Title: Causal Effect Identification in the Presence of Latent Confounding with a Single Imperfect Proxy Variable
Primary area: causal reasoning
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 method 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 a straightforward identification of the causal effect of interest. Consequently, our method is designed to first derive several candidate solutions from cross-cumulants and then identify the valid solution via independence tests. With a sufficient sample size, if the causal effect is identifiable, our method returns its true value; if it is unidentifiable, our method explicitly reports unidentifiability. Our code is available at https://anonymous.4open.science/r/gH81VfT903h4l6Qz0k7