Approximate Weighted First-Order Model Counting: Exploiting Fast Approximate Model Counters and Symmetry
This addresses inference challenges in first-order probabilistic models, offering a practical solution with theoretical guarantees, though it builds incrementally on existing approximate model counters.
The paper tackles the problem of weighted first-order model counting for probabilistic inference in first-order representations like Markov logic networks, presenting ApproxWFOMC, an anytime method that provides bounds on the count. The result shows that the algorithm outperforms existing approximate and exact techniques, with PAC guarantees on the bounds.
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.