# GmGM: a Fast Multi-Axis Gaussian Graphical Model

arXiv: https://arxiv.org/abs/2211.02920 · HTML: https://mlsanity.com/paper/2211.02920/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 45 references that are in the map.
- First posted on arXiv 5 Nov 2022.

## Builds on (most cited first, 6 of 6)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Ensemble Clustering for Graphs: Comparisons and Applications](https://mlsanity.com/paper/1903.08012/) (2019)
- [SG-PALM: a Fast Physically Interpretable Tensor Graphical Model](https://mlsanity.com/paper/2105.12271/) (2021)
- [Scalable Bigraphical Lasso: Two-way Sparse Network Inference for Count Data](https://mlsanity.com/paper/2203.07912/) (2022)
- [Network inference in matrix-variate Gaussian models with non-independent noise](https://mlsanity.com/paper/1312.1622/) (2013)

## Built on by (most cited first, 2 of 2)

- [Making Multi-Axis Gaussian Graphical Models Scalable to Millions of Cells](https://mlsanity.com/paper/2407.19892/) (2024)
- [Making Multi-Axis Models Robust to Multiplicative Noise: How, and Why?](https://mlsanity.com/paper/2603.26327/) (2026)

## Abstract (arXiv)

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.