  Inferring causal structures from experimentation is a central task in many
domains. For example, in biology, recent advances allow us to obtain
single-cell expression data under multiple interventions such as drugs or gene
knockouts. However, the targets of the interventions are often uncertain or
unknown and the number of observations limited. As a result, standard causal
discovery methods can no longer be reliably used. To fill this gap, we propose
a Bayesian framework (BaCaDI) for discovering and reasoning about the causal
structure that underlies data generated under various unknown experimental or
interventional conditions. BaCaDI is fully differentiable, which allows us to
infer the complex joint posterior over the intervention targets and the causal
structure via efficient gradient-based variational inference. In experiments on
synthetic causal discovery tasks and simulated gene-expression data, BaCaDI
outperforms related methods in identifying causal structures and intervention
targets.
