A Consistent Estimator for Confounding Strength
Not on the map. Why?
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.
Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 13 of its 51 references that are in the map. First posted on arXiv 3 Nov 2022.
Builds on
13 of 51 references.
References · 13
- 2015Causal inference using invariant prediction: identification and confidence intervalscited by 533
- 2019Surprises in High-Dimensional Ridgeless Least Squares Interpolationcited by 508
- 2015High-Dimensional Asymptotics of Prediction: Ridge Regression and Classificationcited by 146
- 2017Invariant Causal Prediction for Nonlinear Modelscited by 140
- 2019Causal Regularizationcited by 21
- 2018Detecting non-causal artifacts in multivariate linear regression modelscited by 16
- 2017Detecting confounding in multivariate linear models via spectral analysiscited by 14
- 2021Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confoundingcited by 9
- 2019We Are Not Your Real Parents: Telling Causal from Confounded using MDLcited by 6
- 2021Simple yet Sharp Sensitivity Analysis for Unmeasured Confoundingcited by 5
- 2018Confounder Detection in High Dimensional Linear Models using First Moments of Spectral Measurescited by 2
- 2022Correcting Confounding via Random Selection of Background Variablescited by 2
1 more
- 2022Interpolation and Regularization for Causal Learningcited by 2
Built on by
Citing papers per year: 2023: 1.
1 paper.