Lifted Inference on Transitive Relations

Wen Pu, Jaesik Choi, Eyal Amir

Abstract: Lifted inference algorithms are able to boost efficiency through exploiting symmetries of the underling first-order probabilistic models. Models with transitive relations (e.g., if X and Y are friends and so are Y and Z, then X and Z will likely be friends) are essential in social network analysis. With n elements in a transitive relation model, the computational complexity of exact propositional inference is O(2n(n-1)/2), making it intractable for large domains. However, no tractable exact inference on the transitive relations has been reported on the transitive relations. In this paper, we report a novel deterministic approximate lifted inference algorithm, which efficiently solves inference problems on the transitive relations without degenerating input models. We introduce an alternative graph representation for first-order probabilistic models with formulas of homogeneous bivariate predicates. The new representation, which is closely related to exponential-family random graph models, leads to an efficient deterministic approximate lifting algorithm by exploiting the asymptotic properties of the state space. We perform experiments to verify the effectiveness of the proposed algorithm.