Using Embeddings to Correct for Unobserved Confounding in Networks

We consider causal inference in the presence of unobserved confounding. We study the case where a proxy is available for the unobserved confounding in the form of a network connecting the units. For example, the link structure of a social network carries information about its members. We show how to effectively use the proxy to do causal inference. The main idea is to reduce the causal estimation problem to a semi-supervised prediction of both the treatments and outcomes. Networks admit high-quality embedding models that can be used for this semisupervised prediction. We show that the method yields valid inferences under suitable (weak) conditions on the quality of the predictive model.