  Consider the problem of determining the effect of a compound on a specific
cell type. To answer this question, researchers traditionally need to run an
experiment applying the drug of interest to that cell type. This approach is
not scalable: given a large number of different actions (compounds) and a large
number of different contexts (cell types), it is infeasible to run an
experiment for every action-context pair. In such cases, one would ideally like
to predict the outcome for every pair while only having to perform experiments
on a small subset of pairs. This task, which we label "causal imputation", is a
generalization of the causal transportability problem. To address this
challenge, we extend the recently introduced synthetic interventions (SI)
estimator to handle more general data sparsity patterns. We prove that, under a
latent factor model, our estimator provides valid estimates for the causal
imputation task. We motivate this model by establishing a connection to the
linear structural causal model literature. Finally, we consider the prominent
CMAP dataset in predicting the effects of compounds on gene expression across
cell types. We find that our estimator outperforms standard baselines, thus
confirming its utility in biological applications.
