  We discuss the problem of bounding partially identifiable queries, such as
counterfactuals, in Pearlian structural causal models. A recently proposed
iterated EM scheme yields an inner approximation of those bounds by sampling
the initialisation parameters. Such a method requires multiple (Bayesian
network) queries over models sharing the same structural equations and
topology, but different exogenous probabilities. This setup makes a compilation
of the underlying model to an arithmetic circuit advantageous, thus inducing a
sizeable inferential speed-up. We show how a single symbolic knowledge
compilation allows us to obtain the circuit structure with symbolic parameters
to be replaced by their actual values when computing the different queries. We
also discuss parallelisation techniques to further speed up the bound
computation. Experiments against standard Bayesian network inference show clear
computational advantages with up to an order of magnitude of speed-up.
