DNNLasso: Scalable Graph Learning for Matrix-Variate Data
Abstract
We consider the problem of jointly learning row-wise and column-wise dependencies of matrix-variate observations, which are modelled separately by two precision matrices. Due to the complicated structure of Kronecker-product precision matrices in the commonly used matrix-variate Gaussian graphical models, a sparser Kronecker-sum structure was proposed recently based on the Cartesian product of graphs. However, existing methods for estimating Kronecker-sum structured precision matrices do not scale well to large scale datasets. In this paper, we introduce DNNLasso, a diagonally non-negative graphical lasso model for estimating the Kronecker-sum structured precision matrix, which outperforms the state-of-the-art methods by a large margin in both accuracy and computational time.
BibTeX
@InProceedings{pmlr-v238-lin24b,
title = {{DNNLasso}: Scalable Graph Learning for Matrix-Variate Data},
author = {Lin, Meixia and Zhang, Yangjing},
booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics},
pages = {316--324},
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/lin24b/lin24b.pdf},
url = {https://proceedings.mlr.press/v238/lin24b.html},
abstract = {We consider the problem of jointly learning row-wise and column-wise dependencies of matrix-variate observations, which are modelled separately by two precision matrices. Due to the complicated structure of Kronecker-product precision matrices in the commonly used matrix-variate Gaussian graphical models, a sparser Kronecker-sum structure was proposed recently based on the Cartesian product of graphs. However, existing methods for estimating Kronecker-sum structured precision matrices do not scale well to large scale datasets. In this paper, we introduce DNNLasso, a diagonally non-negative graphical lasso model for estimating the Kronecker-sum structured precision matrix, which outperforms the state-of-the-art methods by a large margin in both accuracy and computational time.}
}