# Causal Inference with the Instrumental Variable Approach and Bayesian Nonparametric Machine Learning

arXiv: https://arxiv.org/abs/2102.01199 · HTML: https://mlsanity.com/paper/2102.01199/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 22 references that are in the map.
- First posted on arXiv 1 Feb 2021.

## Builds on (most cited first, 2 of 2)

- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Fully Nonparametric Bayesian Additive Regression Trees](https://mlsanity.com/paper/1807.00068/) (2018)

## Built on by (most cited first, 2 of 2)

- [Heterogeneous Treatment Effect Estimation under Noncompliance in the Illinois Workplace Wellness Study with Bayesian Tree Ensembles](https://mlsanity.com/paper/2408.07765/) (2024)
- [Generative Learner for Distributional Causal Effects](https://mlsanity.com/paper/2503.17894/) (2025)

## Abstract (arXiv)

We provide a new flexible framework for inference with the instrumental variable model. Rather than using linear specifications, functions characterizing the effects of instruments and other explanatory variables are estimated using machine learning via Bayesian Additive Regression Trees (BART). Error terms and their distribution are inferred using Dirichlet Process mixtures. Simulated and real examples show that when the true functions are linear, little is lost. But when nonlinearities are present, dramatic improvements are obtained with virtually no manual tuning.