CAREER: Computer-Intensive Statistical Inference on High-Dimensional and Massive Data: From Theoretical Foundations to Practical Computations

职业：高维海量数据的计算机密集统计推断：从理论基础到实际计算

• 批准号: 1752614
• 负责人: Xiaohui Chen
• 金额: $ 40万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2018
• 资助国家: 美国
• 起止时间: 2018-07-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1752614&HistoricalAwards=false
• 关键词: CAREER; Computer; Intensive; Statistical; Inference

In an era of Big Data, computer-intensive statistical inference faces unprecedented challenges and opportunities. High-dimensional and massive data are now emerging in scientific areas including biomedical engineering, environmental science, financial econometrics, array signal processing, and social networks, among many others. An important associated research challenge is to develop efficient methods to extract information and quantify its uncertainty for a large number of variables and measurements. Data-driven statistical inferential procedures for uncertainty quantification via the bootstrap methods are often computationally intensive for high-dimensional large-scale datasets. On the computational side, this research project will make use of distributed inference via the parallel high-performance computing technique, which is an essential ingredient to speed up bootstrap calculations. On the statistical side, this research will introduce a general framework for studying the performance of various bootstrap methods. This research project aims to lead to a comprehensive understanding of the fundamental tradeoff between statistical and computational concerns in quantifying uncertainty for a broad class of inferential procedures, thus providing guidance to practically optimize statistical accuracy and computational cost in potential real applications. Both undergraduate and graduate students are involved in the project.The overarching goal of this research project is to provide new insights and deepen the theoretical understanding of strengths and fundamental limitations of fully data-dependent inferential procedures (such as bootstraps) in the high-dimensional and massive data framework on two classical problems: i) change point detection and identification; ii) computationally-aware statistical inference for U-statistics. The research aims to develop statistically correct and computationally scalable inferential procedures when the dimension can be larger (or even much larger) than the sample size. In contrast to existing work, the methods under development have strong theoretical guarantees, are robust under mild assumptions, require no tuning, and are easy to parallelize. Of practical interest, the research will develop needed software tools for researchers from disciplines with applications of high-dimensional and nonparametric statistics. Theoretical contributions of the proposed research include establishing new approximation and coupling theorems (under weaker regularity conditions than existing literature) in high-dimensional and infinite-dimensional spaces of increasing dimension and complexity, where classical probability tools such as the central limit theorem and extreme value theory are no longer applicable. The mathematical theory is of independent interest and will provide powerful new tools to analyze other statistical procedures on high-dimensional and nonparametric models.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.

在大数据时代，计算机密集型统计推断面临着前所未有的挑战和机遇。现在，在科学领域，包括生物医学工程，环境科学，金融计量经济学，阵列信号处理和社交网络等科学领域正在出现高维和大量数据。一个重要的相关研究挑战是开发有效的方法来提取信息并量化大量变量和测量的不确定性。通过引导方法进行不确定性定量的数据驱动的统计推理程序通常在高维大规模数据集的计算密集程度上是计算密集型的。在计算方面，该研究项目将通过平行的高性能计算技术利用分布式推理，这是加快自举计算的重要组成部分。在统计方面，这项研究将引入一个一般框架，用于研究各种自举方法的性能。该研究项目旨在使统计和计算问题之间的基本权衡对量化广泛的推论程序的不确定性进行全面了解，从而为潜在的实际应用中的统计准确性和计算成本提供指导，从而提供指导。本科生和研究生都参与了该项目。该研究项目的总体目标是提供新的见解，并加深对优势的理论理解和对高维和大规模数据框架在两个经典问题上完全依赖数据的推论程序（例如引导程序）的基本限制：i）变化点检测和识别； ii）对U统计量的计算意识到的统计推论。该研究的目的是在尺寸大于样本量大（甚至更大）时开发统计正确和计算可扩展的推论程序。与现有工作相反，所开发的方法具有强大的理论保证，在轻度假设下，不需要调整并且易于平行。令人感兴趣的是，该研究将为来自学科的研究人员开发所需的软件工具，并具有高维和非参数统计的应用。拟议研究的理论贡献包括在高维和无限维空间中建立新的近似值和耦合定理（在弱规则条件下），以增加维度和复杂性，其中经典概率工具（例如中心限制理论）不再适用。数学理论具有独立的兴趣，将提供有力的新工具来分析有关高维和非参数模型的其他统计程序。该奖项反映了NSF的法定任务，并被认为是通过基金会的智力优点和更广泛的影响来通过评估来支持的。

项目成果

Mean-field nonparametric estimation of interacting particle systems

• 发表时间: 2022-05
• 作者: Rentian Yao;Xiaohui Chen;Yun Yang

Hanson–Wright inequality in Hilbert spaces with application to $K$-means clustering for non-Euclidean data

希尔伯特空间中的汉森赖特不等式及其应用于非欧几里得数据的 $K$ 均值聚类

• DOI: 10.3150/20-bej1251
• 发表时间: 2021
• 期刊: Bernoulli
• 影响因子: 1.5
• 作者: Chen, Xiaohui;Yang, Yun
• 通讯作者: Yang, Yun

Diffusion K-means clustering on manifolds: Provable exact recovery via semidefinite relaxations

• DOI: 10.1016/j.acha.2020.03.002
• 发表时间: 2021-02-19
• 期刊: APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
• 影响因子: 2.5
• 作者: Chen, Xiaohui;Yang, Yun
• 通讯作者: Yang, Yun

Sketch-and-Lift: Scalable Subsampled Semidefinite Program for K-means Clustering

• 发表时间: 2022-01
• 作者: Yubo Zhuang;Xiaohui Chen;Yun Yang

Cutoff for Exact Recovery of Gaussian Mixture Models

• DOI: 10.1109/tit.2021.3063155
• 发表时间: 2021-06-01
• 期刊: IEEE TRANSACTIONS ON INFORMATION THEORY
• 影响因子: 2.5
• 作者: Chen, Xiaohui;Yang, Yun
• 通讯作者: Yang, Yun