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2020 High-dimensional joint estimation of multiple directed Gaussian graphical models
Yuhao Wang, Santiago Segarra, Caroline Uhler
Electron. J. Statist. 14(1): 2439-2483 (2020). DOI: 10.1214/20-EJS1724


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.


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Yuhao Wang. Santiago Segarra. Caroline Uhler. "High-dimensional joint estimation of multiple directed Gaussian graphical models." Electron. J. Statist. 14 (1) 2439 - 2483, 2020.


Received: 1 August 2019; Published: 2020
First available in Project Euclid: 1 July 2020

zbMATH: 07235716
MathSciNet: MR4118334
Digital Object Identifier: 10.1214/20-EJS1724

Primary: 62F12
Secondary: 62F30

Keywords: Causal inference , Graphical model , High-dimensional statistics , linear structural equation model


Vol.14 • No. 1 • 2020
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