# The Sylvester Graphical Lasso (SyGlasso)

arXiv: https://arxiv.org/abs/2002.00288 · HTML: https://mlsanity.com/paper/2002.00288/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Feb 2020.

## Built on by (most cited first, 10 of 10)

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- [SG-PALM: a Fast Physically Interpretable Tensor Graphical Model](https://mlsanity.com/paper/2105.12271/) (2021)
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- [Learning Cartesian Product Graphs with Laplacian Constraints](https://mlsanity.com/paper/2402.08105/) (2024)
- [Online Graph Topology Learning from Matrix-valued Time Series](https://mlsanity.com/paper/2107.08020/) (2021)
- [Multiway Ensemble Kalman Filter](https://mlsanity.com/paper/2112.04322/) (2021)
- [Interpretable and Scalable Graphical Models for Complex Spatio-temporal Processes](https://mlsanity.com/paper/2301.06021/) (2023)
- [Learning Kronecker-Structured Graphs from Smooth Signals](https://mlsanity.com/paper/2505.09822/) (2025)
- [Making Multi-Axis Models Robust to Multiplicative Noise: How, and Why?](https://mlsanity.com/paper/2603.26327/) (2026)

## Abstract (arXiv)

This paper introduces the Sylvester graphical lasso (SyGlasso) that captures multiway dependencies present in tensor-valued data. The model is based on the Sylvester equation that defines a generative model. The proposed model complements the tensor graphical lasso (Greenewald et al., 2019) that imposes a Kronecker sum model for the inverse covariance matrix by providing an alternative Kronecker sum model that is generative and interpretable. A nodewise regression approach is adopted for estimating the conditional independence relationships among variables. The statistical convergence of the method is established, and empirical studies are provided to demonstrate the recovery of meaningful conditional dependency graphs. We apply the SyGlasso to an electroencephalography (EEG) study to compare the brain connectivity of alcoholic and nonalcoholic subjects. We demonstrate that our model can simultaneously estimate both the brain connectivity and its temporal dependencies.