文章基本信息

标题：High-dimensional joint estimation of multiple directed Gaussian graphical models
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作者：Yuhao Wang ; Santiago Segarra ; Caroline Uhler 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：1
页码：2439-2483
DOI：10.1214/20-EJS1724
语种：English
出版社：Institute of Mathematical Statistics
摘要：We consider the problem of jointly estimating multiple related directed acyclic graph (DAG) models based on high-dimensional data from each graph. This problem is motivated by the task of learning gene regulatory networks based on gene expression data from different tissues, developmental stages or disease states. We prove that under certain regularity conditions, the proposed $\ell _{0}$-penalized maximum likelihood estimator converges in Frobenius norm to the adjacency matrices consistent with the data-generating distributions and has the correct sparsity. In particular, we show that this joint estimation procedure leads to a faster convergence rate than estimating each DAG model separately. As a corollary, we also obtain high-dimensional consistency results for causal inference from a mix of observational and interventional data. For practical purposes, we propose jointGES consisting of Greedy Equivalence Search (GES) to estimate the union of all DAG models followed by variable selection using lasso to obtain the different DAGs, and we analyze its consistency guarantees. The proposed method is illustrated through an analysis of simulated data as well as epithelial ovarian cancer gene expression data.
关键词：Causal inference; linear structural equation model; high-dimensional statistics; graphical model