# Detecting confounding in multivariate linear models via spectral analysis

arXiv: https://arxiv.org/abs/1704.01430 · HTML: https://mlsanity.com/paper/1704.01430/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Apr 2017.

## Built on by (most cited first, 14 of 14)

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- [Detecting hidden confounding in observational data using multiple environments](https://mlsanity.com/paper/2205.13935/) (2022)
- [Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding](https://mlsanity.com/paper/2103.15106/) (2021)
- [Scalable Computation of Causal Bounds](https://mlsanity.com/paper/2308.02709/) (2023)
- [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)
- [Interpolation and Regularization for Causal Learning](https://mlsanity.com/paper/2202.09054/) (2022)
- [An Analysis of Causal Effect Estimation using Outcome Invariant Data Augmentation](https://mlsanity.com/paper/2510.25128/) (2025)
- [Detecting Unobserved Confounders: A Kernelized Regression Approach](https://mlsanity.com/paper/2601.00200/) (2026)
- [A Consistent Estimator for Confounding Strength](https://mlsanity.com/paper/2211.01903/) (2022)
- [Investigating the validity of structure learning algorithms in identifying risk factors for intervention in patients with diabetes](https://mlsanity.com/paper/2403.14327/) (2024)
- [Controlling for discrete unmeasured confounding in nonlinear causal models](https://mlsanity.com/paper/2408.05647/) (2024)
- [An overview of the quantitative causality analysis and causal graph reconstruction based on a rigorous formalism of information flow](https://mlsanity.com/paper/2112.14839/) (2021)
- [Evaluating Bivariate Causal Statements Based on Mutual Compatibility](https://mlsanity.com/paper/2606.00278/) (2026)

## Abstract (arXiv)

We study a model where one target variable Y is correlated with a vector X:=(X_1,...,X_d) of predictor variables being potential causes of Y. We describe a method that infers to what extent the statistical dependences between X and Y are due to the influence of X on Y and to what extent due to a hidden common cause (confounder) of X and Y. The method relies on concentration of measure results for large dimensions d and an independence assumption stating that, in the absence of confounding, the vector of regression coefficients describing the influence of each X on Y typically has `generic orientation' relative to the eigenspaces of the covariance matrix of X. For the special case of a scalar confounder we show that confounding typically spoils this generic orientation in a characteristic way that can be used to quantitatively estimate the amount of confounding.