We present a graph-theoretic model of discourse based on the Questions Under Discussion (QUD) framework. Questions and assertions are treated as edges connecting discourse states in a rooted graph, modeling the introduction and resolution of various QUDs as paths through this graph. The amount of common ground presupposed by interlocutors at any given point in a discourse corresponds to graphical depth. We introduce a new task-oriented dialogue corpus and show that experts, presuming a richer common ground, initiate discourse at a deeper level than novices. The QUD-graph model thus enables us to quantify the experthood of a speaker relative to a fixed domain and to characterize the ways in which rich common ground facilitates more efficient communication.

Discriminatively trained undirected graphical models have had wide empirical success, and there has been increasing interest in toolkits that ease their application to complex relational data. The power in relational models is in their repeated structure and tied parameters; at issue is how to define these structures in a powerful and flexible way. Rather than using a declarative language, such as SQL or first-order logic, we advocate using an imperative language to express various aspects of model structure, inference, and learning. By combining the traditional, declarative, statistical semantics of factor graphs with imperative definitions of their construction and operation, we allow the user to mix declarative and procedural domain knowledge, and also gain significant efficiencies. We have implemented such imperatively defined factor graphs in a system we call Factorie, a software library for an object-oriented, strongly-typed, functional language. In experimental comparisons to Markov Logic Networks on joint segmentation and coreference, we find our approach to be 3-15 times faster while reducing error by 20-25%-achieving a new state of the art.