Bayesian networks (BN) are a popular representation for reasoning under uncertainty. The analysis of many real-world use cases, that in principle can be modeled by BNs, suffers however from the computational complexity of inference. Inference methods based on Weighted Model Counting (WMC) reduce the cost of inference by exploiting patterns exhibited by the probabilities associated with BN nodes. However, these methods require a computationally intensive compilation step in search of these patterns, which effectively prohibits the handling of larger BNs. In this paper, we propose a solution to this problem by extending WMC methods with a framework called Compositional Weighted Model Counting (CWMC). CWMC reduces compilation cost by partitioning a BN into a set of subproblems, thereby scaling the application of state-of-the-art innovations in WMC to scenarios where inference cost could previously not be amortized over compilation cost. The framework supports various target representations that are less or equally succinct as decision-DNNF. At the same time, its inference time complexity $\mathcal{O}(n\exp (w))$, where n is the number of variables and w is the tree-width, is comparable to mainstream algorithms based on variable elimination, clustering and conditioning.

贝叶斯网络 (BN) 是在不确定性下进行推理的流行表示。然而，对许多现实世界用例的分析，原则上可以由 BN 建模，但会受到推理的计算复杂性的影响。基于加权模型计数 (WMC) 的推理方法通过利用与 BN 节点相关联的概率表现出的模式来降低推理成本。然而，这些方法需要一个计算密集型的编译步骤来搜索这些模式，这有效地禁止了更大的 BN 的处理。在本文中，我们提出了通过使用称为组合加权模型计数的框架扩展 WMC 方法来解决此问题的方法(CWMC)。CWMC 通过将 BN 划分为一组子问题来降低编译成本，从而将 WMC 中最先进的创新应用扩展到推理成本以前无法通过编译成本摊销的场景。该框架支持各种目标表示，这些表示不如决策 DNNF 简洁或同样简洁。同时，其推理时间复杂度$\mathcal{哦}(n\mathrm{经验值}(瓦))$，其中n是变量的数量，w是树的宽度，可与基于变量消除、聚类和条件的主流算法相媲美。