# Detecting hidden confounding in observational data using multiple environments

arXiv: https://arxiv.org/abs/2205.13935 · HTML: https://mlsanity.com/paper/2205.13935/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 55 references that are in the map.
- First posted on arXiv 27 May 2022.

## Builds on (most cited first, 12 of 12)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Causal Effect Inference with Deep Latent-Variable Models](https://mlsanity.com/paper/1705.08821/) (2017)
- [Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder](https://mlsanity.com/paper/1609.08816/) (2016)
- [Counterfactual Probabilities: Computational Methods, Bounds and Applications](https://mlsanity.com/paper/1302.6784/) (2013)
- [Removing Hidden Confounding by Experimental Grounding](https://mlsanity.com/paper/1810.11646/) (2018)
- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Data](https://mlsanity.com/paper/2203.15756/) (2022)
- [Combining Observational and Randomized Data for Estimating Heterogeneous Treatment Effects](https://mlsanity.com/paper/2202.12891/) (2022)
- [Using Experiments to Correct for Selection in Observational Studies](https://mlsanity.com/paper/2006.09676/) (2020)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Semi-Supervised Learning, Causality and the Conditional Cluster Assumption](https://mlsanity.com/paper/1905.12081/) (2019)
- [Detecting confounding in multivariate linear models via spectral analysis](https://mlsanity.com/paper/1704.01430/) (2017)

## Built on by (most cited first, 13 of 13)

- [TabPFN-2.5: Advancing the State of the Art in Tabular Foundation Models](https://mlsanity.com/paper/2511.08667/) (2025)
- [Prediction-powered Generalization of Causal Inferences](https://mlsanity.com/paper/2406.02873/) (2024)
- [Do Finetti: On Causal Effects for Exchangeable Data](https://mlsanity.com/paper/2405.18836/) (2024)
- [Hidden yet quantifiable: A lower bound for confounding strength using randomized trials](https://mlsanity.com/paper/2312.03871/) (2023)
- [Benchmarking Observational Studies with Experimental Data under Right-Censoring](https://mlsanity.com/paper/2402.15137/) (2024)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [Detecting and Measuring Confounding Using Causal Mechanism Shifts](https://mlsanity.com/paper/2409.17840/) (2024)
- [Falsification of Unconfoundedness by Testing Independence of Causal Mechanisms](https://mlsanity.com/paper/2502.06231/) (2025)
- [Detecting Unobserved Confounders: A Kernelized Regression Approach](https://mlsanity.com/paper/2601.00200/) (2026)
- [Interpretable Clustering with Adaptive Heterogeneous Causal Structure Learning in Mixed Observational Data](https://mlsanity.com/paper/2509.04415/) (2025)
- [Big Data and the Computational Social Science of Entrepreneurship and Innovation](https://mlsanity.com/paper/2505.08706/) (2025)
- [Uncovering Bias Mechanisms in Observational Studies](https://mlsanity.com/paper/2506.01191/) (2025)
- [Identifying Structural Biases from Causal Mechanism Shifts](https://mlsanity.com/paper/2606.18834/) (2026)

## Abstract (arXiv)

A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify this assumption from a single dataset. Under the assumption of independent causal mechanisms underlying the data-generating process, we demonstrate a way to detect unobserved confounders when having multiple observational datasets coming from different environments. We present a theory for testable conditional independencies that are only absent when there is hidden confounding and examine cases where we violate its assumptions: degenerate & dependent mechanisms, and faithfulness violations. Additionally, we propose a procedure to test these independencies and study its empirical finite-sample behavior using simulation studies and semi-synthetic data based on a real-world dataset. In most cases, the proposed procedure correctly predicts the presence of hidden confounding, particularly when the confounding bias is large.