Divide and conquer for causal computation

Structural causal models are a powerful framework for causal and counterfactual inference, extending the capabilities of traditional Bayesian networks. These models comprise endogenous and exogenous variables, where the exogenous variables frequently lack clear semantic interpretation. Exogenous variables are typically unobservable, rendering certain counterfactual queries unidentifiable. In such cases, standard inference algorithms for Bayesian networks are insufficient. Recent methods attempt to bound unidentifiable queries through imprecise estimation of exogenous probabilities. However, these methods become computationally infeasible as the cardinality of the exogenous variables increases, thereby constraining the complexity of applicable models. In this paper we study a divide-and-conquer approach that decomposes a general causal model into a set of submodels with low-cardinality exogenous variables, enabling exact calculation of any query within these submodels. By aggregating results from the submodels, efficient approximations of bounds for queries in the original model are obtained. Our proposal is able to handle models with variables of any cardinality assuming that there are no unobserved confounders. We show that the method is theoretically robust, and experimental results demonstrate that it achieves more accurate bounds with lower computational costs compared to existing techniques.