f387624df552cea2f369918c5e1e12bc-Reviews.html

The paper presents a lifted generalization of decomposition trees used to analyze and effective specify a computation tree for the analysis of lifted graphical models. The paper is exceptionally well-written -- it uses a clean notation and is full of examples to guide the reader's understanding. From a quality perspective, this paper is among the top rank of papers I've reviewed for NIPS. The idea is also novel and seemingly worthy of publication -- first-order decision trees (FODTs) strike me as a useful internal data structure for guiding the application of lifted inference. Yet, on the other hand, it should be pointed out that FODTs don't permit novel lifted computations, they only help one organize them and analyze a notion of width which bounds the computational complexity of evaluation w.r.t. an FODT. In some sense the ability to do this computational analysis would have been implicit in any prior implementation that had to recursively break down a model and apply operations, namely the cited work of Milch et al, but again this paper formalizes the recursive structure and analysis in a way that I'm not aware has been done before.