Learning causal structures from observation and 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, a key challenge is that often the targets of the interventions are uncertain or unknown. Thus, standard causal discovery methods can no longer be used. To fill this gap, we propose a Bayesian framework (BaCaDI) for discovering the causal structure that underlies data generated under various unknown experimental/interventional conditions. BaCaDI is fully differentiable and operates in the continuous space of latent probabilistic representations of both causal structures and interventions. This enables us to approximate complex posteriors via gradient-based variational inference and to reason about the epistemic uncertainty in the predicted structure. In experiments on synthetic causal discovery tasks and simulated gene-expression data, BaCaDI outperforms related methods in identifying causal structures and intervention targets. Finally, we demonstrate that, thanks to its rigorous Bayesian approach, our method provides well-calibrated uncertainty estimates.

@inproceedings{hagele2023bacadi,
	author = {H{\"a}gele, Alexander and Rothfuss, Jonas and Lorch, Lars and Somnath, Vignesh Ram and Sch{\"o}lkopf, Bernhard and Krause, Andreas},
  booktitle = {Proc. International Conference on Artificial Intelligence and Statistics (AISTATS)},
	month = {April},
	title = {BaCaDI: Bayesian Causal Discovery with Unknown Interventions},
	year = {2023}}