A Consistent Estimator for Confounding Strength
This work addresses the challenge of causal inference in high-dimensional settings for researchers in statistics and machine learning, representing an incremental improvement over prior methods.
The paper tackled the problem of estimating confounding strength in observational data, showing that an existing estimator is inconsistent and deriving a new consistent estimator using random matrix theory.
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 Schölkopf (2018) and show that it is generally not consistent. We then use tools from random matrix theory to derive an adapted, consistent estimator.