Correcting Confounding via Random Selection of Background Variables

TL;DR

This paper introduces a novel method to identify causal relationships by analyzing the stability of regression coefficients across different background feature selections, effectively distinguishing causality from confounding.

Contribution

The paper presents a new criterion and statistic for causal inference that outperforms existing algorithms and is supported by theoretical convergence guarantees.

Findings

Method outperforms state-of-the-art algorithms on simulated data

Encouraging results obtained on real-world data

V statistic converges to zero if and only if no causal drivers are present

Abstract

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.