DNNLasso: Scalable Graph Learning for Matrix-Variate Data
Meixia Lin Yangjing Zhang
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.