# Instrumental Variables in Causal Inference and Machine Learning: A Survey

arXiv: https://arxiv.org/abs/2212.05778 · HTML: https://mlsanity.com/paper/2212.05778/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 51 of its 232 references that are in the map.
- First posted on arXiv 12 Dec 2022.

## Builds on (most cited first, 30 of 51)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [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)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Towards Causal Representation Learning](https://mlsanity.com/paper/2102.11107/) (2021)
- [A Survey on Causal Inference](https://mlsanity.com/paper/2002.02770/) (2020)
- [Deep Stable Learning for Out-Of-Distribution Generalization](https://mlsanity.com/paper/2104.07876/) (2021)
- [Kernel Instrumental Variable Regression](https://mlsanity.com/paper/1906.00232/) (2019)
- [Score matching enables causal discovery of nonlinear additive noise models](https://mlsanity.com/paper/2203.04413/) (2022)
- [Off-policy evaluation for slate recommendation](https://mlsanity.com/paper/1605.04812/) (2016)
- [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)
- [Stable Learning via Sample Reweighting](https://mlsanity.com/paper/1911.12580/) (2019)
- [Learning Deep Features in Instrumental Variable Regression](https://mlsanity.com/paper/2010.07154/) (2020)
- [Treatment effect estimation with disentangled latent factors](https://mlsanity.com/paper/2001.10652/) (2020)
- [Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning](https://mlsanity.com/paper/2002.04518/) (2020)
- [Approximate Residual Balancing: De-Biased Inference of Average Treatment Effects in High Dimensions](https://mlsanity.com/paper/1604.07125/) (2016)
- [Adversarial Estimation of Riesz Representers](https://mlsanity.com/paper/2101.00009/) (2020)
- [Instrumental Variable Value Iteration for Causal Offline Reinforcement Learning](https://mlsanity.com/paper/2102.09907/) (2021)
- [Invariant Feature Learning for Generalized Long-Tailed Classification](https://mlsanity.com/paper/2207.09504/) (2022)
- [Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach](https://mlsanity.com/paper/2007.01290/) (2020)
- [Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression](https://mlsanity.com/paper/1508.03365/) (2015)
- [Sequential Causal Imitation Learning with Unobserved Confounders](https://mlsanity.com/paper/2208.06276/) (2022)
- [Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables](https://mlsanity.com/paper/1611.09925/) (2016)
- [The Variational Method of Moments](https://mlsanity.com/paper/2012.09422/) (2020)

## Built on by (most cited first, 10 of 10)

- [Adaptive Instrument Design for Indirect Experiments](https://mlsanity.com/paper/2312.02438/) (2023)
- [When Graph Neural Network Meets Causality: Opportunities, Methodologies and An Outlook](https://mlsanity.com/paper/2312.12477/) (2023)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [Aligning Language Models with Observational Data: Opportunities and Risks from a Causal Perspective](https://mlsanity.com/paper/2506.00152/) (2025)
- [Dual Causal Inference: Integrating Backdoor Adjustment and Instrumental Variable Learning for Medical VQA](https://mlsanity.com/paper/2604.20306/) (2026)
- [Estimating Bidirectional Causal Effects with Large Scale Online Kernel Learning](https://mlsanity.com/paper/2511.05050/) (2025)
- [Disentangled Instrumental Variables for Causal Inference with Networked Observational Data](https://mlsanity.com/paper/2602.07765/) (2026)
- [Causal Discovery Should Embrace the Wisdom of the Crowd](https://mlsanity.com/paper/2603.02678/) (2026)
- [CIV-DG: Conditional Instrumental Variables for Domain Generalization in Medical Imaging](https://mlsanity.com/paper/2603.25202/) (2026)
- [BGM-IV: AI-Powered Bayesian Generative Modeling for Instrumental Variable Regression with High-Dimensional Covariates](https://mlsanity.com/paper/2605.07029/) (2026)

## Abstract (arXiv)

Causal inference is the process of using assumptions, study designs, and estimation strategies to draw conclusions about the causal relationships between variables based on data. This allows researchers to better understand the underlying mechanisms at work in complex systems and make more informed decisions. In many settings, we may not fully observe all the confounders that affect both the treatment and outcome variables, complicating the estimation of causal effects. To address this problem, a growing literature in both causal inference and machine learning proposes to use Instrumental Variables (IV). This paper serves as the first effort to systematically and comprehensively introduce and discuss the IV methods and their applications in both causal inference and machine learning. First, we provide the formal definition of IVs and discuss the identification problem of IV regression methods under different assumptions. Second, we categorize the existing work on IV methods into three streams according to the focus on the proposed methods, including two-stage least squares with IVs, control function with IVs, and evaluation of IVs. For each stream, we present both the classical causal inference methods, and recent developments in the machine learning literature. Then, we introduce a variety of applications of IV methods in real-world scenarios and provide a summary of the available datasets and algorithms. Finally, we summarize the literature, discuss the open problems and suggest promising future research directions for IV methods and their applications. We also develop a toolkit of IVs methods reviewed in this survey at https://github.com/causal-machine-learning-lab/mliv.