典的统计推理范式，要么只在大量数据样本存在的情况下有效，要么根本忽略了估计器的计算成本，对于许多新兴的机器学习和大数据分析应用来说，变得非常不充分，甚至不可靠。为了在高维中解决上述紧迫问题，需要引入新的理论工具，以便全面了解各种算法和任务的性能限制。该项目的目标有四个方面：首先，发展一种现代理论，以表征经典统计算法在高维上的精确性能。第二，建议对经典统计推断程序进行适当的修正，以适应样本匮乏的情况。第三，如果可能的话，开发计算效率高的算法，可以证明达到基本的统计极限。最后，第四，如果不能满足基本的统计限制，确定潜在的计算障碍。拟议研究计划的变革潜力在于通过统计学，近似理论，统计物理，数学优化和信息论的新组合发展基础统计数据分析理论，提供可扩展的统计推断和学习算法。在这个项目中开发的理论和算法将对各种工程和科学应用产生直接影响，如大规模机器学习、DNA测序、遗传疾病分析和自然语言处理。这一合作项目为学生培训提供了跨大学的机会，我们致力于通过长期指导和外展活动，吸引和帮助STEM领域代表性不足的学生和女性学生。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。

This research aims to address the pressing challenges on learning and inference from large-dimensional data. Contemporary sensing and data acquisition technologies produce data at an unprecedented rate. A ubiquitous challenge in modern data applications is thus to efficiently and reliably extract relevant information and associated insights from a deluge of data. In the meantime, this challenge is exacerbated by the unprecedented growth of relevant features one needs to reason about, which oftentimes even outpaces the growth of data samples. Classical statistical inference paradigms, which either only work in the presence of an enormous number of data samples, or ignore the computational cost of the estimators at all, become highly insufficient, or even unreliable, for many emerging applications of machine learning and big-data analytics. To address the above pressing issues in high dimensions, novel theoretical tools need to be brought in the picture in order to provide a comprehensive understanding of the performance limits of various algorithms and tasks. The goal of this project is four-fold: First, to develop a modern theory to characterize precise performance of classical statistical algorithms in high dimensions. Second, to suggest proper corrections of classical statistical inference procedures to accommodate the sample-starved regime. Third, to develop computationally efficient algorithms that can provably attain the fundamental statistical limits, if possible. Finally, forth, to identify potential computational barriers if the fundamental statistical limits cannot be met. The transformative potential of the proposed research program is in the development of foundational statistical data analytics theory through a novel combination of statistics, approximation theory, statistical physics, mathematical optimization, and information theory, offering scalable statistical inference and learning algorithms. The theory and algorithms developed within this project will have direct impact on various engineering and science applications such as large-scale machine learning, DNA sequencing, genetic disease analysis, and natural language processing. This collaborative program provides cross-university opportunities for students training, and we are committed to engaging and helping underrepresented and women students in STEM through long-term mentorships and outreach activities.This research aims to address the pressing challenges on learning and inference from large-dimensional data. Contemporary sensing and data acquisition technologies produce data at an unprecedented rate. A ubiquitous challenge in modern data applications is thus to efficiently and reliably extract relevant information and associated insights from a deluge of data. In the meantime, this challenge is exacerbated by the unprecedented growth of relevant features one needs to reason about, which oftentimes even outpaces the growth of data samples. Classical statistical inference paradigms, which either only work in the presence of an enormous number of data samples, or ignore the computational cost of the estimators at all, become highly insufficient, or even unreliable, for many emerging applications of machine learning and big-data analytics. To address the above pressing issues in high dimensions, novel theoretical tools need to be brought in the picture in order to provide a comprehensive understanding of the performance limits of various algorithms and tasks. The goal of this project is four-fold: First, to develop a modern theory to characterize precise performance of classical statistical algorithms in high dimensions. Second, to suggest proper corrections of classical statistical inference procedures to accommodate the sample-starved regime. Third, to develop computationally efficient algorithms that can provably attain the fundamental statistical limits, if possible. Finally, forth, to identify potential computational barriers if the fundamental statistical limits cannot be met. The transformative potential of the proposed research program is in the development of foundational statistical data analytics theory through a novel combination of statistics, approximation theory, statistical physics, mathematical optimization, and information theory, offering scalable statistical inference and learning algorithms. The theory and algorithms developed within this project will have direct impact on various engineering and science applications such as large-scale machine learning, DNA sequencing, genetic disease analysis, and natural language processing. This collaborative program provides cross-university opportunities for students training, and we are committed to engaging and helping underrepresented and women students in STEM through long-term mentorships and outreach activities.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.