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This article proposes a novel causal discovery and inference method calledGrIVET for a Gaussian directed acyclic graph with unmeasured confounders.GrIVET consists of an order-based causal discovery method and alikelihood-based inferential procedure. For causal discovery, we generalize theexisting peeling algorithm to estimate the ancestral relations and candidateinstruments in the presence of hidden confounders. Based on this, we propose anew procedure for instrumental variable estimation of each direct effect byseparating it from any mediation effects. For inference, we develop a newlikelihood ratio test of multiple causal effects that is able to account forthe unmeasured confounders. Theoretically, we prove that the proposed methodhas desirable guarantees, including robustness to invalid instruments anduncertain interventions, estimation consistency, low-order polynomial timecomplexity, and validity of asymptotic inference. Numerically, GrIVET performswell and compares favorably against state-of-the-art competitors. Furthermore,we demonstrate the utility and effectiveness of the proposed method through anapplication inferring regulatory pathways from Alzheimer's disease geneexpression data.

Discovery and inference of a causal network with hidden confounding