Discovery and inference of a causal network with hidden confounding

This article proposes a novel causal discovery and inference method called GrIVET for a Gaussian directed acyclic graph with unmeasured confounders. GrIVET consists of an order-based causal discovery method and a likelihood-based inferential procedure. For causal discovery, we generalize the existing peeling algorithm to estimate the ancestral relations and candidate instruments in the presence of hidden confounders. Based on this, we propose a new procedure for instrumental variable estimation of each direct effect by separating it from any mediation effects. For inference, we develop a new likelihood ratio test of multiple causal effects that is able to account for the unmeasured confounders. Theoretically, we prove that the proposed method has desirable guarantees, including robustness to invalid instruments and uncertain interventions, estimation consistency, low-order polynomial time complexity, and validity of asymptotic inference. Numerically, GrIVET performs well and compares favorably against state-of-the-art competitors. Furthermore, we demonstrate the utility and effectiveness of the proposed method through an application inferring regulatory pathways from Alzheimer's disease gene expression data.