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CAREER: Inference for High-Dimensional Structures via Subspace Learning: Statistics, Computation, and Beyond

职业：通过子空间学习推理高维结构：统计、计算及其他

基本信息

批准号：
2203741
负责人：
Anru Zhang
金额：
$ 40万
依托单位：
Duke University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-10-01 至 2025-06-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2203741&HistoricalAwards=false
关键词：
CAREER Inference Dimensional Structures via

项目摘要

High-dimensional arrays commonly arise from modern scientific and technological research and have been a central topic in modern statistics and data science. Some areas such as genetics, microbiome studies, brain imaging, hyperspectral imaging, etc., yield a large amount of high-dimensional array data; while in some other areas, data can be recast into high-dimensional array form to facilitate analysis. In these situations, the target parameter is often high-dimensional/high-order, but the important information may lie in dimension-reduced subspaces induced by various structural conditions. How to efficiently exploit these subspaces poses significant statistical and computational challenges. This project aims to address these challenges from a perspective of subspace learning. By taking into account dimension-reduced and low-order subspaces, the PI aims to address a series of statistical and machine learning questions by developing new methodologies and theories with statistical and computational advantages. This project will progress along three major directions: (i) fast estimation and inference for high-dimensional arrays via important subspace sketching; (ii) high-order clustering with theoretical guarantees; (iii) ultrahigh-order tensor singular value decomposition via a tensor-train parameterization. The research will be applicable to a variety of topics involving high-dimensional matrix and tensor data, such as genetics and genomes, reinforcement learning, neuroimaging analysis, material science, recommender design, etc. The PI will also develop user-friendly software packages for the new algorithms and make them available for public use. The PI is committed to training students, especially those from groups underrepresented in STEM, through involvement in the research project.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.

高维数组是现代科学技术研究中的一个重要课题，也是现代统计学和数据科学的一个重要研究方向。一些领域如遗传学、微生物组研究、脑成像、高光谱成像等，产生大量的高维数组数据;而在其他一些领域，数据可以重新转换为高维数组形式以便于分析。在这些情况下，目标参数通常是高维/高阶的，但重要的信息可能在于由各种结构条件诱导的降维子空间。如何有效地利用这些子空间提出了重大的统计和计算挑战。该项目旨在从子空间学习的角度解决这些挑战。通过考虑降维和低阶子空间，PI旨在通过开发具有统计和计算优势的新方法和理论来解决一系列统计和机器学习问题。该项目将沿着三个主要方向进行：（i）通过重要子空间草图对高维阵列的快速估计和推断;（ii）具有理论保证的高阶聚类;（iii）通过张量序列参数化的超高阶张量奇异值分解。该研究将适用于涉及高维矩阵和张量数据的各种主题，例如遗传学和基因组，强化学习，神经成像分析，材料科学，推荐器设计等，PI还将为新算法开发用户友好的软件包，并将其提供给公众使用。PI致力于通过参与研究项目来培训学生，特别是那些来自STEM领域代表性不足的群体的学生。该奖项反映了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审查标准进行评估，被认为值得支持。