Lifted Variable Elimination: A Novel Operator and Completeness Results
This work addresses a theoretical gap in probabilistic inference for AI researchers, providing a more robust foundation for lifted methods, though it is incremental as it builds on existing completeness results.
The paper tackles the limited theoretical understanding of lifted probabilistic inference methods by introducing a novel operator called group inversion for lifted variable elimination (LVE) and proving that LVE with this operator is complete for domain-lifted inference, matching the completeness of weighted first-order model counting for 2-logvar models.
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.