In many applications we have both observational and (randomized)
interventional data. We propose a Gaussian likelihood framework for joint
modeling of such different data-types, based on global parameters consisting of
a directed acyclic graph (DAG) and correponding edge weights and error
variances. Thanks to the global nature of the parameters, maximum likelihood
estimation is reasonable with only one or few data points per intervention. We
prove consistency of the BIC criterion for estimating the interventional Markov
equivalence class of DAGs which is smaller than the observational analogue due
to increased partial identifiability from interventional data. Such an
improvement in identifiability has immediate implications for tighter bounds
for inferring causal effects. Besides methodology and theoretical derivations,
we present empirical results from real and simulated data.

该研究提出了一种基于高斯似然框架的有向无环图模型，用于联合建模观察数据和干预数据，以及通过 BIC 准则对干预马尔可夫等价类进行一致性估计，从而改善了干预数据的部分可鉴别性，提供更紧密的因果效应推断。