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

RI：中：协作研究：算法高维统计：最优性、计算障碍和高维校正

• 批准号: 1900140
• 负责人: Yuxin Chen
• 金额: $ 38.5万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-08-01 至 2022-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1900140&HistoricalAwards=false
• 关键词: RI; Medium; Collaborative; Research; Algorithmic

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.

该研究旨在解决从大维度数据中学习和推理的紧迫挑战。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，现代数据应用中普遍存在的挑战是从大量数据中有效可靠地提取相关信息和相关见解。与此同时，人们需要推理的相关特征的前所未有的增长加剧了这一挑战，这往往超过了数据样本的增长。经典的统计推断范式，要么只在存在大量数据样本的情况下工作，要么完全忽略估计器的计算成本，对于许多新兴的机器学习和大数据分析应用来说，变得非常不足，甚至不可靠。为了解决上述高维度的紧迫问题，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。这个项目的目标是四重：第一，发展一个现代的理论来描述经典统计算法在高维中的精确性能。第二，建议适当纠正经典的统计推断程序，以适应样本匮乏的制度。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，确定潜在的计算障碍，如果基本的统计限制不能得到满足。拟议的研究计划的变革潜力是通过统计学，近似理论，统计物理学，数学优化和信息论的新组合来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。 该项目开发的理论和算法将直接影响各种工程和科学应用，如大规模机器学习，DNA测序，遗传疾病分析和自然语言处理。该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的导师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。这项研究旨在解决从大规模数据中学习和推理的紧迫挑战。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，现代数据应用中普遍存在的挑战是从大量数据中有效可靠地提取相关信息和相关见解。与此同时，人们需要推理的相关特征的前所未有的增长加剧了这一挑战，这往往超过了数据样本的增长。经典的统计推断范式，要么只在存在大量数据样本的情况下工作，要么完全忽略估计器的计算成本，对于许多新兴的机器学习和大数据分析应用来说，变得非常不足，甚至不可靠。为了解决上述高维度的紧迫问题，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。这个项目的目标是四重：第一，发展一个现代的理论来描述经典统计算法在高维中的精确性能。第二，建议适当纠正经典的统计推断程序，以适应样本匮乏的制度。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，确定潜在的计算障碍，如果基本的统计限制不能得到满足。拟议的研究计划的变革潜力是通过统计学，近似理论，统计物理学，数学优化和信息论的新组合来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。 该项目开发的理论和算法将直接影响各种工程和科学应用，如大规模机器学习，DNA测序，遗传疾病分析和自然语言处理。这个合作项目为学生提供跨大学的培训机会，我们致力于通过长期的指导和推广活动，吸引和帮助在STEM领域代表性不足的学生和女性学生。这个奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响力审查标准进行评估，被认为值得支持。

项目成果

Inference and uncertainty quantification for noisy matrix completion

• DOI: 10.1073/pnas.1910053116
• 发表时间: 2019-11-12
• 期刊: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• 影响因子: 11.1
• 作者: Chen, Yuxin;Fan, Jianqing;Yan, Yuling
• 通讯作者: Yan, Yuling

Nonconvex Low-Rank Symmetric Tensor Completion from Noisy Data

• 发表时间: 2019-11
• 期刊: ArXiv
• 作者: Changxiao Cai;Gen Li;H. Poor;Yuxin Chen

Nonconvex Matrix Factorization From Rank-One Measurements

• DOI: 10.1109/tit.2021.3050427
• 发表时间: 2018-02
• 期刊: IEEE Transactions on Information Theory
• 影响因子: 2.5
• 作者: Yuanxin Li;Cong Ma;Yuxin Chen;Yuejie Chi

Uncertainty Quantification for Nonconvex Tensor Completion: Confidence Intervals, Heteroscedasticity and Optimality

• DOI: 10.1109/tit.2022.3205781
• 发表时间: 2020-06
• 期刊: IEEE Transactions on Information Theory
• 影响因子: 2.5
• 作者: Changxiao Cai;H. Poor;Yuxin Chen

Communication-Efficient Distributed Optimization in Networks with Gradient Tracking and Variance Reduction

• 发表时间: 2019-09
• 期刊: J. Mach. Learn. Res.
• 作者: Boyue Li;Shicong Cen;Yuxin Chen;Yuejie Chi