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.

翻译：我们讨论了在Pearl结构因果模型中界定部分可识别查询（如反事实）边界的问题。最近提出的迭代期望最大化方案通过对初始化参数进行采样，获得了这些边界的内近似。该方法需要在对共享相同结构方程和拓扑但具有不同外生概率的模型上执行多次（贝叶斯网络）查询。这种设置使得将底层模型编译为算术电路具有优势，从而带来显著的推理加速。我们展示了单次符号知识编译如何使我们获得电路结构，其中符号参数在计算不同查询时被替换为实际值。我们还讨论了进一步加速边界计算的并行化技术。与标准贝叶斯网络推理相比，实验显示出明显的计算优势，加速比可达一个数量级。