Joint estimation of multiple dependent Gaussian graphical models with applications to mouse genomics

• 成果类型: Article
• 署名作者: Xie, Yuying; Liu, Yufeng; Valdar, William
• 署名单位: Michigan State University; University of North Carolina; University of North Carolina Chapel Hill; University of North Carolina; University of North Carolina Chapel Hill
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asw035
• 发表日期: 2016
• 页码: 493511
• 关键词: inverse covariance estimation; maximum-likelihood; variable selection; Matrix Estimation; SPARSE; Lasso; obesity

摘要

Gaussian graphical models are widely used to represent conditional dependencies among random variables. In this paper, we propose a novel estimator for data arising from a group of Gaussian graphical models that are themselves dependent. A motivating example is that of modelling gene expression collected on multiple tissues from the same individual: here the multivariate outcome is affected by dependencies acting not only at the level of the specific tissues, but also at the level of the whole body; existing methods that assume independence among graphs are not applicable in this case. To estimate multiple dependent graphs, we decompose the problem into two graphical layers: the systemic layer, which affects all outcomes and thereby induces cross-graph dependence, and the category-specific layer, which represents graph-specific variation. We propose a graphical EM technique that estimates both layers jointly, establish estimation consistency and selection sparsistency of the proposed estimator, and confirm by simulation that the EM method is superior to a simpler one-step method. We apply our technique to mouse genomics data and obtain biologically plausible results.