  Contagion effect refers to the causal effect of peers' behavior on the
outcome of an individual in social networks. Contagion can be confounded due to
latent homophily which makes contagion effect estimation very hard: nodes in a
homophilic network tend to have ties to peers with similar attributes and can
behave similarly without influencing one another. One way to account for latent
homophily is by considering proxies for the unobserved confounders. However, as
we demonstrate in this paper, existing proxy-based methods for contagion effect
estimation have a very high variance when the proxies are high-dimensional. To
address this issue, we introduce a novel framework, Proximal Embeddings
(ProEmb), that integrates variational autoencoders with adversarial networks to
create low-dimensional representations of high-dimensional proxies and help
with identifying contagion effects. While VAEs have been used previously for
representation learning in causal inference, a novel aspect of our approach is
the additional component of adversarial networks to balance the representations
of different treatment groups, which is essential in causal inference from
observational data where these groups typically come from different
distributions. We empirically show that our method significantly increases the
accuracy and reduces the variance of contagion effect estimation in
observational network data compared to state-of-the-art methods.
