# Heterogeneous causal effects with imperfect compliance: a Bayesian machine learning approach

arXiv: https://arxiv.org/abs/1905.12707 · HTML: https://mlsanity.com/paper/1905.12707/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 May 2019.

## Built on by (most cited first, 6 of 6)

- [Estimating individual treatment effects under unobserved confounding using binary instruments](https://mlsanity.com/paper/2208.08544/) (2022)
- [A flexible Bayesian g-formula for causal survival analyses with time-dependent confounding](https://mlsanity.com/paper/2402.02306/) (2024)
- [Robust and Heterogenous Odds Ratio: Estimating Price Sensitivity for Unbought Items](https://mlsanity.com/paper/2106.11389/) (2021)
- [Heterogeneous Treatment Effect Estimation under Noncompliance in the Illinois Workplace Wellness Study with Bayesian Tree Ensembles](https://mlsanity.com/paper/2408.07765/) (2024)
- [Conditional Front-door Adjustment for Heterogeneous Treatment Assignment Effect Estimation Under Non-adherence](https://mlsanity.com/paper/2505.05677/) (2025)
- [From Tokens to Policy: Causal and Interpretable Heterogeneous Treatment Effects Identification](https://mlsanity.com/paper/2606.17010/) (2026)

## Abstract (arXiv)

This paper introduces an innovative Bayesian machine learning algorithm to draw interpretable inference on heterogeneous causal effects in the presence of imperfect compliance (e.g., under an irregular assignment mechanism). We show, through Monte Carlo simulations, that the proposed Bayesian Causal Forest with Instrumental Variable (BCF-IV) methodology outperforms other machine learning techniques tailored for causal inference in discovering and estimating the heterogeneous causal effects while controlling for the familywise error rate (or - less stringently - for the false discovery rate) at leaves' level. BCF-IV sheds a light on the heterogeneity of causal effects in instrumental variable scenarios and, in turn, provides the policy-makers with a relevant tool for targeted policies. Its empirical application evaluates the effects of additional funding on students' performances. The results indicate that BCF-IV could be used to enhance the effectiveness of school funding on students' performance.