基于消息传递的逻辑和算术约束混合概率推理的扩展
Scaling up Hybrid Probabilistic Inference with Logical and Arithmetic Constraints via Message Passing
摘要：
加权模型集成（Weighted Model Integration，简称WIM）是一个非常吸引人的概率推理框架：它允许通过可满足性模理论（Satisfiability Modulo Theories，简称SMT）的语言来表达变量既连续又离散的真实世界问题的复杂依赖关系，以及计算具有复杂逻辑和算术约束的概率查询。然而，现有的非线性规划求解器还没有准备好扩展到这些问题。它们要么完全忽略了问题的内在依赖结构，要么局限于限制性太强的结构。为了缩小这一差距，我们推导出一个因式分解的形式主义，使我们能够设计一个可扩展的基于消息传递，MP-BSSOVER。也就是说，MP-SVM是第一个SVM求解器，它允许：1）对整个树结构的SVM问题进行精确推理; 2）在线性时间内计算所有边缘密度; 3）摊销查询间的推理。实验结果表明，我们的求解器显着优于现有的非线性规划求解器在一个大的基准集。
英文摘要：
Weighted model integration (WMI) is a very appealing framework for probabilistic inference: it allows to express the complex dependencies of real-world problems where variables are both continuous and discrete, via the language of Satisfiability Modulo Theories (SMT), as well as to compute probabilistic queries with complex logical and arithmetic constraints. Yet, existing WMI solvers are not ready to scale to these problems. They either ignore the intrinsic dependency structure of the problem at all, or they are limited to too restrictive structures. To narrow this gap, we derive a factorized formalism of WMI enabling us to devise a scalable WMI solver based on message passing, MP-WMI. Namely, MP-WMI is the first WMI solver which allows to: 1) perform exact inference on the full class of tree-structured WMI problems; 2) compute all marginal densities in linear time; 3) amortize inference inter query. Experimental results show that our solver dramatically outperforms the existing WMI solvers on a large set of benchmarks.
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。
