Probabilistic circuits (PCs) are a class of tractable probabilistic models, which admit efficient inference routines depending on their structural properties. In this paper, we introduce md-vtrees, a novel structural formulation of (marginal) determinism in structured decomposable PCs, which generalizes previously proposed classes such as probabilistic sentential decision diagrams. Crucially, we show how mdvtrees can be used to derive tractability conditions and efficient algorithms for advanced inference queries expressed as arbitrary compositions of basic probabilistic operations, such as marginalization, multiplication and reciprocals, in a sound and generalizable manner. In particular, we derive the first polytime algorithms for causal inference queries such as backdoor adjustment on PCs. As a practical instantiation of the framework, we propose MDNets, a novel PC architecture using md-vtrees, and empirically demonstrate their application to causal inference.

翻译：概率电路（PCs）是一类可处理的概率模型，其高效推理算法依赖于结构特性。本文提出md-vtrees——结构化可分解PCs中（边际）确定性的一种新型结构形式，该形式推广了诸如概率语句决策图等先前提出的类别。关键在于，我们展示了如何利用md-vtrees推导可处理性条件，并设计高效算法，以可靠且可推广的方式处理由基本概率运算（如边际化、乘法和倒数）任意组合构成的高级推理查询。特别地，我们首次推导出针对PCs上因果推理查询（如后门调整）的多项式时间算法。作为该框架的实践实例，我们提出基于md-vtrees的新型PC架构MDNets，并通过实验证明其在因果推理中的应用。