Linked Causal Variational Autoencoder for Inferring Paired Spillover Effects

Modeling spillover effects from observational data is an important problem in economics, business, and other fields of research. % It helps us infer the causality between two seemingly unrelated set of events. For example, if consumer spending in the United States declines, it has spillover effects on economies that depend on the U.S. as their largest export market. In this paper, we aim to infer the causation that results in spillover effects between pairs of entities (or units), we call this effect as \textit{paired spillover}. To achieve this, we leverage the recent developments in variational inference and deep learning techniques to propose a generative model called Linked Causal Variational Autoencoder (LCVA). Similar to variational autoencoders (VAE), LCVA incorporates an encoder neural network to learn the latent attributes and a decoder network to reconstruct the inputs. However, unlike VAE, LCVA treats the \textit{latent attributes as confounders that are assumed to affect both the treatment and the outcome of units}. Specifically, given a pair of units $u$ and $\bar{u}$, their individual treatment and outcomes, the encoder network of LCVA samples the confounders by conditioning on the observed covariates of $u$, the treatments of both $u$ and $\bar{u}$ and the outcome of $u$. Once inferred, the latent attributes (or confounders) of $u$ captures the spillover effect of $\bar{u}$ on $u$. Using a network of users from job training dataset (LaLonde (1986)) and co-purchase dataset from Amazon e-commerce domain, we show that LCVA is significantly more robust than existing methods in capturing spillover effects.