Distribution-Conditioned Adversarial Variational Autoencoder for Valid Instrumental Variable Generation

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.