A Divide and Conquer Approach for Solving Structural Causal Models

Structural causal models permit causal and counterfactual reasoning, and can be regarded as an extension of Bayesian networks. The model consists of endogenous and exogenous variables, with exogenous variables often being of unknown semantic interpretation. Consequently, they are typically non-observable, with the result that counterfactual queries may be unidentifiable. In this setting, standard inference algorithms for Bayesian networks are insufficient. Recent methods attempt to bound unidentifiable queries through imprecise estimation of exogenous probabilities. However, these approaches become unfeasible with growing cardinality of the exogenous variables. This paper proposes a divide and conquer method that transforms a general causal model into a set of models with low-cardinality exogenous variables, for which any query can be calculated exactly. Bounds for a query in the original model are then efficiently approximated by aggregating the results for the set of smaller models. Experimental results demonstrate that these bounds can be computed with lower error levels and less resource consumption compared to existing methods.