Graphs are a powerful tool for the study of dynamic processes, where a set of interconnected entities change their states according to the time-varying behavior of an underlying complex system. For instance, in a social network, an individual's opinions are influenced by their contacts; while, in a traffic network, traffic conditions are spatially localized due to the fact that vehicles are often constrained to move along roads. Understanding the interplay between structure and dynamics in networked systems enables new models, algorithms, and data structures for managing and learning from large amounts of data arising from these processes.
In this talk, I will overview my recent work on the analysis of dynamic graph processes, which consists of temporal data embedded on the vertices/edges of a graph. More specifically, I will show how sampling and spectral graph theory can be applied to effectively represent data from such processes. I will also propose efficient algorithms for learning Interleaved Markov Models (IHMMs). These are powerful latent variable models that enable the clustering of discrete sequences without training data and lead to interesting challenges in terms of inference. Furthermore, I will briefly discuss how graphs can be modified in order to control a process of interest via network design and introduce three ongoing projects that were motivated by the research developed in this thesis.