Generative Causal Inference

Abstract: Generative Bayesian Computation (GBC) methods are developed for Casual Inference. Generative methods are simulation-based methods that use a large training dataset to represent posterior distributions as a map (a.k.a. optimal transport) to a base distribution. They avoid the use of MCMC by replacing the conditional posterior inference problem with a supervised learning problem. We further propose the use Quantile ReLU networks which are density free and hence apply in a variety of Econometric settings where data generating processes are specified by deterministic latent variables updates or as moment constraints. Generative approaches directly simulate large samples of observables and unobservable (parameters, latent variables) and then apply high-dimensional quantile regression to learn a nonlinear transport map from base distribution to parameter inference. We illustrate our methodology in the field of causal inference. Our approach can also handle nonlinearity and heterogeneity. Finally, we conclude with the directions for future research.