We consider the problem of learning causal Directed Acyclic Graphs (DAGs) using combinations of observational and interventional experimental data. Current methods tailored to this setting assume that interventions either destroy parent-child relations of the intervened (target) nodes or only alter such relations without modifying the parent sets, even when the intervention targets are unknown. We relax this assumption by proposing a Bayesian method for causal discovery from general interventions, which allow for modifications of the parent sets of the unknown targets. Even in this framework, DAGs and general interventions may be identifiable only up to some equivalence classes. We provide graphical characterizations of such interventional Markov equivalence and devise compatible priors for Bayesian inference that guarantee score equivalence of indistinguishable structures. We then develop a Markov Chain Monte Carlo (MCMC) scheme to approximate the posterior distribution over DAGs, intervention targets and induced parent sets. Finally, we evaluate the proposed methodology on both simulated and real protein expression data.

翻译：我们研究了利用观测数据与干预实验数据组合来学习因果有向无环图（DAG）的问题。当前针对该场景的专用方法假设干预操作要么破坏被干预（目标）节点的父子关系，要么仅改变此类关系而不修改父节点集，即使干预目标未知时也是如此。我们通过提出一种适用于通用干预的贝叶斯因果发现方法放宽了这一假设，该方法允许修改未知目标的父节点集。即使在此框架下，DAG与通用干预可能仅能辨识至某些等价类。我们给出了此类干预马尔可夫等价的图形化刻画，并为贝叶斯推断设计了保证不可区分结构得分等价的兼容先验分布。随后我们开发了马尔可夫链蒙特卡洛（MCMC）方案，用以逼近DAG、干预目标及诱导父节点集的后验分布。最后，我们通过模拟数据与真实蛋白质表达数据对所提方法进行了评估。