Modeling and Inference for Dynamic Network Analysis

该项目将启动对网络数据和其他复杂数据结构的统计模型的系统研究，这些数据结构通常来自相互作用和自组织过程，如蛋白质折叠，基因表达，神经功能，经济活动和社会行为。 该项目的重点是解决无法通过统计建模和推断的常见方法来处理的新挑战，这些方法通常依赖于以下假设：（i）统计规律性，（ii）由数据外部力量驱动的短程动态，以及（iii）数据的可代表性，作为对代表性单元样本进行的孤立测量的集合。 在复杂的数据问题中，这些假设经常被违反，其特征在于：（i）数据的不同组件之间的高度交互，（ii）由内源反馈机制驱动的动态行为，以及（iii）数据结构的部分或完全不可约化。该项目将产生新的方法，理论成果，并在这些设置的统计推断概念的见解。除了将对各科学领域产生影响的实质性技术贡献外，该项目的研究将通过PI参加向跨学科受众传播概率和统计的论坛而广泛传播给公众。 PI培训研究生，每周举办一次关于概率和统计基础的研讨会，并在他的网站上上传视频供公众访问。此外，PI还大力倡导同行评议改革和开源出版，并将在Researchers.One（一家非盈利出版机构）上公开发表该项目的所有工作，以提高跨学科同行评议的质量和可访问性。为了实现这些目标，该项目将开发用于分析动态和复杂网络数据结构的严格理论和强大的统计方法。 期望的成果包括网络分析的新理论、模型、方法和概念，对现代网络分析统计工具的范围和局限性的更深入理解，以及跨学科网络数据建模的一般框架。模型开发是该项目的核心，重点是将最近提出的边缘和关系可交换网络模型、重新布线模型和图值Levy过程模型的模型类扩展为潜在空间关系模型和网络值的灵活统计框架。自回归和状态空间模型。 根据这些模型，该项目将为统计网络分析的未来发展提供一个理论框架和一系列方法工具。 该项目将借鉴广泛主题的概念和技术，包括贝叶斯非参数化，空间统计，时间序列，概率论，随机过程和计算，以及图论，组合数学和代数的数学概念。 因此，这项研究将为整个数学科学的学科做出重大贡献，在这些学科中，网络和复杂数据分析与蛋白质组学、基因组学、经济学、社会科学、金融学、生物学、计算机科学和物理学以及统计学和相关领域（如数据科学、人工智能、该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

The project will initiate a systematic study of statistical models for network data and other complex data structures which commonly arise from interacting and self-organizing processes such as protein folding, gene expression, neural functioning, economic activity, and social behavior. A focus of the project is to address novel challenges that cannot be handled by common approaches to statistical modeling and inference, which often rely on assumptions of (i) statistical regularity, (ii) short range dynamics driven by forces exogenous to the data, and (iii) representability of the data as the aggregation of isolated measurements taken on a representative sample of units. These assumptions are often violated in complex data problems, which are characterized by (i) high levels of interaction among different components of the data, (ii) dynamical behaviors driven by endogenous feedback mechanisms, and (iii) partial or complete irreducibility of the data structure. The project will produce new methodologies, theoretical results, and conceptual insights for statistical inference in these settings. Beyond substantive technical contributions, which will have an impact across scientific domains, research from the project will be widely disseminated to the general public through the PI's participation in forums for communicating probability and statistics to interdisciplinary audiences. The PI trains graduate students and runs a weekly seminar on the Foundations of Probability and Statistics, with videos uploaded for open public access at his website. In addition, the PI advocates strongly for peer review reform and open source publication, and will publish all work from this project for public peer review on Researchers.One, a non-profit publishing outlet aimed at increasing the quality and accessibility of peer review across research disciplines.To achieve these aims the project will develop rigorous theory and robust statistical methods for analyzing dynamic and complex network data structures. Desired outcomes include new theory, models, methods, and concepts for network analysis, a deeper understanding of the scope and limitations of statistical tools for modern network analysis, and a general framework for modeling network data that arises across scientific disciplines. Model development lies at the core of the project, with a focus on extending recently proposed model classes of edge and relationally exchangeable network models, rewiring models, and graph-valued Levy process models to a flexible statistical framework for latent space relational models and network-valued autoregressive and state space models. From these models, the project will produce a theoretical framework as well as a range of methodological tools for future developments in statistical network analysis. The project will draw on concepts and techniques from a wide range of topics including Bayesian nonparametrics, spatial statistics, time series, probability theory, stochastic processes, and computing, as well as mathematical concepts from graph theory, combinatorics, and algebra. The research will, therefore, contribute substantially to disciplines across the mathematical sciences, where network and complex data analysis have become increasingly relevant for scientific research in proteomics, genomics, economics, social science, finance, biology, computer science, and physics as well as methodologically driven disciplines within statistics and related fields, such as data science, artificial intelligence, and machine learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.