# Sparse Graphical Modelling via the Sorted L1-Norm

arXiv: https://arxiv.org/abs/2204.10403 · HTML: https://mlsanity.com/paper/2204.10403/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2022.

## Built on by (most cited first, 3 of 3)

- [Strong Screening Rules for Group-based SLOPE Models](https://mlsanity.com/paper/2405.15357/) (2024)
- [Hypergraphs on high dimensional time series sets using signature transform](https://mlsanity.com/paper/2507.15802/) (2025)
- [Beyond False Discovery Rate: A Stepdown Group SLOPE Approach for Grouped Variable Selection](https://mlsanity.com/paper/2603.00955/) (2026)

## Abstract (arXiv)

Sparse graphical modelling has attained widespread attention across various academic fields. We propose two new graphical model approaches, Gslope and Tslope, which provide sparse estimates of the precision matrix by penalizing its sorted L1-norm, and relying on Gaussian and T-student data, respectively. We provide the selections of the tuning parameters which provably control the probability of including false edges between the disjoint graph components and empirically control the False Discovery Rate for the block diagonal covariance matrices. In extensive simulation and real world analysis, the new methods are compared to other state-of-the-art sparse graphical modelling approaches. The results establish Gslope and Tslope as two new effective tools for sparse network estimation, when dealing with both Gaussian, t-student and mixture data.