Modeling and Inference for Dynamic Network Analysis

动态网络分析的建模和推理

• 批准号: 2015365
• 负责人: Harry Crane
• 金额: $ 16万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2020
• 资助国家: 美国
• 起止时间: 2020-07-01 至 2024-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2015365&HistoricalAwards=false
• 关键词: Modeling; Inference; Dynamic; Network; Analysis

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.

该项目将启动网络数据和其他复杂数据结构统计模型的系统研究，这些数据结构通常来自蛋白质折叠、基因表达、神经功能、经济活动和社会行为等相互作用和自组织过程。该项目的一个重点是解决统计建模和推理的常用方法无法处理的新挑战，这些方法通常依赖于以下假设：(i)统计规律性，（ii）由数据外生力驱动的短期动态，以及（iii）数据的可表征性，即对具有代表性的单位样本进行的孤立测量的集合。这些假设在复杂的数据问题中经常被违反，这些数据问题的特点是：(i)数据的不同组成部分之间的高水平交互，（ii）由内生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。该项目将为这些背景下的统计推断产生新的方法、理论结果和概念见解。除了将对科学领域产生影响的实质性技术贡献之外，该项目的研究还将通过PI参加向跨学科受众传播概率和统计的论坛，向公众广泛传播。PI培训研究生，每周举办一次关于概率与统计基础的研讨会，并将视频上传到他的网站上供公众访问。此外，PI大力倡导同行评议改革和开源出版，并将在《研究者》上发表该项目的所有成果，供公众同行评议。一个是非营利出版机构，旨在提高跨学科同行评议的质量和可及性。为了实现这些目标，该项目将发展严格的理论和稳健的统计方法来分析动态和复杂的网络数据结构。期望的结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的理解，以及跨科学学科出现的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交换网络模型、重新连接模型和图值Levy过程模型的模型类扩展到潜在空间关系模型和网络值自回归和状态空间模型的灵活统计框架。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、空间统计、时间序列、概率论、随机过程和计算，以及图论、组合学和代数中的数学概念。因此，这项研究将对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、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、人工智能和机器学习）的科学研究越来越相关。该奖项反映了美国国家科学基金会的法定使命，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。