On the Completeness and Complexity of Lifted Temporal Inference

For static lifted inference algorithms, completeness, i.e., domain liftability, is extensively studied. However, so far no domain liftability results for temporal lifted inference algorithms exist. In this paper, we contribute the first completeness and complexity analysis for a temporal lifted algorithm, the so-called lifted dynamic junction tree algorithm (LDJT), which is the only exact lifted temporal inference algorithm out there. To handle temporal aspects efficiently, LDJT uses conditional independences to proceed in time, leading to restrictions w.r.t. elimination orders. We show that these restrictions influence the domain liftability results and show that one particular case while proceeding in time, has to be excluded from FO². Additionally, for the complexity of LDJT, we prove that the lifted width is in even more cases smaller than the corresponding treewidth in comparison to static inference.