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

arXiv: https://arxiv.org/abs/2605.07029 · HTML: https://mlsanity.com/paper/2605.07029/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 15 of 15)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Instrumental Variables in Causal Inference and Machine Learning: A Survey](https://mlsanity.com/paper/2212.05778/) (2022)
- [Fast Instrument Learning with Faster Rates](https://mlsanity.com/paper/2205.10772/) (2022)
- [An AI-powered Bayesian generative modeling approach for causal inference in observational studies](https://mlsanity.com/paper/2501.00755/) (2025)
- [Learning Decision Policies with Instrumental Variables through Double Machine Learning](https://mlsanity.com/paper/2405.08498/) (2024)
- [An AI-powered Bayesian Generative Modeling Approach for Arbitrary Conditional Inference](https://mlsanity.com/paper/2601.05355/) (2026)
- [Missingness-aware Data Imputation via AI-powered Bayesian Generative Modeling](https://mlsanity.com/paper/2605.01676/) (2026)

## Abstract (arXiv)

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.