MultiSPPL: extending SPPL with multivariate leaf nodes
SPPL  is an expressive probabilistic programming language with exact inference where users express their models using a DSL which compiles to generalized sum-product networks (SPNs)  with univariate leaves. Despite its expressiveness, SPPL does not support inference in linear-Gaussian state-space models which are a widely used class of probabilistic models that support exact in- ference. As such, SPPL does not support useful algorithms such as linear regression or Kalman filtering. This limitation stems from the fact that SPPL only supports univariate leaves in its SPN rep- resentation of programs. In this abstract, first, we specify a com- putational interface for the leaves of SPNs which ensures closure under conditioning, providing the ability to perform exact infer- ence. Second, we observe that certain multivariate distributions– such as the multivariate Gaussian–support our interface suggesting the possibility of extending SPPL to use multivariate leaves. Third, we discuss the design considerations involving PPLs that use this extended class of SPNs to express probability distributions.