We address the problem of representing context-specific causal models based on both observational and experimental data collected under general (e.g. hard or soft) interventions by introducing a new family of context-specific conditional independence models called CStrees. This family is defined via a novel factorization criterion that allows for a generalization of the factorization property defining general interventional DAG models. We derive a graphical characterization of model equivalence for observational CStrees that extends the Verma and Pearl criterion for DAGs. This characterization is then extended to CStree models under general, context-specific interventions. To obtain these results, we formalize a notion of context-specific intervention that can be incorporated into concise graphical representations of CStree models. We relate CStrees to other context-specific models, showing that the families of DAGs, CStrees, labeled DAGs and staged trees form a strict chain of inclusions. We end with an application of interventional CStree models to a real data set, revealing the context-specific nature of the data dependence structure and the soft, interventional perturbations.

翻译：我们通过引入一种称为CStrees的新型上下文特定条件独立模型族，解决了基于在一般（如硬性或软性）干预下收集的观测和实验数据来表示上下文特定因果模型的问题。该模型族通过一种新颖的分解准则定义，该准则允许推广定义一般干预DAG模型的分解性质。我们推导了观测CStrees模型等价性的图形化表征，扩展了适用于DAGs的Verma和Pearl准则。随后，该表征被进一步扩展到一般性、上下文特定干预下的CStree模型。为了获得这些结果，我们形式化了一种可被纳入CStree模型简洁图形表示中的上下文特定干预概念。我们将CStrees与其他上下文特定模型联系起来，表明DAGs、CStrees、标记DAGs和阶段树族构成一个严格的包含链。最后，我们将干预CStree模型应用于一个真实数据集，揭示了数据依赖结构及软性干预扰动的上下文特定本质。