[Paper Review] Instrumental Variables in Causal Inference and Machine Learning: A Survey

Anpeng Wu, Kun Kuang+2 more|arXiv (Cornell University)|Dec 12, 2022

Advanced Causal Inference Techniques5 citations

TL;DR

This survey provides a comprehensive overview of instrumental variable (IV) methods in causal inference and machine learning, systematically categorizing IV techniques—two-stage least squares, control function, and IV evaluation—across linear and non-linear models. It identifies key challenges in IV application, such as valid IV discovery and unmeasured confounding, and proposes future research directions, including data-driven IV identification and integration with confounder control.

ABSTRACT

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.

Motivation & Objective

• To address the limitations of correlation-based machine learning models in out-of-distribution generalization due to unmeasured confounders.
• To provide a systematic review of instrumental variable (IV) methods for causal inference in observational data, especially when unmeasured confounders exist.
• To bridge classical causal inference with modern machine learning by integrating IV techniques into non-linear and high-dimensional models.
• To identify open problems in IV application, such as valid IV discovery and relaxing strict IV assumptions.
• To promote reproducibility by compiling benchmark datasets and open-source implementations in a dedicated toolkit.

Proposed method

• Categorizes IV methods into three streams: two-stage least squares (2SLS) with IVs, control function (CFN) with IVs, and evaluation of IV validity.
• Reviews classical 2SLS and CFN estimators under linear and non-linear models, including vanilla 2SLS, sieve estimators, and machine learning-based 2SLS for non-linearities.
• Introduces structural assumptions for IV identification: relevance (IV affects treatment), exclusion restriction (IV affects outcome only via treatment), and unconfoundedness (no common causes with outcome).
• Proposes data-driven approaches to discover valid IVs using conditional independence testing and causal discovery algorithms.
• Introduces frameworks like DRIVE for domain adaptation and CiiV for adversarial robustness, using IVs to learn domain-invariant representations.
• Proposes data fusion strategies combining small-scale RCTs with large observational data to reduce confounding bias when IVs are unavailable.

Experimental results

Research questions

• RQ1 How can instrumental variables be used to estimate causal effects in the presence of unmeasured confounders when traditional unconfoundedness assumptions fail?
• RQ2 What are the key methodological advances in applying IVs to non-linear and high-dimensional machine learning models?
• RQ3 How can valid instrumental variables be automatically discovered from observational data using statistical and causal discovery techniques?
• RQ4 What are the limitations of current IV assumptions (e.g., exclusion restriction), and how can they be relaxed using mediators or unmeasured confounder recovery?
• RQ5 How can IV-based methods be integrated with confounder control and data fusion to improve robustness in real-world causal inference?

Key findings

• Two-stage least squares (2SLS) and control function (CFN) methods remain foundational for IV estimation, with modern extensions enabling non-linear and high-dimensional applications.
• Machine learning-enhanced 2SLS and CFN estimators significantly improve causal effect estimation in complex, non-linear settings such as recommendation systems and computer vision.
• Valid IVs can be discovered using conditional independence testing and causal discovery algorithms, offering a path toward automated IV identification.
• The exclusion restriction assumption remains the most challenging and untestable, requiring strong domain knowledge or structural modeling.
• Data fusion of small-scale RCTs with large observational data enables robust causal inference even when valid IVs are not available.
• Real-world applications in advertising, medicine, reinforcement learning, and computer vision demonstrate the practical value of IV methods in improving model stability and interpretability.