Inference for a Large Directed Acyclic Graph with Unspecified Interventions
Chunlin Li, Xiaotong Shen, Wei Pan; 24(73):1−48, 2023.
Abstract
The statistical inference of directed relations, given unspecified interventions where the intervention targets are unknown, presents a significant challenge. In this article, we propose a method to test hypothesized directed relations with unspecified interventions. We first establish conditions to ensure an identifiable model. Unlike classical inference, testing directed relations requires identifying the ancestors and relevant interventions of hypothesis-specific primary variables. To accomplish this, we introduce a peeling algorithm based on nodewise regressions that establishes a topological order of primary variables. Additionally, we demonstrate that the peeling algorithm yields a consistent estimator in low-order polynomial time. Secondly, we propose a likelihood ratio test integrated with a data perturbation scheme to account for the uncertainty in identifying ancestors and interventions. We also show that the distribution of a data perturbation test statistic converges to the target distribution. Numerical examples are provided to demonstrate the utility and effectiveness of the proposed methods, including an application to infer gene regulatory networks.
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