Approximation and Learning in High Dimensions

研究者和她的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等学科之间的相互作用，因为它们影响学习理论和学习算法的发展。研讨会重点讨论了以下主题：测度不等式的集中及其在概率界学习中的应用，核逼近方法及其在支持向量机和其他学习算法中的作用，以及高维数据稀疏逼近的快速算法。理解智力以及它如何在学习和吸收信息中表现出来，是一项重大的科学挑战。它是设计有效分析数据和提取重要信息的系统的关键。研究智力这方面的科学学科被称为学习理论。分析数据的中心任务是回归，它描述了采样值是数据一部分的变量之间的关系（例如，物体的位置和速度以及观察到这些变量的时间），以及数据分类，它根据数据组成部分的值对数据集的每个元素进行分类。本次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家族的关系，以及用于高维数据稀疏近似的快速计算方法。该研讨会通过汇集来自不同学科的研究人员来考虑这些主题，提高了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的交叉点。它在国防和民用领域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，国土安全等应用的快速数据分类，以及人类视觉系统的建模。

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.