GmGM: a fast multi-axis Gaussian graphical model
Ethan B. Andrew, David Westhead, Luisa Cutillo
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.
BibTeX
@InProceedings{pmlr-v238-andrew24a,
title = {{GmGM}: a fast multi-axis {G}aussian graphical model},
author = {Andrew, Ethan B. and Westhead, David and Cutillo, Luisa},
booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
pages = {2053--2061},
year = {2024},
editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen},
volume = {238},
series = {Proceedings of Machine Learning Research},
month = {02--04 May},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v238/andrew24a/andrew24a.pdf},
url = {https://proceedings.mlr.press/v238/andrew24a.html},
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.}
}