一阶分解树
First-Order Decomposition Trees
摘要：
提升试图通过利用模型中的对称性来加速概率推理。精确提升的推理方法，就像它们的命题对应物一样，通过递归地分解模型和问题来工作。在命题的情况下，存在形式结构，如分解树（dtree），表示这样的分解，并允许我们确定推理的复杂性先验。然而，目前没有等效的结构，也没有类似的复杂性结果提升推理。在本文中，我们引入了FO-dtree，它将命题dtree提升到一阶水平。我们展示了这些树可以描述一个概率逻辑模型的提升推理解决方案（在提升操作序列方面），并对提升推理的复杂性进行了理论分析，提出了树的提升宽度的新概念。
英文摘要：
Lifting attempts to speed up probabilistic inference by exploiting symmetries in the model. Exact lifted inference methods, like their propositional counterparts, work by recursively decomposing the model and the problem. In the propositional case, there exist formal structures, such as decomposition trees (dtrees), that represent such a decomposition and allow us to determine the complexity of inference a priori. However, there is currently no equivalent structure nor analogous complexity results for lifted inference. In this paper, we introduce FO-dtrees, which upgrade propositional dtrees to the first-order level. We show how these trees can characterize a lifted inference solution for a probabilistic logical model (in terms of a sequence of lifted operations), and make a theoretical analysis of the complexity of lifted inference in terms of the novel notion of lifted width for the tree.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
