DNNLasso: Scalable Graph Learning for Matrix-Variate Data
- URL: http://arxiv.org/abs/2403.02608v1
- Date: Tue, 5 Mar 2024 02:49:00 GMT
- Title: DNNLasso: Scalable Graph Learning for Matrix-Variate Data
- Authors: Meixia Lin and Yangjing Zhang
- Abstract summary: We introduce a diagonally non-negative graphical lasso model for estimating the Kronecker-sum structured precision matrix.
DNNLasso outperforms the state-of-the-art methods by a large margin in both accuracy and computational time.
- Score: 2.7195102129095003
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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. Our code is available at
https://github.com/YangjingZhang/DNNLasso.
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