# Joint Estimation of Multiple Dependent Gaussian Graphical Models with Applications to Mouse Genomics

arXiv: https://arxiv.org/abs/1608.08659 · HTML: https://mlsanity.com/paper/1608.08659/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2016.

## Built on by (most cited first, 1 of 1)

- [Exploration of the search space of Gaussian graphical models for paired data](https://mlsanity.com/paper/2303.05561/) (2023)

## Abstract (arXiv)

Gaussian graphical models are widely used to represent conditional dependence 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 modeling 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 simple one-step method. We apply our technique to mouse genomics data and obtain biologically plausible results.