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.

翻译：本文提出了一种名为GrIVET的新型因果发现与推断方法，适用于存在未测量混杂因子的高斯有向无环图。GrIVET包含基于排序的因果发现方法和基于似然的推断流程。在因果发现方面，我们推广了现有的剥壳算法，用于在存在隐藏混杂因素时估计祖先关系和候选工具变量。基于此，我们提出了一种新的工具变量估计程序，通过将每个直接效应与任何中介效应分离来对其进行估计。在推断方面，我们开发了一种新的多重因果效应似然比检验，能够解释未测量的混杂因子。理论上，我们证明了所提方法具有理想保证，包括对无效工具变量和不确定干预的鲁棒性、估计一致性、低阶多项式时间复杂度以及渐近推断的有效性。数值实验表明，GrIVET性能优越，优于当前最先进的竞争方法。此外，我们通过从阿尔茨海默病基因表达数据中推断调控通路的应用实例，展示了所提方法的实用性和有效性。