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

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 研究者和她的同事组织了一次关于学习理论的研讨会，以激发概率、逼近理论和数值算法等学科之间的相互作用，因为它们影响着学习理论和学习算法的发展。 研讨会强调以下主题：测度不等式的集中及其在学习中概率界限的应用、近似的核方法及其在支持向量机和其他学习算法中的作用，以及高维数据稀疏近似的快速算法。 了解智力及其在学习和吸收信息中的表现是最大的科学挑战之一。 它是设计有效分析数据和提取基本信息的系统的关键。 研究智力这一方面的科学学科称为学习理论。 分析数据的核心任务是回归，它描述变量之间的关系，这些变量的采样值是数据的一部分（例如，对象的位置和速度以及观察这些变量的时间），以及数据分类，它对数据集中的每个元素进行分类数据分量值的术语。 本研讨会强调学习理论的特定方面：帮助选择分散数据的良好表示的概率界限、特定的近似方法及其与称为支持向量机的一般分类技术系列的关系，以及用于高维数据稀疏近似的快速计算方法。该研讨会通过汇集不同学科的研究人员来考虑这些主题，从而提高国家在科学学习理论方面的能力。 学习理论处于人工智能、统计推断和数学数据分析之间的十字路口。 它在国防和民用领域都有无数现有和潜在的应用。 其中典型的是无人驾驶车辆的导航、国土安全等应用的数据快速分类以及人类视觉系统的建模。