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

迭代测试程序和极值随机结构的高维缩放限制

• 批准号: 1613072
• 负责人: Andrew Nobel
• 金额: $ 37.5万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-08-01 至 2020-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1613072&HistoricalAwards=false
• 关键词: Iterative; testing; procedures; dimensional; scaling

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.

在过去的十年中，网络和网络模型在包括经济学，神经科学，基因组学和生物医学在内的各个领域的使用和重要性都在增加。这些领域的工作推动了有关复杂网络的建模和推断的统计研究的增加。 PI将追求统计网络研究中的几个新方向，一个关键主题是在复杂，随机和几何网络理论上的最新工作的应用和扩展。特别是，PI将开发迭代测试方法，以识别大型数据集中的关系变化，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，以为迭代测试程序提供理论支持，并解决有关大型高维数据集之间有关复杂关联的推断的更广泛的统计问题。方法论开发和应用将与UNC的基因组学，生物医学和社会学研究人员合作，与PI和Co-Pi与之建立了长期合作。在很大程度上，由于网络在各个领域的使用和重要性的越来越多，在统计社区中有很多工作致力于测试和估算高维数据集中变量之间关联的问题。与这种统计活动同时，概率组合学领域的最新发展显着提高了我们对捕获高维物体关联的离散随机结构的理解。 PI将带来许多此类概率工具来承担基于关联的推理问题。特别是，PI将开发和实施一个迭代测试程序，该过程在图中识别自我相关的顶点集，并在高维数据集中的自我相关的变量集。在迭代测试程序的框架内，他们将开发一些针对几个应用问题的计算有效方法：在两个样本研究中挖掘块相关差异的挖掘，并鉴定在每个样本中使用两个或更多测量平台评估的研究中相互关联变量的组。作为后一个问题的特殊情况，他们将开发工具，以增强基因组研究的力量，这些研究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在概率组合中适应和扩展现有技术，以为迭代测试程序提供支持理论，并解决有关相关测试和估计的更广泛的统计问题。这些方法的开发和应用将与UNC的基因组学，生物医学和社会学研究人员合作，与PI和CO-PI与之建立长期合作。