DNNLasso: Scalable Graph Learning for Matrix-Variate Data

Meixia Lin, Yangjing Zhang
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:316-324, 2024.

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.

Cite this Paper

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.} }
Endnote
%0 Conference Paper %T DNNLasso: Scalable Graph Learning for Matrix-Variate Data %A Meixia Lin %A Yangjing Zhang %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-lin24b %I PMLR %P 316--324 %U https://proceedings.mlr.press/v238/lin24b.html %V 238 %X 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.
APA
Lin, M. & Zhang, Y.. (2024). DNNLasso: Scalable Graph Learning for Matrix-Variate Data. Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:316-324 Available from https://proceedings.mlr.press/v238/lin24b.html.

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