Contagion Effect Estimation Using Proximal Embeddings

Contagion effect refers to the causal effect of peer behavior on the outcome of an individual in social networks. Contagion can be hard to estimate when it is confounded by latent homophily because 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 estimating 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. We also demonstrate its applicability to two real-world scenarios, estimating contagion on social media and in adolescent smoking behavior.