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: 1222390
• 负责人: Peter Binev
• 金额: $ 30万
• 依托单位: University South Carolina Research Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1222390&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.

研究人员和他们的合作者研究如何组织和查询高维数据，以提取相关内容，同时避免所谓的维度诅咒。该团队正在开发基于稀疏性、适应性和变量减少的新的分析和数值方法。重点放在开发一个连贯的理论，导致复杂的最先进的数值算法，可以在各种情况下应用。本练习是许多科学问题的重要组成部分，因为它补充和支持了理论、实验和模拟的科学方法。这个项目特别感兴趣的一个背景是学习任务，如回归和分类。研究小组正在开发可量化的学习框架和算法，系统地打破高维障碍，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是如此复杂，以至于它们挑战着这个国家最复杂的计算资源。例如，在对物理和生物系统进行建模方面，例如在大气建模方面；在最优设计(最优控制和形状优化)方面；以及在理解社会网络方面，例如在威胁检测中出现的网络方面。这些问题的复杂性禁止使用传统的现成计算技术来解决它们。这个研究团队开发了新的计算工具，这些工具导致了用于检测和捕获此类复杂系统解决方案中的关键信息的最先进算法。该项目的重点是对威胁检测、损害评估和遏制中出现的数据进行处理。这需要同时分析从不同模式和各种传感器获得的数据。例如，新算法被应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与基因测序相关的高维问题的新方法。