Causal Effect Identification in the Presence of Latent Confounding with a Single Imperfect Proxy Variable

Xiu-Chuan Li, Tongliang Liu

Keywords: Causal effect identification, latent confounders

Abstract: We consider the problem of identifying the causal effect of a treatment on an outcome in the presence of latent confounding. Many existing works utilize proxies of the latent confounder to adjust for it indirectly, typically requiring multiple proxies. Within the framework of latent variable linear non-Gaussian acyclic model (lvLiNGAM), we propose a causal effect identification procedure requiring only a single proxy. Moreover, this proxy can be agnostic, which means that: first, it can have an arbitrary causal relationship with the treatment/outcome; second, this causal relationship is not required to be known a priori. The complexity of the agnostic proxy precludes identifying the causal effect via a simple analytical formula. Consequently, our procedure is designed to first derive several candidate solutions from cross-cumulants and then isolate the valid solution by examining certain independence relationships. We present and prove a series of new theoretical results, which collectively establish the soundness of our procedure: given the observational population distribution, it correctly identifies the true causal effect when identifiable, and correctly reports unidentifiability otherwise. Also, we conduct experiments to validate the correctness of our theoretical results.

Primary Area: causal reasoning

Submission Number: 11612