Distribution-Conditioned Adversarial Variational Autoencoder for Valid Instrumental Variable Generation

Xinshu Li, Lina Yao

Abstract: Instrumental variables (IVs), widely applied in economics and healthcare, enable consistent counterfactual prediction in the presence of hidden confounding factors, effectively addressing endogeneity issues. The prevailing IV-based counterfactual prediction methods typically rely on the availability of valid IVs (satisfying Relevance, Exclusivity, and Exogeneity), a requirement which often proves elusive in real-world scenarios. Various data-driven techniques are being developed to create valid IVs (or representations of IVs) from a pool of IV candidates. However, most of these techniques still necessitate the inclusion of valid IVs within the set of candidates. This paper proposes a distribution-conditioned adversarial variational autoencoder to tackle this challenge. Specifically: 1) for Relevance and Exclusivity, we deduce the corresponding evidence lower bound following the Bayesian network structure and build the variational autoencoder; accordingly, 2) for Exogeneity , we design an adversarial game to encourage latent factors originating from the marginal distribution, compelling the independence between IVs and other outcome-related factors. Extensive experimental results validate the effectiveness, stability and generality of our proposed model in generating valid IV factors in the absence of valid IV candidates.