Collaborative Research: Fine-Grained Statistical Inference in High Dimension: Actionable Information, Bias Reduction, and Optimality

协作研究：高维细粒度统计推断：可操作信息、减少偏差和最优性

• 批准号: 2014279
• 负责人: Yuxin Chen
• 金额: $ 10万
• 依托单位: Princeton University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2025-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2014279&HistoricalAwards=false
• 关键词: Collaborative; Research; Fine; Grained; Statistical

Emerging data science applications require efficient extraction of actionable insights from large and messy datasets. The number of relevant features often overwhelms the volume of data that is available, which dramatically complicates the statistical inference tasks and subsequent decision making. In the existing statistical literature, most of theory aims at understanding the average or global behavior of a statistical estimator in high dimensions. In many applications, however, it is often the case that the goal is not to explore the global behavior of a parameter estimator, but rather to perform inference and reasoning on its local, yet important, operational properties. The techniques and methods developed in the project will further advance the interplay between a broad range of areas including high-dimensional statistics, harmonic analysis, statistical physics, optimization, complex analysis, and statistical machine learning. The project provides research training opportunities for graduate students.This project pursues fine-grained inferential procedures and theory, aimed at enlarging the uncertainty assessment toolbox for various low-complexity models in high dimensions. Focusing on a few stylized problems, this research program consists of four major thrusts: (1) construct optimal confidence intervals for linear functionals of eigenvectors in low-rank matrix estimation; (2) design fine-grained hypothesis testing procedures for sparse regression under general designs; (3) develop entry-wise inference schemes for principal component analysis with missing data; and (4) conduct reliable and adaptive statistical eigen-analysis under minimal eigen-gaps. Emphasis is placed on algorithms that are model-agnostic and fully adaptive to data heteroscedasticity. Addressing these issues calls for the development of new statistical theory that enables reliable inference for a broad class of local properties underlying the unknown parameters.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.

新兴的数据科学应用程序需要有效地从大而混乱的数据集中提取可起作用的见解。相关功能的数量通常淹没了可用的数据量，这极大地使统计推断任务和随后的决策变得复杂。在现有的统计文献中，大多数理论旨在了解高维度统计估计器的平均或全球行为。但是，在许多应用中，通常情况下，目标不是探索参数估计器的全局行为，而是在其本地但重要的操作属性上执行推理和推理。 项目中开发的技术和方法将进一步推进广泛领域之间的相互作用，包括高维统计，谐波分析，统计物理学，优化，复杂分析和统计机器学习。该项目为研究生提供了研究培训机会。该项目追求细粒度的推论程序和理论，旨在扩大高维度各种低复杂模型的不确定性评估工具箱。该研究计划着眼于一些程式化的问题，包括四个主要推力：（1）在低级别基质估计中，特征向量线性功能的最佳置信区间； （2）设计在一般设计下稀疏回归的精细颗粒假设测试程序； （3）开发出参赛推理方案，用于主要组件分析，并且缺少数据； （4）在最小的本征间内进行可靠和适应性统计本征分析。重点放在模型敏捷的算法上，并且完全适应数据异质性。解决这些问题需要开发新的统计理论，该理论能够对未知参数的一系列本地财产进行可靠的推论。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的智力优点和更广泛影响的审查标准通过评估来获得支持的。

项目成果

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

Learning Mixtures of Low-Rank Models

• DOI: 10.1109/tit.2021.3065700
• 发表时间: 2020-09
• 期刊: IEEE Transactions on Information Theory
• 影响因子: 2.5
• 作者: Yanxi Chen;Cong Ma;H. Poor;Yuxin Chen

Sample Complexity of Asynchronous Q-Learning: Sharper Analysis and Variance Reduction

• DOI: 10.1109/tit.2021.3120096
• 发表时间: 2020-06
• 期刊: IEEE Transactions on Information Theory
• 影响因子: 2.5
• 作者: Gen Li;Yuting Wei;Yuejie Chi;Yuantao Gu;Yuxin Chen

Breaking the Sample Size Barrier in Model-Based Reinforcement Learning with a Generative Model

• DOI: 10.1287/opre.2023.2451
• 发表时间: 2020-05
• 期刊: Oper. Res.
• 作者: Gen Li;Yuting Wei;Yuejie Chi;Yuantao Gu;Yuxin Chen