# Correcting Confounding via Random Selection of Background Variables

arXiv: https://arxiv.org/abs/2202.02150 · HTML: https://mlsanity.com/paper/2202.02150/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 71 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 20 of 20)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [The Risks of Invariant Risk Minimization](https://mlsanity.com/paper/2010.05761/) (2020)
- [A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms](https://mlsanity.com/paper/1901.10912/) (2019)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Invariance, Causality and Robustness](https://mlsanity.com/paper/1812.08233/) (2018)
- [Does Invariant Risk Minimization Capture Invariance?](https://mlsanity.com/paper/2101.01134/) (2021)
- [The Blessings of Multiple Causes](https://mlsanity.com/paper/1805.06826/) (2018)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [Causal Regularization](https://mlsanity.com/paper/1906.12179/) (2019)
- [Kernel Conditional Moment Test via Maximum Moment Restriction](https://mlsanity.com/paper/2002.09225/) (2020)
- [Detecting non-causal artifacts in multivariate linear regression models](https://mlsanity.com/paper/1803.00810/) (2018)
- [Spectral Deconfounding via Perturbed Sparse Linear Models](https://mlsanity.com/paper/1811.05352/) (2018)
- [Causal Feature Selection via Orthogonal Search](https://mlsanity.com/paper/2007.02938/) (2020)
- [High-dimensional simultaneous inference with the bootstrap](https://mlsanity.com/paper/1606.03940/) (2016)
- [Doubly Debiased Lasso: High-Dimensional Inference under Hidden Confounding](https://mlsanity.com/paper/2004.03758/) (2020)
- [A lava attack on the recovery of sums of dense and sparse signals](https://mlsanity.com/paper/1502.03155/) (2015)
- [A Scalable Conditional Independence Test for Nonlinear, Non-Gaussian Data](https://mlsanity.com/paper/1401.5031/) (2014)
- [Testing goodness-of-fit and conditional independence with approximate co-sufficient sampling](https://mlsanity.com/paper/2007.09851/) (2020)
- [Permutation testing in high-dimensional linear models: an empirical investigation](https://mlsanity.com/paper/2001.01466/) (2020)

## Built on by (most cited first, 2 of 2)

- [Partial Identification of Dose Responses with Hidden Confounders](https://mlsanity.com/paper/2204.11206/) (2022)
- [A Consistent Estimator for Confounding Strength](https://mlsanity.com/paper/2211.01903/) (2022)

## Abstract (arXiv)

We propose a method to distinguish causal influence from hidden confounding in the following scenario: given a target variable Y, potential causal drivers X, and a large number of background features, we propose a novel criterion for identifying causal relationship based on the stability of regression coefficients of X on Y with respect to selecting different background features. To this end, we propose a statistic V measuring the coefficient's variability. We prove, subject to a symmetry assumption for the background influence, that V converges to zero if and only if X contains no causal drivers. In experiments with simulated data, the method outperforms state of the art algorithms. Further, we report encouraging results for real-world data. Our approach aligns with the general belief that causal insights admit better generalization of statistical associations across environments, and justifies similar existing heuristic approaches from the literature.