Causal Effect Estimation with Mixed Latent Confounders and Post-treatment Variables
Keywords: Causal Inference, Latent Post-treatment Bias, Proxy of Confounders, Identifiable VAE
Abstract: In recent years, causal inference from observational data has attracted considerable attention among researchers. One main obstacle for inferring causal effects from observational data is the handling of confounders. As direct measurement of confounders may not always be feasible, recent methods seek to adjust the confounding effects based on proxy variables, which are high-dimensional features researchers postulated to be determined by the latent confounders. However, observed features may scramble both latent confounders and post-treatment variables simultaneously in observational study, where existing methods risk distorting the estimation by unintentionally controlling variables affected by the treatment. In this paper, we systematically investigate the latent post-treatment bias in causal inference. We first derive the bias of existing methods when the selected proxies scramble both latent confounders and post-treatment variables, which we demonstrate can be arbitrarily bad. We then propose a novel Confounder-identifiable VAE (CiVAE) to address the bias, built upon the assumption that the prior of latent variables belongs to the general exponential family with at least one invertible sufficient statistic in the factorized part. Based on this, we show that latent confounders and latent post-treatment variables can be properly distinguished. Furthermore, we show that latent confounders can be identified up to simple bijective transformations. Finally, we prove that the true causal effects can be unbiasedly estimated with transformed confounder proxies. Experiments on both simulated and real-world datasets demonstrate that CiVAE is significantly more robust than existing methods.
Primary Area: causal reasoning
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 3104
Loading