# DNNLasso: Scalable Graph Learning for Matrix-Variate Data

arXiv: https://arxiv.org/abs/2403.02608 · HTML: https://mlsanity.com/paper/2403.02608/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 37 references that are in the map.
- First posted on arXiv 5 Mar 2024.

## Builds on (most cited first, 3 of 3)

- [Covariance Estimation in High Dimensions via Kronecker Product Expansions](https://mlsanity.com/paper/1302.2686/) (2013)
- [Tensor Graphical Lasso (TeraLasso)](https://mlsanity.com/paper/1705.03983/) (2017)
- [EiGLasso for Scalable Sparse Kronecker-Sum Inverse Covariance Estimation](https://mlsanity.com/paper/2105.09872/) (2021)

## Built on by (most cited first, 1 of 1)

- [Making Multi-Axis Gaussian Graphical Models Scalable to Millions of Cells](https://mlsanity.com/paper/2407.19892/) (2024)

## Abstract (arXiv)

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.