# Making Multi-Axis Gaussian Graphical Models Scalable to Millions of Cells

arXiv: https://arxiv.org/abs/2407.19892 · HTML: https://mlsanity.com/paper/2407.19892/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 29 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [From Louvain to Leiden: guaranteeing well-connected communities](https://mlsanity.com/paper/1810.08473/) (2018)
- [Adjusting for Chance Clustering Comparison Measures](https://mlsanity.com/paper/1512.01286/) (2015)
- [Tensor Graphical Lasso (TeraLasso)](https://mlsanity.com/paper/1705.03983/) (2017)
- [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)
- [GmGM: a Fast Multi-Axis Gaussian Graphical Model](https://mlsanity.com/paper/2211.02920/) (2022)
- [Kronecker-structured Covariance Models for Multiway Data](https://mlsanity.com/paper/2212.01721/) (2022)
- [High Dimensional Semiparametric Scale-Invariant Principal Component Analysis](https://mlsanity.com/paper/1402.4507/) (2014)
- [DNNLasso: Scalable Graph Learning for Matrix-Variate Data](https://mlsanity.com/paper/2403.02608/) (2024)

## Abstract (arXiv)

Motivation: Networks underlie the generation and interpretation of many biological datasets: gene networks shed light on the regulatory structure of the genome, and cell networks can capture structure of the tumor micro-environment. However, most methods that learn such networks make the faulty 'independence assumption'; to learn the gene network, they assume that no cell network exists. 'Multi-axis' methods, which do not make this assumption, fail to scale beyond a few thousand cells or genes. This limits their applicability to only the smallest datasets. Results: We develop a multi-axis method capable of processing million-cell datasets within minutes. This was previously impossible, and unlocks the use of such methods on modern scRNA-seq datasets, as well as more complex datasets. We show that our method yields novel biological insights from real single-cell data, and compares favorably to the existing hdWGCNA methodology. In particular, it identifies long non-coding RNA genes that potentially have a regulatory or functional role in neuronal development. Availability and implementation: Our methodology is available as a Python package GmGM on PyPI (https://pypi.org/project/GmGM/0.5.3/). The code for all experiments performed in this paper is available on GitHub (https://github.com/BaileyAndrew/GmGM-Bioinformatics). Contact: sceba@leeds.ac.uk Supplementary information: Our proofs, and some additional experiments, are available in the supplementary material. Keywords: gaussian graphical models, multi-axis models, transcriptomics, multi-omics, scalability