Learning causal Bayesian networks (CBNs) from data is challenging when the available information consists of a mixture of observational and interventional samples collected under heterogeneous experimental conditions. Standard structure learning algorithms either ignore interventions or treat them only as hard background constraints, and most of them do not exploit context-specific independence (CSI) patterns that arise in realistic high-dimensional domains. In this paper we introduce Interventional DN2CN, a two-stage method that extends dependency-network-to-causal-network (DN2CN) approaches to the mixed-regime setting. In the first stage, we learn a regime-aware dependency network whose local conditional distributions are represented by shallow decision trees that explicitly condition on both parent variables and an intervention indicator. This representation captures CSI and allows us to detect invariance and change of local mechanisms across different experimental regimes. In the second stage, we convert the (generally cyclic) dependency network into an acyclic causal Bayesian network by (i) removing edges that are incompatible with intervention targets and regime-specific invariance constraints, and (ii) orienting remaining undirected edges using a combination of mutual information, stability across regimes, and simple intervention-based orientation rules. We formalize the problem setting, describe the algorithm, and discuss identifiability conditions that arise from combining CSI with intervention information. We then outline an empirical evaluation on both synthetic benchmarks and a real biological network, comparing Interventional DN2CN with purely observational DN2CN and with classical constraint-based and score-based learners that incorporate intervention targets. Our results design aims to show that explicitly modeling regime-dependent context-specific structure improves both structural recovery and causal effect estimation, particularly for nodes adjacent to manipulated variables. We conclude by discussing limitations and potential extensions to dynamic settings and latent variable models.
Learning causal Bayesian networks (CBNs) from data is challenging when the available information consists of a mixture of observational and interventional samples collected under heterogeneous experimental conditions. Standard structure learning algorithms either ignore interventions or treat them only as hard background constraints, and most of them do not exploit context-specific independence (CSI) patterns that arise in realistic high-dimensional domains. In this paper we introduce Interventional DN2CN, a two-stage method that extends dependency-network-to-causal-network (DN2CN) approaches to the mixed-regime setting. In the first stage, we learn a regime-aware dependency network whose local conditional distributions are represented by shallow decision trees that explicitly condition on both parent variables and an intervention indicator. This representation captures CSI and allows us to detect invariance and change of local mechanisms across different experimental regimes. In the second stage, we convert the (generally cyclic) dependency network into an acyclic causal Bayesian network by (i) removing edges that are incompatible with intervention targets and regime-specific invariance constraints, and (ii) orienting remaining undirected edges using a combination of mutual information, stability across regimes, and simple intervention-based orientation rules. We formalize the problem setting, describe the algorithm, and discuss identifiability conditions that arise from combining CSI with intervention information. We then outline an empirical evaluation on both synthetic benchmarks and a real biological network, comparing Interventional DN2CN with purely observational DN2CN and with classical constraint-based and score-based learners that incorporate intervention targets. Our results design aims to show that explicitly modeling regime-dependent context-specific structure improves both structural recovery and causal effect estimation, particularly for nodes adjacent to manipulated variables. We conclude by discussing limitations and potential extensions to dynamic settings and latent variable models.
