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.

翻译：摘要：本文介绍了高斯多图模型，该模型用于构建矩阵与张量数据的稀疏图表示。我们通过同时学习共享坐标轴的多个张量上的此类表示，拓展了该领域的先前工作——这对分析多模态数据集（如多组学数据中遇到的）至关重要。本算法仅需对每个坐标轴进行一次特征分解，在非泛化情况下实现了比先前工作快一个数量级的速度提升。这使得我们的方法能够应用于大规模多模态数据集（如单细胞多组学数据），而这类数据在先前方法中难以处理。我们在合成数据和五个真实世界数据集上验证了模型的有效性。