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arXiv · 2403.02608

DNNLasso: Scalable Graph Learning for Matrix-Variate Data

Meixia Lin·Yangjing Zhang
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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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Meixia Lin, Yangjing Zhang. 2024-03-05. DNNLasso: Scalable Graph Learning for Matrix-Variate Data. https://arxiv.org/abs/2403.02608

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