Sampling and Inference in Network Analysis

复杂网络的研究构成了一个跨学科的研究领域，通过关注各种感兴趣的系统中组件的基本相互依赖性，超越了传统的知识领域。这样的例子比比皆是，从社会网络到人与自然的耦合系统，从金融网络到疾病系统，从电信网络到能源和电力系统。这些组成部分之间的相互联系往往是我们最棘手的全球重大挑战问题的核心，包括气候变化、能源需求、安全、健康和保健、生计和贫困。对这些复杂系统和通常是大规模网络的研究——了解它们的内在特性，它们的结构随时间或外部因素的变化，个体到粗粒度模块化社区的多尺度行为——可以在解决这些重大挑战问题时为个人、组织和整个社会提供重要的见解。该项目旨在为大型潜在动态网络的建模和分析开发健壮且可扩展的采样方法。抽样通常被吹捧为一种有效地对抗估计总体相关特征的固有复杂性的手段。对网络进行采样是很复杂的，因为它们是由两个单元（节点和边）组成的，它们并不总是很好地嵌套。一个关键目标将是研究并提供一个健全的数学基础，以及用于网络分析和建模的以节点为中心和以边缘为中心的采样方法的高性能工具。从社会网络和网络生物学中提取高性能工具用于现实世界应用的目标同样重要，并且对于跨学科性质的持续创新是必要的。本研究将阐明静态和动态网络环境下图采样和概率推理的理论基础。从教育的角度来看，研究人员将在这个跨学科领域培养下一代研究生，并积极鼓励本科生和少数民族的参与。

The study of complex networks constitutes an interdisciplinary area of inquiry that transcends traditional knowledge domains by focusing on the fundamental interdependencies of components within various systems-of-interest. Examples abound from social networks to coupled human and natural systems, from financial networks to disease systems, and from telecommunication networks to energy and power systems. It is the interconnection among these components that often sit at the heart of our most vexing global grand challenge problems, including climate change, energy demands, security, health and wellness, and livelihood and poverty. The study of such complex systems and often large scale networks -- understanding their intrinsic properties, changes to their structure over time or due to external factors, multi-scale behavior of individuals to coarser grained modular communities -- can afford important insights to individuals, organizations and society at large when tackling such grand challenge problems. This project seeks to develop robust and scalable sampling methods for the modeling and analysis of large, potentially dynamic, networks. Sampling is often touted as a means to efficiently combat the inherent complexity of estimating the relevant characteristics of a population. Sampling a network is complicated because they are composed of two units (nodes and edges) that are not always nicely nested. A key objective will be to study and provide a sound mathematical basis along with high performance tools for both node-centric and edge-centric sampling methodologies for the analysis and modeling of networks. The objective of realizing high performance tools for real world applications, drawn from social networks and network biology, will be equally significant, and is necessary for sustained innovation of an inter-disciplinary nature. This research will shed light on the theoretical underpinnings of graph sampling and probabilistic inference in both the static and dynamic network contexts. From an educational standpoint, the investigators will train the next generation of graduate students in this interdisciplinary arena and will also actively encourage participation of undergraduates and under-represented minorities.