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.

中文翻译：

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近似加权一阶模型计数：利用快速近似模型计数器和对称性

我们研究了对称加权一阶模型计数任务并提出了 ApproxWFOMC，这是一种在存在未加权一阶模型计数预言机的情况下有效限制加权一阶模型计数的新方法。该算法可应用于各种一阶概率表示中的推理，例如马尔可夫逻辑网络和概率逻辑程序。对于许多应用来说至关重要的是，我们不对输入句子的形式做任何假设。相反，我们的算法通过对句子文字的可能真实基础的数量施加基数约束来利用问题中固有的对称性。在实践中使用近似的基于散列的模型计数器ApproxMC3实现一阶模型计数oracle，我们展示了我们的算法如何在一阶概率模型中优于现有的近似和精确推理技术。我们另外在生成的边界上提供 PAC 保证。