# A Consistent Estimator for Confounding Strength

arXiv: https://arxiv.org/abs/2211.01903 · HTML: https://mlsanity.com/paper/2211.01903/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 51 references that are in the map.
- First posted on arXiv 3 Nov 2022.

## Builds on (most cited first, 13 of 13)

- [Causal inference using invariant prediction: identification and confidence intervals](https://mlsanity.com/paper/1501.01332/) (2015)
- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification](https://mlsanity.com/paper/1507.03003/) (2015)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Causal Regularization](https://mlsanity.com/paper/1906.12179/) (2019)
- [Detecting non-causal artifacts in multivariate linear regression models](https://mlsanity.com/paper/1803.00810/) (2018)
- [Detecting confounding in multivariate linear models via spectral analysis](https://mlsanity.com/paper/1704.01430/) (2017)
- [Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding](https://mlsanity.com/paper/2103.15106/) (2021)
- [We Are Not Your Real Parents: Telling Causal from Confounded using MDL](https://mlsanity.com/paper/1901.06950/) (2019)
- [Simple yet Sharp Sensitivity Analysis for Unmeasured Confounding](https://mlsanity.com/paper/2104.13020/) (2021)
- [Confounder Detection in High Dimensional Linear Models using First Moments of Spectral Measures](https://mlsanity.com/paper/1803.06852/) (2018)
- [Correcting Confounding via Random Selection of Background Variables](https://mlsanity.com/paper/2202.02150/) (2022)
- [Interpolation and Regularization for Causal Learning](https://mlsanity.com/paper/2202.09054/) (2022)

## Built on by (most cited first, 1 of 1)

- [Sequential Underspecified Instrument Selection for Cause-Effect Estimation](https://mlsanity.com/paper/2302.05684/) (2023)

## Abstract (arXiv)

Regression on observational data can fail to capture a causal relationship in the presence of unobserved confounding. Confounding strength measures this mismatch, but estimating it requires itself additional assumptions. A common assumption is the independence of causal mechanisms, which relies on concentration phenomena in high dimensions. While high dimensions enable the estimation of confounding strength, they also necessitate adapted estimators. In this paper, we derive the asymptotic behavior of the confounding strength estimator by Janzing and Sch"olkopf (2018) and show that it is generally not consistent. We then use tools from random matrix theory to derive an adapted, consistent estimator.