Inference of Network Structure from Grouped Data

从分组数据推断网络结构

• 批准号: 1513004
• 负责人: Yunpeng Zhao
• 金额: $ 12万
• 依托单位: George Mason University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1513004&HistoricalAwards=false
• 关键词: Inference; Network; Structure; Grouped; Data

Networks, which can be viewed as data structures consisting of nodes (vertices) connected by links (edges), have drawn wide attention in a variety of scientific and engineering areas. The applications include friendship and collaboration networks in social sciences, food webs and gene regulatory networks in biology, network games in economics, the Internet and World Wide Web in computer science, as well as many others. Traditionally, statistical network analysis focuses on modeling explicit network structure. For physical networks, like power grids, links between nodes are well defined and can usually be directly observed. By contrast, explicit network structure may not be observable in other fields, especially in social sciences and biology. In these areas, the raw data available is usually behavior of nodes, which is generally presumed to be the result of latent network structure. This project will study the problem of reconstructing implicit networks from a special data structure--grouped data. Each observation of such data is a group of individuals which are observed to appear together. The project is composed of three parts, all concerning rigorous statistical methods for network inference from grouped data. The first part focuses on networks with continuous edge weights. The PI considers two intriguing properties -- self-sparsity and identifiability of Star Model (recently introduced by the PI and his PhD student), and proposes L1 regularization and low-rank matrix factorization in order to reduce the complexity of this model. In the second part, networks with binary links are considered. The PI proposes to study two different methods to estimate the network structures, including a global model based on Erdos-Renyi process and a non-parametric criterion based on subgraph densities. In the third part, the PI considers dependency structure among groups. The Markov property is assumed here, that is, a group generated at any time point only depends on the group structure at the previous time point and the latent network. The PI proposes an intuitive In-and-Out Model under the Markov assumption. The contribution of this project is twofold. Firstly, it is expected that the concept of implicit networks and the study of network inference from grouped data will change some fundamental viewpoints of statistical network analysis. Secondly, the rigorous statistical methods proposed in this project bring new challenging theoretical and computational questions, which will significantly advance the theoretical understanding and computational techniques in this area.

网络可以被看作是由链接（边）连接的节点（顶点）组成的数据结构，在各种科学和工程领域引起了广泛的关注。这些应用包括社会科学领域的友谊和合作网络、生物学领域的食物网和基因调控网络、经济学领域的网络游戏、计算机科学领域的互联网和万维网等。传统上，统计网络分析侧重于对显式网络结构建模。对于物理网络，如电网，节点之间的连接是明确定义的，通常可以直接观察到。相比之下，在其他领域，特别是在社会科学和生物学领域，可能无法观察到明确的网络结构。在这些领域中，可用的原始数据通常是节点的行为，这通常被认为是潜在网络结构的结果。本项目将研究从一种特殊的数据结构——分组数据重构隐式网络的问题。对这些数据的每次观察都是一组被观察到一起出现的个体。该项目由三个部分组成，都涉及从分组数据中进行网络推断的严格统计方法。第一部分主要研究具有连续边权的网络。PI考虑了两个有趣的特性——自稀疏性和可识别性（最近由PI和他的博士生引入），并提出了L1正则化和低秩矩阵分解以降低该模型的复杂性。在第二部分中，考虑了二元链路网络。PI提出了两种不同的网络结构估计方法，包括基于Erdos-Renyi过程的全局模型和基于子图密度的非参数准则。在第三部分，PI考虑了群体之间的依赖结构。这里假设马尔可夫性质，即在任何时间点生成的群只取决于前一个时间点的群结构和潜在网络。在马尔可夫假设下，PI提出了一种直观的输入和输出模型。这个项目的贡献是双重的。首先，隐式网络的概念和分组数据网络推理的研究将改变统计网络分析的一些基本观点。其次，本项目提出的严谨的统计方法带来了新的具有挑战性的理论和计算问题，这将大大促进该领域的理论认识和计算技术。