ATD Collaborative Research: Theory and Algorithms for High Dimensional Learning

ATD协作研究：高维学习的理论和算法

• 批准号: 1222715
• 负责人: Ronald DeVore
• 金额: $ 24.89万
• 依托单位: Texas A&M University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1222715&HistoricalAwards=false
• 关键词: ATD; Collaborative; Research; Theory; Algorithms

The investigators and their collaborators study how to organize and query high dimensional data in order to extract relevant content while avoiding the so-called curse of dimensionality. The team is developing new analytical and numerical methods based on sparsity, adaptivity, and variable reduction. The focus is placed on developing a coherent theory that results in sophisticated state-of-the-art numerical algorithms that can be applied in a variety of settings. This activity is a critical component of many scientific problems since it complements and supports the scientific methods of theory, experimentation, and simulation. A setting of particular interest to this project is learning tasks such as regression and classification. The research team is developing quantifiable frameworks and algorithms for learning that systematically break down the high dimensional barriers and exploit empirical data collections. Many scientic problems, vital to the security, economy, and health of our nation, are so complex that they challenge this nation's most sophisticated computational resources. Examples occur in modeling physical and biological systems, e.g. in atmospheric modeling; in optimal design (optimal control and shape optimization); and also in understanding social networks such as those that occur in threat detection. The complexity of these problems prohibits the use of traditional off-the-shelf computational techniques for their solution. This research team develops new computational tools that lead to state of the art algorithms for detecting and the capturing critical information held in the solution of such complex systems. An emphasis in this project is the processing of data that arise in threat detection, damage assessment, and containment. This requires the simultaneous analysis of data obtained from different modalities and a variety of sensors. The new algorithms are applied, for example, to identify and track the migration of airborne biological and chemical contaminants. Another application area is the development of new approaches to high dimensional problems related to gene sequencing.

研究人员及其合作者研究如何组织和查询高维数据，以便提取相关内容，同时避免所谓的维数灾难。 该团队正在开发基于稀疏性、适应性和变量缩减的新分析和数值方法。重点是开发一个连贯的理论，产生可应用于各种环境的复杂的、最先进的数值算法。这项活动是许多科学问题的关键组成部分，因为它补充和支持理论、实验和模拟的科学方法。该项目特别感兴趣的一个设置是回归和分类等学习任务。研究团队正在开发可量化的学习框架和算法，系统地打破高维障碍并利用经验数据收集。许多对我们国家的安全、经济和健康至关重要的科学问题非常复杂，以至于对这个国家最先进的计算资源提出了挑战。例子发生在物理和生物系统建模中，例如大气建模；优化设计（优化控制和形状优化）； 以及理解社交网络，例如威胁检测中出现的社交网络。这些问题的复杂性使得无法使用传统的现成计算技术来解决它们。该研究团队开发了新的计算工具，这些工具可以产生最先进的算法，用于检测和捕获此类复杂系统解决方案中的关键信息。该项目的重点是处理威胁检测、损害评估和遏制中产生的数据。 这需要同时分析从不同方式和各种传感器获得的数据。例如，新算法可用于识别和跟踪空气中生物和化学污染物的迁移。另一个应用领域是开发解决与基因测序相关的高维问题的新方法。