Lifted Variable Elimination: A Novel Operator and Completeness Results
  Various methods for lifted probabilistic inference have been proposed, but
our understanding of these methods and the relationships between them is still
limited, compared to their propositional counterparts. The only existing
theoretical characterization of lifting is for weighted first-order model
counting (WFOMC), which was shown to be complete domain-lifted for the class of
2-logvar models. This paper makes two contributions to lifted variable
elimination (LVE). First, we introduce a novel inference operator called group
inversion. Second, we prove that LVE augmented with this operator is complete
in the same sense as WFOMC.
