Reviews: New Liftable Classes for First-Order Probabilistic Inference

This paper makes a concrete contribution to lifted probabilistic inference, showing that the domain recursion rule can be used to solve certain interesting problems that are intractable for state-of-the-art lifted inference software. The insights here seem likely to be incorporated into upcoming versions of those packages. However, some of the statements in the paper are not sufficiently precise. The description of the domain recursion rule itself (p. 5, top) is much less precise than the definition in the 2011 paper that introduced it. It's not clear what the preconditions are for applying the rule or exactly how it transforms the theory. Also, the description mentions caching (line 175), but it would be helpful to explain how the inference algorithm ends up making multiple calls to the cache.