Inference of directed relations given some unspecified interventions, that is, the target of each intervention is unknown, is challenging. In this article, we test hypothesized directed relations with unspecified interventions. First, we derive conditions to yield an identifiable model. Unlike classical inference, testing directed relations requires identifying ancestors and relevant interventions of hypothesis-specific primary variables. Towards this end, we propose a peeling algorithm based on nodewise regressions to establish a topological order of primary variables. Moreover, we prove that the peeling algorithm yields a consistent estimator in low order polynomial time. Second, we propose a likelihood ratio test integrated with a data perturbation scheme to account for the uncertainty of identifying ancestors and interventions. Also, we show that the distribution of a data perturbation test statistic converges to the target distribution. Numerical examples demonstrate the utility and effectiveness of the proposed methods, including an application to infer gene regulatory networks. The implementation of the proposed methods is available at https://github.com/chunlinli/intdag.

翻译：根据一些未具体说明的干预措施,即每项干预措施的目标不明,对直接关系所作的推断是具有挑战性的。在本条中,我们检验与未说明的干预措施的假设性直接关系。首先,我们得出可以确定模型的条件。与传统的推断不同,测试性直接关系需要确定祖先和具体假设主要变量的相关干预措施。为此,我们提议基于无偏向回归的剥皮算法,以建立主要变量的地貌顺序。此外,我们证明剥皮算法在低顺序多元时间里产生了一个一致的估量器。第二,我们建议结合数据渗透性计划进行概率比率测试,以说明识别祖先和干预措施的不确定性。此外,我们还表明数据侵扰性测试统计数据的分布与目标分布一致。数字实例表明拟议方法的效用和效力,包括用于推导基因管理网络的应用。拟议方法的实施见https://github.com/chunlinli/intdag。