We present the Sum-Product Probabilistic Language (SPPL), a new system that automatically delivers exact solutions to a broad range of probabilistic inference queries. SPPL symbolically represents the full distribution on execution traces specified by a probabilistic program using a generalization of sum-product networks. SPPL handles continuous and discrete distributions, many-to-one numerical transformations, and a query language that includes general predicates on random variables. We formalize SPPL in terms of a novel translation strategy from probabilistic programs to a semantic domain of sum-product representations, present new algorithms for exactly conditioning on and computing probabilities of queries, and prove their soundness under the semantics. We present techniques for improving the scalability of translation and inference by automatically exploiting conditional independences and repeated structure in SPPL programs. We implement a prototype of SPPL with a modular architecture and evaluate it on a suite of common benchmarks, which establish that our system is up to 3500x faster than state-of-the-art systems for fairness verification; up to 1000x faster than state-of-the-art symbolic algebra techniques; and can compute exact probabilities of rare events in milliseconds.

中文翻译：

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通过 Sum-Product 表示的概率程序中的精确符号推理

我们介绍了 Sum-Product Probabilistic Language (SPPL)，这是一个新系统，可以自动为广泛的概率推理查询提供精确的解决方案。SPPL 象征性地表示由使用 sum-product 网络的泛化的概率程序指定的执行轨迹的完整分布。SPPL 处理连续和离散分布、多对一数值转换以及包含随机变量通用谓词的查询语言。我们根据从概率程序到和积表示的语义域的新翻译策略来形式化 SPPL，提出用于精确调节和计算查询概率的新算法，并证明它们在语义下的合理性。我们提出了通过自动利用 SPPL 程序中的条件独立性和重复结构来提高翻译和推理可扩展性的技术。我们实现了一个具有模块化架构的 SPPL 原型，并在一套通用基准上对其进行评估，这表明我们的系统比最先进的公平性验证系统快 3500 倍；比最先进的符号代数技术快 1000 倍；并且可以以毫秒为单位计算罕见事件的准确概率。比最先进的符号代数技术快 1000 倍；并且可以以毫秒为单位计算罕见事件的准确概率。比最先进的符号代数技术快 1000 倍；并且可以以毫秒为单位计算罕见事件的准确概率。