Ranking Large Information Sets

对大型信息集进行排名

• 批准号: 1131053
• 负责人: Mariana Olvera-Cravioto
• 金额: $ 32.5万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1131053&HistoricalAwards=false
• 关键词: Ranking; Large; Information; Sets

The objective of this research project is to develop statistical tools and construct efficient simulation methods for validation and testing. Rapidly growing webs of interconnected, dynamic and complex information sets, e.g., the World Wide Web (WWW), scientific data, social networks, news, national security data, etc., are reaching unprecedented scales. Hence, effective methods for ordering/ranking these data sets are of utmost importance for making the best use of this wealth of information. Given that the scale and complexity of these information sets will continue to increase in the future, a new probabilistic approach for understanding their average behavior is needed in the same way that statistical mechanics was needed for understanding large sets of molecules. To this end, statistical tools will be developed for the analysis of a variety of dynamic, distributed, and possibly nonlinear information ranking algorithms. The novel statistical methodology to be developed will provide a framework for designing ranking algorithms with a pre-specified behavior. As a complement to the analytical work, efficient simulation methods will be constructed for the validation of modeling assumptions and for testing the second-order properties of ranking algorithms and information webs.If successful, the results of this research will provide a new framework for the analysis and design of customized ranking algorithms with a predetermined typical behavior, which will result in algorithms better tailored to the diverse requirements of specific application areas. Given that the work will pursue analytically tractable approximation methods, it is expected that it will provide a considerable amount of new insights and design rules of thumb for ranking algorithms. Furthermore, the developed mathematical techniques will significantly enrich the existing literature on weighted stochastic recursions, heavy-tailed large deviations, weighted branching processes, and efficient simulation methods. This work is also expected to have a substantial broader impact, since the preceding mathematical disciplines are heavily used in a wide variety of application areas that include the analysis of algorithms, biology, and statistical mechanics.

该研究项目的目的是开发统计工具和构建有效的仿真方法进行验证和测试。 互连，动态和复杂的信息集的快速增长的网络，例如万维网（www），科学数据，社交网络，新闻，国家安全数据等，都达到了前所未有的量表。 因此，订购/排名这些数据集的有效方法对于充分利用这些信息至关重要。 鉴于这些信息集的规模和复杂性将在未来继续增加，因此需要一种新的概率方法来理解其平均行为，就像理解大量分子所需的统计力学一样。 为此，将开发统计工具，以分析各种动态，分布式和可能的非线性信息排名算法。要开发的新型统计方法将为设计具有预先指定行为的排名算法提供一个框架。 作为对分析工作的补充，将构建有效的模拟方法，以验证建模假设并测试排名算法和信息网的二阶属性。如果成功的结果将为您提供针对特定典型的典型行为的自定义排名算法的分析和设计的新框架，以适用于特定的典型行为。鉴于这项工作将采用可分析的近似方法，因此预计它将为排名算法提供大量新的见解和设计规则。此外，开发的数学技术将显着丰富有关加权随机递归，重尾大偏差，加权分支过程和有效仿真方法的现有文献。预计这项工作将产生更大的影响，因为先前的数学学科大量用于各种应用领域，包括分析算法，生物学和统计力学。