Generalized Counting for Lifted Variable Elimination

Lifted probabilistic inference methods exploit symmetries in the structure of probabilistic models to perform inference more efficiently. In lifted variable elimination, the symmetry among a group of interchangeable random variables is captured by counting formulas, and exploited by operations that handle such formulas. In this paper we generalize the structure of counting formulas and present a set of inference operators that introduce and eliminate these formulas from the model. This generalization expands the range of problems that can be solved in a lifted way. Our work is closely related to the recently introduced method of joint conversion. Due to its more fine grained formulation, however, our approach can provide more efficient solutions than joint conversion.