  Causal discovery, the task of inferring causal structure from data, promises
to accelerate scientific research, inform policy making, and more. However,
causal discovery algorithms over larger sets of variables tend to be brittle
against misspecification or when data are limited. To mitigate these
challenges, we train a supervised model that learns to predict a larger causal
graph from the outputs of classical causal discovery algorithms run over
subsets of variables, along with other statistical hints like inverse
covariance. Our approach is enabled by the observation that typical errors in
the outputs of classical methods remain comparable across datasets.
Theoretically, we show that this model is well-specified, in the sense that it
can recover a causal graph consistent with graphs over subsets. Empirically, we
train the model to be robust to erroneous estimates using diverse synthetic
data. Experiments on real and synthetic data demonstrate that this model
maintains high accuracy in the face of misspecification or distribution shift,
and can be adapted at low cost to different discovery algorithms or choice of
statistics.
