Learning causal structure poses a combinatorial search problem that typically involves evaluating structures using a score or independence test. The resulting search is costly, and designing suitable scores or tests that capture prior knowledge is difficult. In this work, we propose to amortize the process of causal structure learning. Rather than searching over causal structures directly, we train a variational inference model to predict the causal structure from observational/interventional data. Our inference model acquires domain-specific inductive bias for causal discovery solely from data generated by a simulator. This allows us to bypass both the search over graphs and the hand-engineering of suitable score functions. Moreover, the architecture of our inference model is permutation invariant w.r.t. the data points and permutation equivariant w.r.t. the variables, facilitating generalization to significantly larger problem instances than seen during training. On synthetic data and semi-synthetic gene expression data, our models exhibit robust generalization capabilities under substantial distribution shift and significantly outperform existing algorithms, especially in the challenging genomics domain.

@inproceedings{lorch2022amortized,
	author = {Lorch, Lars and Sussex, Scott and Rothfuss, Jonas and Krause, Andreas and Sch{\"o}lkopf, Bernhard},
	booktitle = {Proc. Neural Information Processing Systems (NeurIPS)},
	month = {December},
	title = {Amortized Inference for Causal Structure Learning},
	year = {2022}}