  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 semi-supervised prediction. We show that the method yields
valid inferences under suitable (weak) conditions on the quality of the
predictive model. We validate the method with experiments on a semi-synthetic
social network dataset. Code is available at
github.com/vveitch/causal-network-embeddings.
