DNNLasso: Scalable Graph Learning for Matrix-Variate Data
This work addresses scalability issues in graph learning for matrix-variate data, offering a more efficient solution for researchers and practitioners dealing with large-scale datasets.
The paper tackles the problem of efficiently learning row-wise and column-wise dependencies in matrix-variate data by proposing DNNLasso, a diagonally non-negative graphical lasso model for estimating Kronecker-sum structured precision matrices, which significantly outperforms state-of-the-art methods in accuracy and computational time.
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.