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.

高维数组通常产生于现代科学技术研究，一直是现代统计学和数据科学的中心课题。遗传学、微生物组研究、脑成像、高光谱成像等领域产生大量高维阵列数据；而在其他一些领域，可以将数据重新转换为高维数组形式，以方便分析。在这些情况下，目标参数通常是高维/高阶的，但重要信息可能位于由各种结构条件引起的降维子空间中。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展：（i）通过重要的子空间草图快速估计和推断高维数组； (ii) 有理论保证的高阶聚类；（iii）通过张量序列参数化进行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、神经影像分析、材料科学、推荐设计等。PI还将开发用户友好的软件包新算法并使它们可供公众使用。 PI 致力于通过参与研究项目来培训学生，特别是来自 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。