Statistical Methods for Network Data

网络数据的统计方法

• 批准号: 1106772
• 负责人: Elizaveta Levina
• 金额: $ 29万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2015-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1106772&HistoricalAwards=false
• 关键词: Statistical; Methods; Network; Data

Network data have become common in a wide range of fields, and a large and diverse community of researchers have studied various aspects of networks, yet statistical methods are rarely applied. This project proposes new theory, methodology, and algorithms that take a principled statistical approach to these problems, assess uncertainty, and establish conditions for desirable properties such as consistency. The focus is primarily on discovering community structure in networks, a common phenomenon in practice and a fundamental question in network analysis. New pseudo-likelihood algorithms are proposed for fitting the block model for networks, as well as several generalizations that allow for non-uniform degree distribution within blocks, removing the main limitation of the classic block model. The pseudo-likelihood based on aggregated data substantially speeds up computation, allowing fitting these models to larger and sparser networks than previously possible. The asymptotic distribution of criteria used for community detection is also studied, which leads to development of significance tests for community structure, consistency conditions, and asymptotically correct partition thresholds, which have important practical implications. New, more robust criteria are also proposed, consistent under weaker conditions. The proposal also develops a formal non-parametric test for comparing two networks, a problem that arises frequently in practice but is currently addressed only through informal comparisons of summary statistics. Finally, covariates on nodes and edges are incorporated into the models and used for predicting unobserved links in the networks. Many of the proposed methods provide the first statistical solutions to the corresponding network problems. Development of statistical methods for community detection in networks, while contributing to the development of core statistical theory and methodology, has direct impact on the interdisciplinary field of network analysis and the study of complex networks. The applications of these are wide-spread, covering such diverse areas as infectious disease modeling, national security, communications, sociology, and genomics. The new statistical tools proposed take a more formal, rigorous approach, and have the potential to change how many scientists approach network analysis.

网络数据已经在广泛的领域中变得普遍，并且大量不同的研究人员已经研究了网络的各个方面，但很少应用统计方法。该项目提出了新的理论，方法和算法，对这些问题采取原则性的统计方法，评估不确定性，并为一致性等理想属性建立条件。 重点是发现网络中的社区结构，这是实践中的一种常见现象，也是网络分析中的一个基本问题。 提出了新的伪似然算法来拟合网络的块模型，以及允许块内非均匀度分布的几种推广，消除了经典块模型的主要限制。 基于聚合数据的伪似然大大加快了计算速度，允许将这些模型拟合到比以前更大、更稀疏的网络中。 用于社区检测的标准的渐近分布也进行了研究，从而导致发展的显着性测试社区结构，一致性条件，渐近正确的分区阈值，这具有重要的实际意义。 新的，更强大的标准也提出了，在较弱的条件下一致。 该提案还为比较两个网络制定了正式的非参数测试，这是一个在实践中经常出现的问题，但目前只能通过汇总统计的非正式比较来解决。 最后，节点和边的协变量被纳入模型，并用于预测网络中未观察到的链接。 许多提出的方法提供了相应的网络问题的第一个统计解决方案。 网络社区检测统计方法的发展，在促进核心统计理论和方法的发展的同时，也直接影响着网络分析和复杂网络研究的跨学科领域。 这些技术的应用非常广泛，涵盖了传染病建模、国家安全、通信、社会学和基因组学等不同领域。 提出的新统计工具采用了更正式、更严格的方法，并有可能改变多少科学家接近网络分析。