CIF: Small: Dynamic Networks: Learning, Inference, and Prediction with Nonparametric Bayesian Methods

复杂的网络无处不在。它们可以是物理的、生物的、社会的和虚拟的。世界上的所有物种都生活在可以被表示为网络的社会中。几乎所有的复杂系统，无论是自然的还是人工的，都是由相互关联的组件组成的网络。所有网络的主要组成部分是它们的节点和节点之间的链接。大多数网络都会随着时间的推移而变化。可以创建新节点，并可以删除旧节点。同样，可以建立新的链接并删除现有的链接。节点可以形成社区，它们可能会在以后离开。节点可以加入另一个社区或创建新的社区。社区可以出现，也可以消失。所有这些现象都可以创造非常丰富的网络动态。在许多科学和工程领域中，了解这些动力学的共同原理、时变的网络结构和调节网络行为的功能是非常重要的。解决这些现象的理论是网络科学的一部分。网络科学的主要目标之一是利用统计信号处理对物理、生物和社会现象进行推理建模。这些愿望是为了提高对这些现象的理解和预测。在这个项目中，研究人员建议通过引入动态网络的新模型以及进行推理和学习的新方法来促进网络科学。PI建议使用一种方法，其中网络模型的复杂性不是预先定义的，而是由观察到的数据确定的。此外，研究人员建议使用基于蒙特卡罗的方法，这些方法可以在模型的非线性和维度方面满足最困难的挑战。

Complex networks are all around us. They can be physical, biological, social, and virtual. All the species in the world live in societies that can be represented as networks. Almost all complex systems, natural or man-made, are networks of interconnected components. The principal ingredients of all networks are their nodes and the links among the nodes. Most networks change with time. New nodes can be created and old ones can be eliminated. Similarly, new links can be established and existing ones removed. The nodes can form communities which they may leave later in time. The nodes may join another community or create a new one. Communities can emerge and disappear. All these phenomena can create very rich network dynamics. Understanding the common principles of these dynamics, the time-varying network structures and the functionalities that regulate network behaviors is of foremost importance in many fields of science and engineering. The theory that addresses these phenomena is a part of Network Science.One of the main objectives of Network Science is to exploit statistical signal processing for inferential modeling of physical, biological, and social phenomena. The aspirations are to improve the understanding and prediction of these phenomena. In this project the investigator proposes to advance Network Science by introducing novel models for dynamic networks and novel ways for making inference and learning about them. The PI proposes to work with a methodology where the complexity of the network model is not predefined a priori but instead, it is determined by the observed data. Furthermore, the investigator proposes to work with Monte Carlo-based methods that can meet the most difficult challenges of the models in terms of their nonlinearities and dimensionalities.