A Consistent Estimator for Confounding Strength

TL;DR

This paper develops a new, consistent estimator for confounding strength in observational data, addressing limitations of previous methods by leveraging random matrix theory to improve causal inference accuracy.

Contribution

It introduces an adapted estimator for confounding strength that is proven to be consistent, overcoming the inconsistency of the previous estimator in high-dimensional settings.

Findings

The original estimator by Janzing and Schölkopf is generally inconsistent.

The adapted estimator achieves consistency in high-dimensional regimes.

Theoretical analysis confirms the estimator's asymptotic properties.

Abstract

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.