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Various methods for lifted probabilistic inference have been proposed, butour understanding of these methods and the relationships between them is stilllimited, compared to their propositional counterparts. The only existingtheoretical characterization of lifting is for weighted first-order modelcounting (WFOMC), which was shown to be complete domain-lifted for the class of2-logvar models. This paper makes two contributions to lifted variableelimination (LVE). First, we introduce a novel inference operator called groupinversion. Second, we prove that LVE augmented with this operator is completein the same sense as WFOMC.

Lifted Variable Elimination: A Novel Operator and Completeness Results