First-order probabilistic languages (FOPLs) combine the expressive power of first-order logic with the uncertainty handling of probability theory. Our group aims to apply these languages to interesting real-world domains. However, as we consider FOPLs of increasing complexity, inference grows difficult; and so, when we define useful languages, we must simultaneously work on developing tractable inference algorithms.
In recent years, several families of FOPLs have been proposed, but no clear consensus has emerged about what the "right" language is, either in general, or in specific application domains. We are investigating these proposed languages with respect to expressive power, efficiency of inference, and ease of modeling.
Much of our current research is inspired by Avi Pfeffer's probabilistic relational models (PRMs), a FOPL family based on semantic networks. We have extended PRMs in several ways, most notably by removing the unique-names assumption, and thus introducing uncertainty over the number of objects present in the system. This has permitted us to apply our work to problems such as data association (vehicle tracking), and, more recently, citation clustering. We plan to continue working on information extraction from the web, and also on problems from computational biology, such as modeling motifs in DNA sequences.
Exact inference in these domains is, in general, not tractable, and so we have developed an approximate approach based on the Markov Chain Monte Carlo algorithm, augmented by intelligent proposal distributions. We are also developing deterministic methods, in which the relational structure of the domain is used to motivate a structured variational approximation to the true posterior.