文章基本信息

标题：Reconstruction of a directed acyclic graph with intervention
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作者：Si Peng ; Xiaotong Shen ; Wei Pan 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2020
卷号：14
期号：2
页码：4133-4164
DOI：10.1214/20-EJS1767
语种：English
出版社：Institute of Mathematical Statistics
摘要：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.
关键词：Causal relations;constrained likelihood;intervention;reconstruction identifiability