Weighted model integration (WMI) extends Weighted model counting (WMC) to the integration of functions over mixed discrete-continuous domains. It has shown tremendous promise for solving inference problems in graphical models and probabilistic programming. Yet, state-of-the-art tools for WMI are limited in terms of performance and ignore the independence structure that is crucial to improving efficiency. To address this limitation, we propose an efficient model integration algorithm for theories with tree primal graphs. We exploit the sparse graph structure by using search to performing integration. Our algorithm greatly improves the computational efficiency on such problems and exploits context-specific independence between variables. Experimental results show dramatic speedups compared to existing WMI solvers on problems with tree-shaped dependencies.

翻译：加权模型集成(WMI)将加权模型计数(WMC)扩大到混合离散连续域的功能集成,显示了解决图形模型和概率性编程中的推论问题的巨大希望。然而,对于WMI来说,最先进的工具在性能方面有限,忽视了对于提高效率至关重要的独立结构。为了解决这一局限性,我们为树质原始图的理论提出了一个高效的模型集成算法。我们利用微薄的图表结构进行搜索,以完成集成。我们的算法极大地提高了这些问题的计算效率,并探索了不同变量之间因地而异的独立性。实验结果显示,与现有的WMI解算法相比,在树型依赖性问题上的快速增长。