Collaborative Research: Network Analysis via Optimal Transport of Markov Embeddings

Networks have been used for many years to model and study a variety of phenomena, including social interactions, co-authorship of scholarly work, and financial interactions. More recently, networks themselves have become objects of study. This research project will develop new statistical approaches for comparing and aligning networks, and will include applications of these methods to problems in computational neuroscience, systems biology, and urban planning. This research will advance the state of network analysis by providing new statistical methods as well as theoretical support for these methods. The broader impacts of the project include applications, collaborations with disciplinary scientists, educational outreach from high school to the graduate level, and community outreach. This research project focuses on the statistical analysis of network data, including the design of new methods, the development of rigorous theoretical support for these methods, and the application of these methods in several relevant scientific domains. The project has four specific objectives. First, investigate optimal transport-based distances for Markov embeddings of networks. Second, develop new methods for network alignment and comparison based on these distances, and apply these or new methods to the problems of model fitting, classification, and node feature prediction. Third, establish rigorous theoretical results concerning the properties of optimal transport distances on networks, investigate relationships between distances and different embedding procedures, and provide theoretical support for the associated methods. Fourth, apply the methods to address problems in computational neuroscience, systems biology, and urban planning. This research will bring together ideas from Markov chains and optimal transport in the setting of network analysis, and the applications of this research will involve the development of efficient, scalable algorithms for analyzing network data. 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.