Combining learned MAGs with unintervened variables

Develop a method to combine the maximal ancestral graph learned from intervened variables with unintervened observed variables in order to enable finer causal discovery over all observed system variables.

Background

When interventions cover only a subset of observed variables, the paper's MAG-based procedure treats the remaining observed variables as latent and therefore learns a graph only over the intervention targets. The authors note that edges in this latent-projected graph need not correspond to edges in the MAG over all observed variables. Consequently, the paper does not resolve how to incorporate the untargeted observed variables into the learned structure for more refined causal discovery.

References

Since edges in this latent projected graph may not exist in the MAG on all observed variables, it is unclear how to combine the learned MAG and unintervened variables for a finer causal discovery.

— Statistical Inference for Causal Discovery under Selection and Latent Variables via Single-Target Interventions  (2609.28856 - Hou et al., 23 Sep 2026) in Section 5, Inference under Selection in the Absence of Latent Variables