The development of efficient exact and approximate algorithms for probabilistic inference is a long-standing goal of artificial intelligence research. Whereas substantial progress has been made in dealing with purely discrete or purely continuous domains, adapting the developed solutions to tackle hybrid domains, characterized by discrete and continuous variables and their relationships, is highly non-trivial. Weighted Model Integration (WMI) recently emerged as a unifying formalism for probabilistic inference in hybrid domains. Despite a considerable amount of recent work, allowing WMI algorithms to scale with the complexity of the hybrid problem is still a challenge. In this paper we highlight some substantial limitations of existing state-of-the-art solutions, and develop an algorithm that combines SMT-based enumeration, an efficient technique in formal verification, with an effective encoding of the problem structure. This allows our algorithm to avoid generating redundant models, resulting in drastic computational savings. Additionally, we show how SMT-based approaches can seamlessly deal with different integration techniques, both exact and approximate, significantly expanding the set of problems that can be tackled by WMI technology. An extensive experimental evaluation on both synthetic and real-world datasets confirms the substantial advantage of the proposed solution over existing alternatives. The application potential of this technology is further showcased on a prototypical task aimed at verifying the fairness of probabilistic programs.

开发用于概率推理的高效精确和近似算法是人工智能研究的长期目标。尽管在处理纯离散或纯连续领域方面已经取得了实质性进展，但采用已开发的解决方案来处理以离散和连续变量及其关系为特征的混合领域是非常重要的。加权模型集成（WMI）最近成为混合领域概率推理的统一形式。尽管最近做了大量工作，但允许 WMI 算法根据混合问题的复杂性进行扩展仍然是一个挑战。在本文中，我们强调了现有最先进解决方案的一些实质性局限性，并开发了一种将基于 SMT 的枚举（形式验证中的有效技术）与问题结构的有效编码相结合的算法。这使得我们的算法能够避免生成冗余模型，从而大大节省计算量。此外，我们还展示了基于 SMT 的方法如何无缝处理不同的集成技术（精确的和近似的），从而显着扩展了 WMI 技术可以解决的问题集。对合成数据集和真实数据集的广泛实验评估证实了所提出的解决方案相对于现有替代方案的巨大优势。该技术的应用潜力在旨在验证概率程序公平性的原型任务上得到了进一步展示。