  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.
