Research Publications

Probabilistic reasoning in the real-world often requires inference in continuous variable graphical models, yet there are few methods for \emph{exact, closed-form} inference when joint distributions are non-Gaussian. To address this inferential deficit, we introduce SVE -- a \emph{symbolic} extension of the well-known \emph{variable elimination} algorithm to perform exact inference in an \emph{expressive} class of mixed discrete and continuous variable graphical models whose conditional probability functions can be well-approximated as piecewise combinations of polynomials with bounded support. Using this representation, we show that we can compute all of the SVE operations \emph{exactly and in closed-form}, which crucially includes \emph{definite integration w.r.t. nonlinear piecewise boundary constraints}. To aid in the efficient computation and compact representation of this solution, we use an extended algebraic decision diagram (XADD) data structure that supports all SVE operations. We provide illustrative results for SVE on probabilistic inference queries inspired by robotics localization and tracking applications that use complex continuous distributions; this represents the first time a general closed-form exact solution has been proposed for this expressive class of discrete/continuous graphical models.