Using Embeddings to Estimate Peer Influence on Social Networks

We address the problem of using observational data to estimate peer contagion effects, the influence of treatments applied to individuals in a network on the outcomes of their neighbours. A main challenge to such estimation is that homophily - the tendency of connected units to share similar latent traits - acts as an unobserved confounder for contagion effects. Informally, it's hard to tell whether your friends have similar outcomes because they were influenced by your treatment, or whether it's due to some common trait that caused you to be friends in the first place. Because these common causes are not usually directly observed, they cannot be simply adjusted for. We describe an approach to perform the required adjustment using node embeddings learned from the network itself. The main aim is to perform this adjustment non-parametrically, without functional form assumptions on either the process that generated the network or the treatment assignment and outcome processes. The key questions we address are: How should the causal effect be formalized? And, when can embedding methods yield causal identification?