Lifted Variable Elimination: A Novel Operator and Completeness Results

TL;DR

This paper introduces a new inference operator called group inversion for lifted variable elimination and proves that with this operator, LVE achieves completeness similar to weighted first-order model counting.

Contribution

It presents a novel operator called group inversion and establishes the completeness of LVE with this operator for lifted probabilistic inference.

Findings

Introduction of group inversion operator

LVE with group inversion is complete for lifted inference

Theoretical equivalence to WFOMC in terms of completeness

Abstract

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.