BGM-IV: AI-Powered Bayesian Generative Modeling for Instrumental Variable Regression with High-Dimensional Covariates

Abstract

Instrumental-variable (IV) regression enables causal estimation under endogeneity, but modern IV problems often involve nonlinear structural effects and high-dimensional covariates. Existing methods typically operate in observed or generic learned feature spaces, and they often yield point estimates without uncertainty quantification. We introduce BGM-IV, a Bayesian generative modeling approach that performs nonlinear IV regression through posterior inference in a causally structured latent space. BGM-IV separates covariate variation by the role in the treatment and outcome mechanism, and accounts for endogeneity through an IV-integrated pseudo-likelihood that averages over instrument-induced treatment variation. The resulting model provides both structural-function estimates and predictive intervals for outcomes under intervention. Across various benchmark datasets, BGM-IV outperforms existing nonlinear IV methods overall, with significant gains in high-dimensional settings, while achieving near-nominal predictive coverage. These results highlight structured latent generative modeling as a flexible approach to uncertainty-aware IV inference with rich covariates. The code of BGM-IV is available at https://github.com/liuq-lab/BGM-IV.