Towards Completeness in Causal Discovery from Soft Interventions with Known Targets

We study causal discovery from soft interventions in the presence of latent confounding. Beyond within-environment conditional independences, soft interventions induce cross-environment invariances that can be encoded using an augmented graph with intervention indicator nodes ($\mathcal{I}$-AUG). Taking its maximal ancestral graph (MAG) yields the $\mathcal{I}$-MAG, which characterizes the interventional Markov equivalence class. Building on this framework, we show that the FCI-inspired learner ($\mathcal{I}$-FCI) by Kocaoglu et al. (2019) is sound but not complete: it may output circle endpoints that are nevertheless compelled by the interventional equivalence class. To exploit intervention-node semantics, we propose two complementary methods. First, we introduce an enumeration-based completion procedure that is sound and theoretically complete, but whose worst-case cost depends on the number of MAGs compatible with the partial graph learned by $\mathcal{I}$-FCI. Second, we derive a set of additional local orientation rules that provably tighten $\mathcal{I}$-FCI without increasing asymptotic complexity. Both methods refine prior outputs in the controlled soft-intervention setting with latent variables.

Causal discovery aims to learn cause-and-effect relationships from data, but this becomes difficult when some important variables are unobserved. This paper studies causal discovery from data collected under known soft interventions, where an intervention changes how a variable behaves without directly setting its value. Prior work represents such interventions by adding special intervention nodes to a graph, but its learning algorithm can still leave some causal directions unresolved even when they are identifiable. We show that these intervention nodes contain additional structural information that can be used to orient more edges. We develop two methods: an exhaustive method that is theoretically complete but can be slow, and a faster rule-based method that efficiently recovers extra causal directions. Experiments on simulated data show that the fast method improves over the prior algorithm while keeping similar runtime.