Doctoral Dissertation Research: Dynamic Network Models for the Scalable Analysis of Networks with Missing or Sampled Joint Edge/Vertex Evolution

在过去的十年中，人们对收集和分析动态网络数据的兴趣急剧增加。这一增长与计算资源和互联网等技术发展相吻合，这些技术允许改进跨时间网络数据的测量、收集和建模。社交网络的例子包括个人之间的友谊、工作线索或紧急信息联系的结构，公司之间的合资企业，以及国家之间的联盟。通过传感器(例如手机)、调查和数据库系统进行的现代数据收集允许进行比过去几十年更大、更详细的动态网络数据收集；然而，即使改进了测量工具，由于设计(例如采样)或设计外(例如机器故障)而丢失数据的问题仍然存在。因此，在大型动态网络上收集数据往往会导致数据丢失，这就需要新的估计和仿真方法。这项博士论文研究项目将使用计算方法、指数族理论和潜在缺失数据框架来开发模型，这些模型将通过真实世界的经验案例进行评估。该项目由几个相互关联的活动组成。这项研究将把目前在社交网络数据统计分析中使用的缺失数据技术扩展到具有和不具有顶点动态的动态网络的上下文。在多重填补的框架下，将发展几种相互竞争的基于似然的缺失数据方法。此外，研究还将通过一系列模拟实验对这些缺失数据模型进行评估，以比较这些缺失数据技术的效率、可扩展性、偏差、准确性和预测精度。本项目将改进和扩展动态网络模型缺失和采样数据方法的研究现状。这些方法将允许改进对动态社交网络过程(例如，在线社交网络、灾难响应网络等)、对社会学家、统计学家、计算机科学家、人口学家、流行病学家和公共政策研究人员具有直接重要性的问题的推断和预测。这项研究中使用的测试案例来自公众感兴趣的真实案例，因此这些方法应该会加强从业者在危害研究、公共卫生和公共政策方面的工作。作为博士论文研究改进奖，提供支持使有前途的学生建立一个强大的，独立的研究事业。

Interest in the collection and analysis of dynamic network data has increased dramatically over the last decade. This growth coincides with technological developments, such as computational resources and the Internet, that allow for improved measurement, collection, and modeling of inter-temporal network data. Examples of social networks include structures of friendships, job leads, or emergency information ties among individuals; joint ventures among firms; and alliances among nations. Modern data collection through sensors (e.g., cellphones), surveys, and database systems has allowed for larger and more detailed dynamic network data collection than was possible in past decades; however, even with improved measurement tools there exists a persistent problem of missing data, either by design (e.g., sampling) or out of design (e.g., machine failure). Thus, the collection of data on large dynamic networks often results in missing data, which requires new methodology for estimation and simulation. This doctoral dissertation research project will employ computational methods, exponential family theory, and a latent missing data framework to develop models that will be evaluated with real-world empirical cases. The project consists of several linked activities. The research will extend current missing data techniques employed in the statistical analysis of social network data to the context of dynamic networks with and without vertex dynamics. Several competing likelihood-based missing data methods under the framework of multiple imputation will be developed. In addition, the research will evaluate these missing data models through a series of simulation experiments to compare the efficiency, scalability, bias, accuracy, and predictive accuracy of these missing data techniques.This project will improve and extend the current state of the art in missing and sampled data methods for dynamic network models. These methods will allow improved inference and prediction for dynamic social network processes (e.g., online social networks, disaster response networks, etc.), problems of immediate importance to sociologists, statisticians, computer scientists, demographers, epidemiologists, and public policy researchers. The test cases used within this research are drawn from real-world cases of interest to the greater public, so these methods should enhance the work of practitioners in hazards research, public health, and public policy. As a Doctoral Dissertation Research Improvement award, support is provided to enable a promising student to establish a strong, independent research career.