GmGM: a Fast Multi-Axis Gaussian Graphical Model
This enables analysis of large multimodal datasets such as single-cell multi-omics, which was previously challenging, though it appears incremental as it generalizes prior work.
The paper tackles the problem of constructing sparse graph representations for matrix- and tensor-variate data, particularly in multimodal datasets like multi-omics, by introducing a fast algorithm that achieves an order of magnitude speedup over prior methods.
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.