  We propose an approach to lifted approximate inference for first-order
probabilistic models, such as Markov logic networks. It is based on performing
exact lifted inference in a simplified first-order model, which is found by
relaxing first-order constraints, and then compensating for the relaxation.
These simplified models can be incrementally improved by carefully recovering
constraints that have been relaxed, also at the first-order level. This leads
to a spectrum of approximations, with lifted belief propagation on one end, and
exact lifted inference on the other. We discuss how relaxation, compensation,
and recovery can be performed, all at the firstorder level, and show
empirically that our approach substantially improves on the approximations of
both propositional solvers and lifted belief propagation.
