Iterative testing procedures and high-dimensional scaling limits of extremal random structures

在过去的十年中，网络和网络模型在经济学、神经科学、基因组学和生物医学等各个领域的使用和重要性越来越高。这些领域的工作推动了关于复杂网络建模和推理的统计研究的增加。PI将在统计网络研究中追求几个新的方向，一个关键主题是在复杂，随机和几何网络理论上的概率最近工作的应用和扩展。特别是，PI将开发迭代测试方法，以识别大型数据集中的相关变化，并增强将遗传变异与基因表达的全球变化联系起来的基因组研究的能力。他们将扩展现有的概率技术，为迭代测试程序提供理论支持，并解决更广泛的统计问题，涉及大型高维数据集特征之间复杂关联的推断。方法的开发和应用将与基因组学，生物医学和社会学的研究人员合作进行，PI和co-PI与他们有着长期的合作关系。在很大程度上是由于网络在各个领域的使用和重要性的增加，统计界已经有大量的工作致力于测试和估计高维数据集中变量之间的关联问题。与此同时，统计活动，概率组合学领域的最新发展显着推进了我们的理解离散随机结构，捕捉关联的高维对象。PI将带来一些这些概率工具，以承担基于关联的推理问题。特别是，PI将开发和实现一个迭代测试程序，识别图形中的自关联顶点集，以及高维数据集中的自关联变量集。在迭代测试程序的框架内，他们将为几个应用问题开发计算效率高的方法：在两个样本研究中挖掘块相关性差异，并在每个样本用两个或多个测量平台进行评估的研究中识别相互关联的变量组。作为后一个问题的特殊情况，他们将开发工具来增强基因组研究的力量，将局部遗传变异与基因表达的全球变化联系起来。 拟议的研究的第二个组成部分是适应和扩展现有的概率组合学技术，提供支持理论的迭代测试程序，并解决更广泛的统计问题的相关性的测试和估计。这些方法的开发和应用将与基因组学，生物医学和社会学研究人员合作进行，PI和co-PI与他们有着长期的合作关系。

Over the past ten years, networks and network models have seen increasing use and importance in a variety of fields, including economics, neuroscience, genomics, and biomedicine. Work in these fields has driven an increase in statistical research concerning modeling of, and inference about, complex networks. The PIs will pursue several new directions in statistical network research, a key theme being the application and extension of recent work in probability on the theory of complex, random and geometric networks. In particular, the PIs will develop iterative testing methods to identify relational changes in large data sets, and to enhance the power of genomic studies that link genetic variation to global changes in gene expression. They will extend existing probabilistic techniques to provide theoretical support for the iterative testing procedure, and to address broader statistical questions concerning inference about complex associations between the features of large, high dimensional data sets. Methodological development and application will be carried out in cooperation with researchers in genomics, biomedicine, and sociology at UNC, with whom the PI and co-PI have long standing collaborations. Motivated in large part by the increasing use and importance of networks in a variety of fields, there has been a great deal of work in the statistics community devoted to the problem of testing and estimating associations between variables in high dimensional data sets. Concurrent with this statistical activity, recent developments in the fields of probabilistic combinatorics have significantly advanced our understanding of discrete random structures that capture the association of high-dimensional objects. The PIs will bring a number of these probabilistic tools to bear on association based inference problems. In particular, the PIs will develop and implement an iterative testing procedure that identifies self-associated sets of vertices in a graph, and self-associated sets of variables in a high dimensional data set. Within the framework of the iterative testing procedure they will develop computationally efficient methods for several applied problems: mining of block correlation differences in two sample studies, and identifying groups of mutually correlated variables in studies where each sample is assessed with two or more measurement platforms. As a special case of the latter problem, they will develop tools to enhance the power of genomic studies that link local genetic variation to global changes in gene expression. A second component of the proposed research is to adapt and extend existing techniques in probabilistic combinatorics to provide supporting theory for the iterative testing procedure, and to address broader statistical questions concerning the testing and estimation of correlations. Development and application of the methods will be carried out in cooperation with researchers in genomics, biomedicine, and sociology at UNC, with whom the PI and co-PI have long standing collaborations.