AF: Medium: Collaborative Research: Beyond Sparsity: Refined Measures of Complexity for Linear Algebra

AF：媒介：协作研究：超越稀疏性：线性代数复杂性的精确度量

• 批准号: 1763315
• 负责人: Christopher Re
• 金额: $ 55.21万
• 依托单位: Stanford University
• 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: 2018-03-15 至 2022-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1763315&HistoricalAwards=false
• 关键词: AF; Medium; Collaborative; Research; Beyond

Modern data science applications exploit structure in real life data using machine learning (including deep learning) algorithms. At the core of most of these systems are algorithms for a branch of mathematics called linear algebra. In particular, a large portion of these algorithms utilize the fact that real life data has properties that can be captured using certain parsimonious linear algebraic structures. This project studies new, more powerful linear algebraic structures and algorithms that exploit these new structures. Given the fundamental importance of these algorithms, ideas generated from this project are expected to be implemented in widely deployed machine learning systems. The outreach component of this project involves (1) a technical workshop for researchers from diverse areas and (2) outreach events for K-12 students.A variety of problems in modern data science have been successfully characterized using a width. For example, one of the most common widths, the rank of a matrix, has a near-ubiquitous use across many applications. This project significantly expands the understanding of several recently proposed widths and extracts their full potential for positive practical outcomes. Furthermore, it contributes to the recently growing work on beyond worst-case analysis in linear algebra, machine learning and coding theory.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.

现代数据科学应用程序利用机器学习（包括深度学习）算法利用现实生活数据中的结构。这些系统大多数的核心是数学分支的算法，称为线性代数。特别是，这些算法中的很大一部分利用了一个事实，即现实生活数据具有可以使用某些简约的线性代数结构捕获的属性。该项目研究了利用这些新结构的新的，更强大的线性代数结构和算法。鉴于这些算法的基本重要性，预计从该项目产生的想法将在广泛部署的机器学习系统中实施。该项目的外展部分涉及（1）针对来自不同领域的研究人员的技术研讨会以及（2）K-12学生的外展活动。现代数据科学中的各种问题已成功地使用宽度来表征。例如，最常见的宽度之一是矩阵的等级，在许多应用程序中都有几乎u的使用。该项目大大扩展了对最近提议的宽度的理解，并提取了其积极实践结果的全部潜力。此外，这有助于最近在线性代数，机器学习和编码理论中进行超越最坏情况分析的工作。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知识分子和更广泛影响的评估评估来支持的。