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

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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.