Bayesian estimation of causal effects in Bayesian networks with local structure

We consider the problem of estimating causal effects from observational categorical data when the data-generating process can be modeled by an unknown causal Bayesian network with local dependence structure in its conditional distributions. Capturing local structure in a categorical Bayesian network may significantly reduce the number of parameters and facilitate the discovery of weak dependencies and edge orientation, which is crucial for causal inference. We extend the Bayesian IDA (BIDA) framework to Bayesian networks with local structure, focusing on a specific class of local independencies called context-specific independencies (CSI). To this end, we build upon previous work that combines Markov chain Monte Carlo methods over DAGs with deterministic greedy optimisation of CSI-trees to learn the full network structure, and propose a local approach for efficient estimation of pairwise causal effects in a given structure, where we apply the same greedy optimisation procedure to infer the conditional distributions involved in the backdoor formula. We evaluate the proposed method in a simulation study in which we simulate data from synthetic Bayesian networks with local structure, as well as a set of benchmark networks.