Weighted model integration (WMI) extends weighted model counting (WMC) in providing a computational abstraction for probabilistic inference in mixed discrete-continuous domains. WMC has emerged as an assembly language for state-of-the-art reasoning in Bayesian networks, factor graphs, probabilistic programs and probabilistic databases. In this regard, WMI shows immense promise to be much more widely applicable, especially as many real-world applications involve attribute and feature spaces that are continuous and mixed. Nonetheless, state-of-the-art tools for WMI are limited and less mature than their propositional counterparts. In this work, we propose a new implementation regime that leverages propositional knowledge compilation for scaling up inference. In particular, we use sentential decision diagrams, a tractable representation of Boolean functions, as the underlying model counting and model enumeration scheme. Our regime performs competitively to state-of-the-art WMI systems but is also shown to handle a specific class of non-linear constraints over non-linear potentials.

中文翻译：

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通过利用知识汇编扩展线性和非线性混合域中的概率推理

加权模型集成 (WMI) 扩展了加权模型计数 (WMC)，为混合离散连续域中的概率推理提供了计算抽象。WMC 已成为贝叶斯网络、因子图、概率程序和概率数据库中最先进推理的汇编语言。在这方面，WMI 显示出更广泛适用的巨大前景，尤其是在许多实际应用程序涉及连续和混合的属性和特征空间时。尽管如此，用于 WMI 的最先进工具是有限的，并且不如它们的命题对应工具成熟。在这项工作中，我们提出了一种新的实现机制，它利用命题知识编译来扩大推理。特别是，我们使用句子决策图，布尔函数的易处理表示，作为底层模型计数和模型枚举方案。我们的机制与最先进的 WMI 系统相比具有竞争力，但也被证明可以处理非线性潜力上的特定类型的非线性约束。