论文标题
来自DAG混合物引起的分布发现的因果结构发现
Causal Structure Discovery from Distributions Arising from Mixtures of DAGs
论文作者
论文摘要
我们考虑由因果模型的混合物引起的分布，其中每个模型均由有向的无环图（DAG）表示。我们提供了这种混合分布的图形表示，并证明该表示形式编码混合物分布的条件独立关系。然后，我们根据此类分布的样本考虑结构学习的问题。由于混合变量是潜在的，因此我们认为可以处理潜在变量的因果结构发现算法，例如FCI。我们表明，这种算法恢复了组件DAG的“联合”，并且可以识别其在组件dag中的条件分布变化的变量。我们在合成和真实数据上证明了我们的结果，表明所推论的图标识了不同混合组件之间变化的节点。作为立即应用，我们证明了如何根据每个混合物组件的结果来检索此因果信息。
We consider distributions arising from a mixture of causal models, where each model is represented by a directed acyclic graph (DAG). We provide a graphical representation of such mixture distributions and prove that this representation encodes the conditional independence relations of the mixture distribution. We then consider the problem of structure learning based on samples from such distributions. Since the mixing variable is latent, we consider causal structure discovery algorithms such as FCI that can deal with latent variables. We show that such algorithms recover a "union" of the component DAGs and can identify variables whose conditional distribution across the component DAGs vary. We demonstrate our results on synthetic and real data showing that the inferred graph identifies nodes that vary between the different mixture components. As an immediate application, we demonstrate how retrieval of this causal information can be used to cluster samples according to each mixture component.
