Ranking Large Information Sets

本研究的目的是开发统计工具，并构建有效的模拟方法进行验证和测试。 互联、动态和复杂的信息集网络迅速增长，例如，万维网（WWW）、科学数据、社交网络、新闻、国家安全数据等，正达到前所未有的规模 因此，对这些数据集进行排序/排序的有效方法对于充分利用这些丰富的信息至关重要。 考虑到这些信息集的规模和复杂性在未来将继续增加，需要一种新的概率方法来理解它们的平均行为，就像需要统计力学来理解大量分子一样。 为此，将开发统计工具，用于分析各种动态、分布式和可能的非线性信息排序算法。新的统计方法将开发提供一个框架，设计排名算法与预先指定的行为。 作为分析工作的补充，将构建有效的模拟方法来验证建模假设，并测试排名算法和信息网络的二阶属性。如果成功，本研究的结果将为分析和设计具有预定典型行为的定制排名算法提供新的框架，这将导致算法更好地适应特定应用领域的不同要求。考虑到这项工作将追求分析上易于处理的近似方法，预计它将为排名算法提供相当多的新见解和经验规则。此外，发达国家的数学技术将显着丰富现有的文献加权随机递归，重尾大偏差，加权分支过程，和有效的模拟方法。这项工作也预计将有一个实质性的更广泛的影响，因为前面的数学学科被大量用于各种各样的应用领域，包括算法分析，生物学和统计力学。

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.