We present a generalization of the local expression language used in the Symbolic Probabilistic Inference (SPI) approach to inference in belief nets [1l, [8]. The local expression language in SPI is the language in which the dependence of a node on its antecedents is described. The original language represented the dependence as a single monolithic conditional probability distribution. The extended language provides a set of operators (*, +, and -) which can be used to specify methods for combining partial conditional distributions. As one instance of the utility of this extension, we show how this extended language can be used to capture the semantics, representational advantages, and inferential complexity advantages of the "noisy or" relationship.

We report on an experimental investigation into opportunities for parallelism in beliefnet inference. Specifically, we report on a study performed of the available parallelism, on hypercube style machines, of a set of randomly generated belief nets, using factoring (SPI) style inference algorithms. Our results indicate that substantial speedup is available, but that it is available only through parallelization of individual conformal product operations, and depends critically on finding an appropriate factoring. We find negligible opportunity for parallelism at the topological, or clustering tree, level.