Over the past few years our research group has undertaken several projects within the broad area of probabilistic and decision-theoretic reasoning. The following lists four particular areas of ongoing effort, with pointers to background material and representative papers. This work has been supported in large part by grants from the Air Force Office of Scientific Research.
The idea of state-space abstraction is to trade off accuracy for computational efficiency by ignoring distinctions in a joint probability distribution. We have applied this approach to inference in Bayesian Networks, using an anytime algorithm that produces increasingly accurate approximations by iteratively refining the state spaces of random variables. Continuing work has investigated the properties of these algorithms theoretically and experimentally, identifying general relationships on abstraction approximations as well as heuristic guides for controlling the abstraction process.