Spectral Methods for Contextualizing relational data

用于关联关系数据的谱方法

• 批准号: 1309998
• 负责人: Karl Rohe
• 金额: $ 12万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-15 至 2017-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1309998&HistoricalAwards=false
• 关键词: Spectral; Methods; Contextualizing; relational; data

Networks (or graphs) can represent the relationships in complex systems with myriad interacting elements. Two primary examples are social networks that represents the set of friendships in a group of people and biological networks that represent the functional relationships between proteins in a living cell. Many substantive questions can be phrased as questions of (a) the network structure and (b) supplementary measurements on the actors and their relationships. This project will provide a statistical framework to simultaneously analyze relational (i.e. network) data and its contextualizing measurements. The primary objective is to study the joint variability between the relational data and covariate measurements on the actors in the network. A secondary objective is to begin studying the joint variability among a sample of networks on the same set of actors. In both objectives, this project will (1) propose a general nonparametric model and a set of simple parametric models, (2) devise fast spectral estimators, and (3) provide estimation theory that examines the statistical performance of the spectral estimators under the nonparametric and parametric models. In the age of big data, data sets are both larger and more complex, often coming from measurements on complex systems with myriad interacting elements; social and biological networks can represent the relationships in complex systems and these substantive questions are, in essence, questions regarding networks. The biological networks in the ENCODE research are an example. Moreover, the relationships in complex systems are often measured with a rich set of supplemental information on the actors and their relationships. This research program will provide a statistical framework, including models, algorithms, and theory, to study the supplemental information in tandem with the network, thereby contextualizing the network and the relationships.

网络(或图)可以表示具有无数交互元素的复杂系统中的关系。两个主要的例子是代表一群人之间的友谊的社会网络和代表活细胞中蛋白质之间的功能关系的生物网络。许多实质性问题可以表述为(A)网络结构和(B)关于行为者及其关系的补充衡量标准的问题。该项目将提供一个统计框架，以同时分析关系(即网络)数据及其背景测量。主要目标是研究网络中参与者的关系数据和协变量测量之间的联合可变性。第二个目标是开始研究同一组行为者上的网络样本之间的联合可变性。在这两个目标中，本项目将(1)提出一个通用的非参数模型和一组简单的参数模型，(2)设计快速谱估计器，以及(3)提供在非参数模型和参数模型下检验谱估计器的统计性能的估计理论。在大数据时代，数据集既大又复杂，往往来自对具有无数交互元素的复杂系统的测量；社会和生物网络可以代表复杂系统中的关系，这些实质性问题本质上是关于网络的问题。ENCODE研究中的生物网络就是一个例子。此外，复杂系统中的关系通常是通过关于参与者及其关系的丰富补充信息来衡量的。这一研究计划将提供一个统计框架，包括模型、算法和理论，以研究与网络相结合的补充信息，从而使网络和关系联系起来。