  We study the symmetric weighted first-order model counting task and present
ApproxWFOMC, a novel anytime method for efficiently bounding the weighted
first-order model count in the presence of an unweighted first-order model
counting oracle. The algorithm has applications to inference in a variety of
first-order probabilistic representations, such as Markov logic networks and
probabilistic logic programs. Crucially for many applications, we make no
assumptions on the form of the input sentence. Instead, our algorithm makes use
of the symmetry inherent in the problem by imposing cardinality constraints on
the number of possible true groundings of a sentence's literals. Realising the
first-order model counting oracle in practice using the approximate
hashing-based model counter ApproxMC3, we show how our algorithm outperforms
existing approximate and exact techniques for inference in first-order
probabilistic models. We additionally provide PAC guarantees on the generated
bounds.
