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

Yuying Xie, Yufeng Liu and William Valdar

Biometrika, 2016, vol. 103, issue 3, 493-511

Abstract: 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.

Date: 2016
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Citations: View citations in EconPapers (1)

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