Approximation and Learning in High Dimensions

高维逼近和学习

• 批准号: 0708470
• 负责人: Guergana Petrova
• 金额: $ 1.5万
• 依托单位: Texas A&M Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0708470&HistoricalAwards=false
• 关键词: Approximation; Learning; Dimensions; Approximation; Learning; Dimensions

Petrova0708470 The investigator and her colleagues organize a workshop onlearning theory to stimulate interactions between the disciplinesof probability, approximation theory, and numerical algorithms asthey affect the development of learning theory and learningalgorithms. The workshop emphasizes the following topics: concentration of measure inequalities and their application toprobability bounds in learning, kernel methods of approximationand their role in support vector machines and other learningalgorithms, and fast algorithms for the sparse approximation ofhigh-dimensional data. Understanding intelligence and how it manifests itself inlearning and in assimilating information is one of the greatscientific challenges. It is a key to designing systems thatefficiently analyze data and extract essential information. Thescientific discipline that studies this aspect of intelligence iscalled learning theory. Central tasks in analyzing data areregression, which describes the relationship between variableswhose sampled values are part of the data (for example, thelocations and speeds of an object and the times when these areobserved), and data classification, which categorizes eachelement of the data set in terms of the values of components ofthe datum. This workshop emphasizes particular aspects oflearning theory: probabilistic bounds to help select goodrepresentations of scattered data, particular approximationmethods and their relation to a general family of classificationtechniques called support vector machines, and fast computationmethods for the sparse approximation of high-dimensional data. The workshop advances the nation's capabilities in scientificlearning theory by bringing together researchers from diversedisciplines to consider these topics. Learning theory sits at acrossroad between aritificial intelligence, statisticalinference, and mathematical data analysis. It has a myriad ofexisting and potential applications in both the defense andcivilian sectors. Typical of these are the navigation ofunmanned vehicles, the fast classification of data for suchapplications as homeland security, and modeling the human visualsystem.

PETROVA0708470研究者及其同事组织了一个关于学习理论的研讨会，以刺激概率，近似理论和数值算法的学科之间的相互作用，这会影响学习理论和学习学院的发展。 研讨会强调了以下主题：量度不平等的集中度及其在学习中的良好性范围，近似值的内核方法以及它们在支持向量机和其他学习方面的作用，以及用于high维数据的稀疏近似值的快速算法。 了解智力及其如何表现出自己的陷入困境和吸收信息是伟大的挑战之一。 它是设计系统可以充分分析数据并提取基本信息的关键。 研究智力的这一方面的学科是学习理论。 分析数据弧度的中心任务，该任务描述了变量之间的关系，这些变量是数据的一部分（例如，对象的theLacation和速度以及这些对象的时间）和数据分类，该数据将数据设置的每个元素分类为数据集值的数据集合值的数据。 该研讨会强调了学习理论的特定方面：概率界限，以帮助选择分散数据的良好表述，特定的近似方法及其与称为支持向量机的一般分类技术家族的关系，以及快速计算方法，以实现高维数据的稀疏近似值。该研讨会通过将来自不同学科的研究人员聚集在一起考虑这些主题，从而提高了美国在科学学习理论中的能力。 学习理论位于ARITICENTICS，统计学和数学数据分析之间。 它在国防和维维利亚部门中都有无数的存在和潜在的应用。 这些典型的是无人车的导航，是诸如国土安全性等数据的快速分类以及对人类视觉效果进行建模。