RI: Small: Uncertainty Quantification for Nonconvex Low-Complexity Models

RI：小：非凸低复杂度模型的不确定性量化

• 批准号: 2218773
• 负责人: Yuxin Chen
• 金额: $ 45万
• 依托单位: University of Pennsylvania
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-01-01 至 2025-09-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2218773&HistoricalAwards=false
• 关键词: RI; Small; Uncertainty; Quantification; Nonconvex

Emerging applications in data science often involve estimating an enormous number of parameters from a highly incomplete and noisy set of measurements. In order for these applications to support modern scientific discovery and decision making, however, it is necessary to seek not merely reasonable estimations for the parameters, but perhaps more crucially, a trustworthy interpretation of the estimations and their implications. For instance, what reassurances can we offer about the quality of the estimates in hand? Can we quantify the uncertainty of our estimates due to the imperfectness of the data? Providing valid and quantitative answers to such questions is a crucial step in ensuring that: the scientific discovery and decision made based on our estimate are informative and trustworthy. Nevertheless, the existing statistical toolbox remains highly inadequate in providing measures of uncertainty for large-scale estimation methods, particularly in those scenarios where the availability of data samples is severely limited. This limits the overall value of the estimates and hampers scientific and decision-making processes. Some example application areas include: joint shape matching in computer vision and water-fat separation in medical imaging. Motivated by the above issues, the overarching goal of this project is to develop new foundational theory that integrates statistical assessment and algorithm design in an end-to-end manner, allowing for optimal inferential procedures for various nonconvex low-complexity models. Blending large-scale optimization techniques with statistical thinking, the proposed project seeks to develop a novel suite of distributional theory that enables valid uncertainty assessment for various nonconvex low-complexity models. Specifically, this project consists of the following research. First, develop a principled approach to construct optimal confidence intervals for unknown continuous parameters, on the basis of novel nonconvex estimation and de-biasing methods. Second, develop fast nonconvex algorithms and efficient uncertainty assessment procedures to reason about unknown discrete variables. Third, investigate the intimate connection between convex relaxation and nonconvex optimization, thus enabling a unified uncertainty quantification framework to accommodate both approaches. All research thrusts are motivated by, and will ultimately be tested on concrete practical applications. This project will significantly advance the fundamental techniques of uncertainty quantification in data-driven applications, and will enrich the foundations for mathematical optimization, data analytics, and statistical modeling.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.

数据科学中的新兴应用通常涉及从高度不完整和噪声的测量集合中估计大量参数。 然而，为了使这些应用程序支持现代科学发现和决策，不仅需要对参数进行合理的估计，而且可能更重要的是，对估计及其含义进行可信的解释。例如，我们可以对手头的估计数的质量提供什么保证？由于数据的不确定性，我们能否量化估计的不确定性？ 为这些问题提供有效和定量的答案是确保以下方面的关键一步：基于我们的估计做出的科学发现和决策是信息丰富和值得信赖的。然而，现有的统计工具箱仍然非常不足以为大规模估算方法提供不确定性的衡量标准，特别是在数据样本严重有限的情况下。这限制了估计数的总体价值，妨碍了科学和决策进程。一些示例应用领域包括：计算机视觉中的关节形状匹配和医学成像中的水脂分离。受上述问题的启发，该项目的总体目标是开发新的基础理论，以端到端的方式集成统计评估和算法设计，为各种非凸低复杂度模型提供最佳推理程序。将大规模优化技术与统计思想相结合，该项目旨在开发一套新的分布理论，为各种非凸低复杂性模型提供有效的不确定性评估。具体而言，该项目包括以下研究。首先，发展一个原则性的方法来构造未知连续参数的最优置信区间，新的非凸估计和去偏方法的基础上。其次，开发快速的非凸算法和有效的不确定性评估程序，以推理未知的离散变量。第三，研究凸松弛和非凸优化之间的密切联系，从而使一个统一的不确定性量化框架，以适应这两种方法。所有的研究重点都是由具体的实际应用所激发的，并最终将在具体的实际应用中进行测试。该项目将显著推进数据驱动应用中不确定性量化的基本技术，并将丰富数学优化、数据分析和统计建模的基础。该奖项反映了NSF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。

项目成果

Fast Global Convergence of Natural Policy Gradient Methods with Entropy Regularization

• DOI: 10.1287/opre.2021.2151
• 发表时间: 2020-07
• 期刊: ArXiv
• 作者: Shicong Cen;Chen Cheng;Yuxin Chen;Yuting Wei;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

Breaking the sample complexity barrier to regret-optimal model-free reinforcement learning

打破样本复杂性障碍，实现后悔最优无模型强化学习

• DOI: 10.1093/imaiai/iaac034
• 发表时间: 2023
• 期刊: Information and Inference: A Journal of the IMA
• 作者: Li, Gen;Shi, Laixi;Chen, Yuxin;Chi, Yuejie
• 通讯作者: Chi, Yuejie

Softmax policy gradient methods can take exponential time to converge

• DOI: 10.1007/s10107-022-01920-6
• 发表时间: 2021-02
• 期刊: Mathematical Programming
• 影响因子: 2.7
• 作者: Gen Li;Yuting Wei;Yuejie Chi;Yuantao Gu;Yuxin Chen

Nonconvex Low-Rank Tensor Completion from Noisy Data

• DOI: 10.1287/opre.2021.2106
• 发表时间: 2021-06-03
• 期刊: OPERATIONS RESEARCH
• 影响因子: 2.7
• 作者: Cai, Changxiao;Li, Gen;Chen, Yuxin
• 通讯作者: Chen, Yuxin