  Recent work has shown promising results in causal discovery by leveraging
interventional data with gradient-based methods, even when the intervened
variables are unknown. However, previous work assumes that the correspondence
between samples and interventions is known, which is often unrealistic. We
envision a scenario with an extensive dataset sampled from multiple
intervention distributions and one observation distribution, but where we do
not know which distribution originated each sample and how the intervention
affected the system, \textit{i.e.}, interventions are entirely latent. We
propose a method based on neural networks and variational inference that
addresses this scenario by framing it as learning a shared causal graph among
an infinite mixture (under a Dirichlet process prior) of intervention
structural causal models. Experiments with synthetic and real data show that
our approach and its semi-supervised variant are able to discover causal
relations in this challenging scenario.
