带逻辑约束的混合概率推理：可处理性和消息传递
Hybrid Probabilistic Inference with Logical Constraints: Tractability and Message Passing
摘要：
加权模型集成（Weighted Model Integration，简称WMM）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）的语言来表达真实世界混合场景的复杂依赖关系，其中变量在本质上是异构的（包括连续和离散）;以及计算具有任意复杂逻辑约束的概率查询。最近的工作表明，在某些假设下，可简化的模型集成（MI）问题，从而有效地允许混合概率推理的体积计算。在本文中，我们介绍了一种新的制定MI通过消息传递计划，允许有效地计算的边际密度和统计矩的所有变量在线性时间。因此，当任意丰富的MI查询符合问题结构时，我们能够摊销推理，这里表示为与SMT公式相关联的原始图。此外，我们从理论上跟踪的易处理边界的确切MI。事实上，我们证明，在原始图的结构要求，使我们的MI算法易于处理-边界的直径和树宽-边界不仅是足够的，但通过MI易于推理的必要条件。
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 hybrid scenarios where variables are heterogeneous in nature (both continuous and discrete) via the language of Satisfiability Modulo Theories (SMT); as well as computing probabilistic queries with arbitrarily complex logical constraints. Recent work has shown WMI inference to be reducible to a model integration (MI) problem, under some assumptions, thus effectively allowing hybrid probabilistic reasoning by volume computations. In this paper, we introduce a novel formulation of MI via a message passing scheme that allows to efficiently compute the marginal densities and statistical moments of all the variables in linear time. As such, we are able to amortize inference for arbitrarily rich MI queries when they conform to the problem structure, here represented as the primal graph associated to the SMT formula. Furthermore, we theoretically trace the tractability boundaries of exact MI. Indeed, we prove that in terms of the structural requirements on the primal graph that make our MI algorithm tractable - bounding its diameter and treewidth - the bounds are not only sufficient, but necessary for tractable inference via MI.
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