Detecting hidden confounding in observational data using multiple environments

Rickard Karlsson, JH Krijthe

Keywords: causal inference, hidden confounding, multiple environments, independent causal mechansisms, independence testing

TL;DR: We show that, when assuming independent causal mechanisms, there exist testable conditional independencies in multi-environment data that are only violated in the presence of hidden confounders.

Abstract: A common assumption in causal inference from observational data is that there is no hidden confounding. Yet it is, in general, impossible to verify the presence of hidden confounding factors from a single dataset. Under the assumption of independent causal mechanisms underlying the data-generating process, we demonstrate a way to detect unobserved confounders when having multiple observational datasets coming from different environments. We present a theory for testable conditional independencies that are only absent when there is hidden confounding and examine cases where we violate its assumptions: degenerate & dependent mechanisms, and faithfulness violations. Additionally, we propose a procedure to test these independencies and study its empirical finite-sample behavior using simulation studies and semi-synthetic data based on a real-world dataset. In most cases, the proposed procedure correctly predicts the presence of hidden confounding, particularly when the confounding bias is large.

Submission Number: 11463