Learning Shadow Variable Representation for Treatment Effect Estimation under Collider Bias

Baohong Li, Haoxuan Li, Ruoxuan Xiong, Anpeng Wu, Fei Wu, Kun Kuang

Abstract: One of the significant challenges in treatment effect estimation is collider bias, a specific form of sample selection bias induced by the common causes of both the treatment and outcome. Identifying treatment effects under collider bias requires well-defined shadow variables in observational data, which are assumed to be related to the outcome and independent of the sample selection mechanism, conditional on the other observed variables. However, finding a valid shadow variable is not an easy task in real-world scenarios and requires domain-specific knowledge from experts. Therefore, in this paper, we propose a novel method that can automatically learn shadow-variable representations from observational data without prior knowledge. To ensure the learned representations satisfy the assumptions of the shadow variable, we introduce a tester to perform hypothesis testing in the representation learning process. We iteratively generate representations and test whether they satisfy the shadow-variable assumptions until they pass the test. With the help of the learned shadow-variable representations, we propose a novel treatment effect estimator to address collider bias. Experiments show that the proposed methods outperform existing treatment effect estimation methods under collider bias and prove their potential application value.

Submission Number: 9098