GmGM: a Fast Multi-Axis Gaussian Graphical Model

TL;DR

GmGM introduces a fast, scalable Gaussian multi-Graphical Model for constructing sparse, multi-modal graph representations of tensor data, enabling efficient analysis of large, complex datasets like multi-omics.

Contribution

It generalizes previous models to learn across multiple tensors sharing axes, with a single eigendecomposition per axis, significantly improving speed and scalability.

Findings

Achieves an order of magnitude speedup over prior methods.

Successfully applied to large multi-omics datasets.

Validated on synthetic and real-world data.

Abstract

This paper introduces the Gaussian multi-Graphical Model, a model to construct sparse graph representations of matrix- and tensor-variate 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 single-cell multi-omics data, which was challenging with previous approaches. We validate our model on synthetic data and five real-world datasets.