UC Santa Barbara

This thesis is dedicated to learning structured representations of data, to be utilized by a diverse set of downstream tasks emerging in numerous application domains such as user modeling, document categorization, and graph representation learning. Despite their notable contextual differences, the common objective behind these studies is our desire to incorporate the rich structure of data into our learned representations (both discrete and continuous) and computations, in ways that are unique to each problem. We provide comprehensive evidence showing that the principled utilization of data structure, regardless of the problem domain, is a key step towards reaching our learning objectives.

The second half of the thesis specifically targets problems centered around a complex family of graphs called flow graphs. Besides nodes and edges, flow graphs capture edge flows of a quantity of interest (e.g., water, power, people) being transported through the graph. As these flows often possess higher-order graph-level dynamics driven by sources/destinations, hotspots, and domain-specific physics, the underlying structure of flow graphs poses unique challenges from a learning viewpoint. In particular, we study two challenging problems: (i) network flow estimation based on partial flow observations, and (ii) data-driven generation of realistic flow graphs as an alternative to domain-specific simulations. During each of these studies, we showcase the complex structural patterns emerging in many real-world flow graphs and propose novel methodologies that can account for such richly structured information.