GmGM: a fast multi-axis Gaussian graphical model

This paper introduces the Gaussian multiGraphical Model, a model to construct sparse graph representations of matrix- and tensorvariate data. We generalize prior work in this area by simultaneously learning this representation across several tensors that share axes, which is necessary to allow the analysis of multimodal datasets such as those encountered in multi-omics. Our algorithm uses only a single eigendecomposition per axis, achieving an order of magnitude speedup over prior work in the ungeneralized case. This allows the use of our methodology on large multi-modal datasets such as singlecell multi-omics data, which was challenging with previous approaches. We validate our model on synthetic data and five real-world datasets.