Inference for a large directed acyclic graph with unspecified interventions
AUTHORs: 
Chunlin Li, Xiaotong Shen, Wei PanAuthors Info & Claims
Chunlin Li, Xiaotong Shen, Wei PanAuthors Info & ClaimsArticle No.: 73, Pages 3261 - 3308
Abstract
Statistical inference of directed relations given some unspecified interventions (i.e., the intervention targets are 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 the ancestors and relevant interventions of hypothesis-specific primary variables. To 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 R implementation is available at https://github.com/chunlinli/intdag.
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January 2023
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Publication History
Accepted: 01 February 2023
Published: 01 January 2023
Revised: 01 January 2023
Received: 01 July 2021
Published in JMLR Volume 24, Issue 1
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