Abstract
Probabilistic circuits (PCs) are a class of tractable probabilistic models, which admit efficient inference routines depending on their properties. In this talk, I will discuss the property of marginal determinism, and 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. I will further show how md-vtrees can be used to derive tractability conditions and efficient algorithms for compositional inference queries, in a sound and generalizable manner. In particular, this enables us to derive the first polytime algorithms for causal inference queries such as backdoor adjustment on PCs.