Open Access
2020 Reconstruction of a directed acyclic graph with intervention
Si Peng, Xiaotong Shen, Wei Pan
Electron. J. Statist. 14(2): 4133-4164 (2020). DOI: 10.1214/20-EJS1767


Identification of causal relations among variables is central to many scientific investigations, as in regulatory network analysis of gene interactions and brain network analysis of effective connectivity of causal relations between regions of interest. Statistically, causal relations are often modeled by a directed acyclic graph (DAG), and hence that reconstruction of a DAG’s structure leads to the discovery of causal relations. Yet, reconstruction of a DAG’s structure from observational data is impossible because a DAG Gaussian model is usually not identifiable with unequal error variances. In this article, we reconstruct a DAG’s structure with the help of interventional data. Particularly, we construct a constrained likelihood to regularize intervention in addition to adjacency matrices to identify a DAG’s structure, subject to an error variance constraint to further reinforce the model identifiability. Theoretically, we show that the proposed constrained likelihood leads to identifiable models, thus correct reconstruction of a DAG’s structure through parameter estimation even with unequal error variances. Computationally, we design efficient algorithms for the proposed method. In simulations, we show that the proposed method enables to produce a higher accuracy of reconstruction with the help of interventional observations.


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Si Peng. Xiaotong Shen. Wei Pan. "Reconstruction of a directed acyclic graph with intervention." Electron. J. Statist. 14 (2) 4133 - 4164, 2020.


Received: 1 May 2020; Published: 2020
First available in Project Euclid: 17 November 2020

zbMATH: 07285582
MathSciNet: MR4175391
Digital Object Identifier: 10.1214/20-EJS1767

Primary: 62-09

Keywords: Causal relations , Constrained likelihood , intervention , reconstruction identifiability

Vol.14 • No. 2 • 2020
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